{"id":3757,"date":"2024-11-25T17:27:34","date_gmt":"2024-11-25T16:27:31","guid":{"rendered":"https:\/\/jhmaths.fr\/?page_id=3757"},"modified":"2025-12-16T15:49:03","modified_gmt":"2025-12-16T14:49:03","slug":"situations-de-recherche","status":"publish","type":"page","link":"https:\/\/jhmaths.fr\/index.php\/situations-de-recherche\/","title":{"rendered":"Situations de recherche"},"content":{"rendered":"\n<details id=\"01\" class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>01 &#8211; La cl\u00f4ture<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"01\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Jean poss\u00e8de une cl\u00f4ture de 75 m\u00e8tres de long pour prot\u00e9ger ses poules. L&rsquo;enclos doit \u00eatre rectangulaire et le plus spacieux possible.<br><br><strong>Comment doit-il faire ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"275\" height=\"183\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/figure.jpg\" alt=\"\" class=\"wp-image-3759\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>02 &#8211; Dans un triangle<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"02\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>$ABC$ est un triangle rectangle en $A$<br>tel que $AB=6$ cm et $AC=4$ cm.<br><br><strong>O\u00f9 faut-il placer $P$ sur l\u2019hypot\u00e9nuse pour que la longueur $IJ$ soit la plus petite possible ? Justifier<\/strong>.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"924\" height=\"667\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/figure.png\" alt=\"\" class=\"wp-image-3760\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/figure.png 924w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/figure-300x217.png 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/figure-768x554.png 768w\" sizes=\"auto, (max-width: 924px) 100vw, 924px\" \/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>03 &#8211; Triangle remarquable autour des droites<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"03\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<ul class=\"wp-block-list\">\n<li>\u00c9tant donn\u00e9es trois droites concourantes $(d_1)$, $(d_2)$ et $(d_3)$,<strong> tracer un triangle $ABC$ dont elles sont les hauteurs.<\/strong><\/li>\n\n\n\n<li>\u00c9tant donn\u00e9es trois droites concourantes $(\\Delta_1)$, $(\\Delta_2)$ et $(\\Delta_3)$, <strong>tracer un triangle $RST$ dont elles sont les m\u00e9dianes.<\/strong><\/li>\n<\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"516\" height=\"416\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/figure-1.png\" alt=\"\" class=\"wp-image-3764\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/figure-1.png 516w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/figure-1-300x242.png 300w\" sizes=\"auto, (max-width: 516px) 100vw, 516px\" \/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>04 &#8211; T\u00eates et pattes<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"04\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Dans la cour d&rsquo;une ferme, il y a des poules et des lapins. J&rsquo;ai pu compter 91 t\u00eates et 324 pattes.<br><br><strong>Combien y a-t-il de poules et de lapins ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"220\" height=\"126\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/04.png\" alt=\"\" class=\"wp-image-3766\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>05 &#8211; Vrai spectacle de fauconnerie<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"05\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Deux faucons sont install\u00e9s sur des tours distantes de 70 m, l&rsquo;un \u00e0 35 m de hauteur et l&rsquo;autre \u00e0 45 m. Un fauconnier doit les r\u00e9ceptionner au sol entre les deux tours. Les rapaces plongeront en m\u00eame temps et voleront \u00e0 la m\u00eame vitesse en ligne droite. <br><strong><br>O\u00f9 le fauconnier doit-il se placer afin que les oiseaux arrivent au m\u00eame instant ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full is-style-rounded\"><img loading=\"lazy\" decoding=\"async\" width=\"380\" height=\"786\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/figure-1.jpg\" alt=\"\" class=\"wp-image-3768\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/figure-1.jpg 380w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/figure-1-145x300.jpg 145w\" sizes=\"auto, (max-width: 380px) 100vw, 380px\" \/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>06 &#8211; Sous la corde<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"06\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Une corde non \u00e9lastique de 101 m\u00e8tres est attach\u00e9e <strong>au sol<\/strong> entre deux piquets distants de 100 m\u00e8tres.<br><br><strong>En tirant la corde en son milieu et en la levant aussi haut que tu le peux, parviendras-tu \u00e0 passer en dessous sans te baisser ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full is-style-rounded\"><img loading=\"lazy\" decoding=\"async\" width=\"320\" height=\"249\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/06.png\" alt=\"\" class=\"wp-image-3777\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/06.png 320w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/06-300x233.png 300w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>07 &#8211; La course \u00e0 20<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"07\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Ratchet propose \u00e0 Clank de jouer avec lui \u00e0 la course \u00e0 20\u2026 <br>Il commence en \u00e9crivant au choix 1 ou 2. <br>Clank ajoute 1 ou 2 au nombre de Ratchet.<br>Ratchet, \u00e0 son tour, ajoute 1 ou 2 au nombre de Clank. <br>Et ainsi de suite, chacun \u00e0 tour de r\u00f4le !<br>Ratchet a vite trouv\u00e9 une strat\u00e9gie pour gagner \u00e0 chaque fois.<br><br><strong>Trouve et explique \u00e0 Clank sa strat\u00e9gie !<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full is-style-rounded\"><img loading=\"lazy\" decoding=\"async\" width=\"241\" height=\"511\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/clank.png\" alt=\"\" class=\"wp-image-3780\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/clank.png 241w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/clank-141x300.png 141w\" sizes=\"auto, (max-width: 241px) 100vw, 241px\" \/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>08 &#8211; Bicarr\u00e9<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"08\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Construire <strong>sans mesurer<\/strong> deux carr\u00e9s de sorte que le deuxi\u00e8me ait une aire qui vaut exactement le double de celle du premier.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"1038\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/08.jpg\" alt=\"\" class=\"wp-image-3783\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/08.jpg 1024w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/08-296x300.jpg 296w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/08-1010x1024.jpg 1010w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/08-768x779.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>09 &#8211; Sans question, cent questions !<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"09\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>La trajectoire d&rsquo;une balle dans l&rsquo;air est donn\u00e9e par :<br>$$f(x)=\\dfrac{150x &#8211; x^2}{145}$$ <br>o\u00f9 $x$ est le temps \u00e9coul\u00e9 depuis le lancer, exprim\u00e9 en secondes, et $f(x)$ la hauteur de l&rsquo;objet \u00e0 l&rsquo;instant $x$, exprim\u00e9e en m\u00e8tres.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"1014\" height=\"487\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/09.jpg\" alt=\"\" class=\"wp-image-3785\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/09.jpg 1014w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/09-300x144.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/09-768x369.jpg 768w\" sizes=\"auto, (max-width: 1014px) 100vw, 1014px\" \/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>10 &#8211; Le bidon<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"10\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>On consid\u00e8re un cylindre de hauteur $h$ et dont la base a pour rayon $r$ (en dm). Ce cylindre doit contenir 5 Litres.<br><br><strong>Quelles sont les possibilit\u00e9s ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"106\" height=\"127\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/10.png\" alt=\"\" class=\"wp-image-3787\" style=\"width:198px;height:auto\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>11 &#8211; C&rsquo;est dans la bo\u00eete, Patron !<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"11\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Voici le patron d&rsquo;une boite sans couvercle d\u00e9coup\u00e9 dans une feuille cartonn\u00e9e de dimensions 24 x 32 (en cm).<br><br><strong>Objectif :<\/strong> <strong>D\u00e9terminer les dimensions de la boite ayant le plus grand volume.<\/strong><br><em>Vous expliquerez pr\u00e9cis\u00e9ment le raisonnement utilis\u00e9<\/em><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full is-resized is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"645\" height=\"838\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/11.jpg\" alt=\"\" class=\"wp-image-3789\" style=\"width:198px;height:auto\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/11.jpg 645w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/11-231x300.jpg 231w\" sizes=\"auto, (max-width: 645px) 100vw, 645px\" \/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>12 &#8211; Plus tu montes, moins \u00e7a compte<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"12\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Un astronaute p\u00e8se $m$ kg sur Terre au niveau de la mer, sa masse apparente (en kg) \u00e0 l\u2019altitude $h$ (en km) au-dessus du niveau de la mer est donn\u00e9 par :<br> $$M= m \\times \\left(\\dfrac{6400}{6400+h}\\right)^2$$<br>L&rsquo;astronaute p\u00e8se 70 kg au niveau de la mer. <br><br><strong>\u00c0 quelle hauteur p\u00e8sera-t-il moins de 2kg ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-full is-resized is-style-rounded\"><img loading=\"lazy\" decoding=\"async\" width=\"2560\" height=\"2560\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/12-scaled.jpg\" alt=\"\" class=\"wp-image-3792\" style=\"width:198px;height:auto\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/12-scaled.jpg 2560w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/12-300x300.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/12-1024x1024.jpg 1024w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/12-150x150.jpg 150w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/12-768x768.jpg 768w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/12-1536x1536.jpg 1536w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/12-2048x2048.jpg 2048w\" sizes=\"auto, (max-width: 2560px) 100vw, 2560px\" \/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>13 &#8211; Quel rectangle ?<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"13\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Un rectangle a un p\u00e9rim\u00e8tre de 110 m et une aire de 714 m\u00b2.<br><br><strong>D\u00e9terminer les mesures de ses c\u00f4t\u00e9s.<\/strong><\/p>\n\n\n\n<p><em>Bonus : Trouvez le lien avec l&rsquo;image ci-contre \u2026<\/em><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large is-resized is-style-default\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/13.jpg\" alt=\"\" style=\"width:198px;height:auto\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>14 &#8211; Le phare<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"14\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<p>Un phare de hauteur 20m est situ\u00e9 \u00e0 700m du pied d&rsquo;une colline. La colline culmine \u00e0 500m, sa base mesure 1000m, et on suppose qu&rsquo; elle a une forme parabolique. <br><br><strong>Quelle est l&rsquo;altitude du point de la colline le plus \u00e9lev\u00e9 que peut \u00e9clairer le phare ? <\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:50%\">\n<figure class=\"wp-block-image size-large is-style-default\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/14.jpg\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>15 &#8211; Cote, cote<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"15\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Un fermier d\u00e9cide de r\u00e9aliser un espace poulailler rectangulaire le long du mur de sa maison (un c\u00f4t\u00e9 mur et trois c\u00f4t\u00e9s cl\u00f4ture). Il veut offrir \u00e0 ses poules 300 m$^2$ d&rsquo;espace.<strong><br><br>Comment peut-il placer les piquets pour que la longueur de cl\u00f4ture \u00e0 acheter soit minimale ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large is-style-rounded\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/15-1.jpg\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>16 &#8211; Objectif : doubler<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"16\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Une \u00e9cole de commerce vient d&rsquo;ouvrir et compte 600 \u00e9tudiants scolaris\u00e9s. Elle \u00e9value \u00e0 7 % par an la progression de ses effectifs et se fixe comme objectif de les doubler avant 10 ans.<br><strong><br>Qu&rsquo;en pensez-vous ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large is-style-rounded\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/16.jpg\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>17 &#8211; Le probl\u00e8me d&rsquo;Erd\u0151s<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"17\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Probl\u00e8me pos\u00e9 par Erd\u0151s au jeune math\u00e9maticien Lajos P\u00f2sa au d\u00e9but d&rsquo;un d\u00eener :<br><br>\u00ab \u00c9tant donn\u00e9 l&rsquo;ensemble des entiers de 1 \u00e0 $2n$, et l&rsquo;un de ses sous ensemble $A$ contenant $n+1$ \u00e9l\u00e9ments. Y a-t-il toujours deux \u00e9l\u00e9ments de $A$ dont l&rsquo;un divise l&rsquo;autre ? \u00bb<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Au dessert, Lajos avait la solution\u2026 et vous ?<\/li>\n\n\n\n<li>Pr\u00e9senter une recherche document\u00e9e sur le math\u00e9maticien Erd\u00f5s en quelques lignes. En particulier, on pourra consulter Tangente n\u00b0152.<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large is-style-rounded\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/17.jpg\" alt=\"\"\/><figcaption class=\"wp-element-caption\">Paule Erd\u0151s<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>18 &#8211; La conjecture de Goldbach<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"18\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-center\">\u00ab<strong>Tout nombre pair est la somme de deux nombres premiers.\u00bb<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-left\">Formul\u00e9e en 1742 par Christian Goldbach, c\u2019est l\u2019un des plus vieux probl\u00e8mes non r\u00e9solus de la th\u00e9orie des nombres et des math\u00e9matiques.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u00c0 l&rsquo;aide de la figure ci-contre, v\u00e9rifier cette conjecture pour tous les nombres entiers inf\u00e9rieurs \u00e0 30.<\/li>\n\n\n\n<li>Exposer une recherche document\u00e9e de quelques lignes sur cette conjecture.<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea251726951&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea251726951\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/18.png\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>cliquer pour agrandir<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>19 &#8211; Marabout de ficelle<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"19\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>On coupe une ficelle de 32 cm de long en deux morceaux avec lesquels on forme un carr\u00e9 et un triangle \u00e9quilat\u00e9ral.<br><strong><br>O\u00f9 doit-on couper la ficelle pour que l&rsquo;aire totale soit la plus petite possible ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea251726d85&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea251726d85\" class=\"wp-block-image size-large is-style-rounded wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/19.jpeg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\">Image g\u00e9n\u00e9r\u00e9e par IA (Bing &#8211; Dalle-E)<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>20 &#8211; Date d&rsquo;anniversaire<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"20\">\n<div class=\"wp-block-column is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Chlo\u00e9 rencontre Alexis et Beno\u00eet en vacances et leur fait deviner sa date d\u2019anniversaire. Elle donne dix dates possibles.<br>Fac\u00e9tieuse et bonne logicienne, elle donne le mois \u00e0 Alexis et le jour \u00e0 Beno\u00eet.<br>Les deux amis tiennent alors cette conversation :<br><br><strong>Alexis <\/strong>: \u00abJe ne connais pas la date anniversaire de Chlo\u00e9, mais je sais que tu ne la connais pas non plus.\u00bb<br><strong>Beno\u00eet <\/strong>: \u00abEffectivement je ne la connaissais pas mais gr\u00e2ce \u00e0 toi, je la connais maintenant.\u00bb<br><strong>Alexis <\/strong>: \u00abAlors moi aussi, je la connais !\u00bb<br><br><strong>Quelle est la date de naissance de Chlo\u00e9 ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea251726fbf&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea251726fbf\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/20.png\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>cliquer pour agrandir<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>21 &#8211; Jeu de hasard<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"21\">\n<div class=\"wp-block-column is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<ol class=\"wp-block-list\">\n<li>On joue \u00e0 un jeu de hasard o\u00f9 on gagne une fois sur 10.<br>Johann affirme : \u00ab\u00a0Donc si on joue 5 fois de suite, on a logiquement une chance sur deux de gagner\u00a0\u00bb.<br><br><strong>Discuter cette affirmation.<\/strong><\/li>\n\n\n\n<li><strong>G\u00e9n\u00e9ralisation :<\/strong> Un jeu est gagnant avec une probabilit\u00e9 $p=\\dfrac{1}{2n}$. On joue $n$ fois.<br><strong><br>Exprimer en fonction de $n$ la probabilit\u00e9 de gagner.<\/strong><\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large is-style-rounded\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/21.jpg\" alt=\"\"\/><figcaption class=\"wp-element-caption\">Johann Bernoulli (1667 &#8211; 1748)<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>22 &#8211; Dilatation de mat\u00e9riaux<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"22\">\n<div class=\"wp-block-column is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Lorsqu&rsquo;un mat\u00e9riau de longueur $L$ subit une variation de temp\u00e9rature $\\Delta T$, ses dimensions varient proportionnellement \u00e0 la variation de temp\u00e9rature : $$\\dfrac{\\Delta L}{L}=\\alpha \\Delta T$$<br>o\u00f9 $\\alpha$ est le coefficient de dilatation propre \u00e0 chaque mat\u00e9riau (voir tableau)<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Une tige de cuivre mesure 3m \u00e0 25\u00b0C. <br><strong>Quelle est sa taille si on la chauffe \u00e0 60\u00b0C ?<\/strong><\/li>\n\n\n\n<li>\u00c0 quelle temp\u00e9rature devrait-on chauffer cette tige pour que sa longueur augmente de 1 cm ?<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea251727ab2&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea251727ab2\" class=\"wp-block-image size-full is-style-default wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"835\" height=\"437\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/22.jpg\" alt=\"\" class=\"wp-image-3865\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/22.jpg 835w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/22-300x157.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/22-768x402.jpg 768w\" sizes=\"auto, (max-width: 835px) 100vw, 835px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><a href=\"https:\/\/fr.wikipedia.org\/wiki\/Dilatation_thermique\">Coefficients de dilatation des \u00e9l\u00e9ments \u00e0 25\u00b0C<\/a><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>23 &#8211; Proportion d&rsquo;\u00e9tudiants<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"23\">\n<div class=\"wp-block-column is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Un groupe d\u2019amis, dont certains ont une carte \u00ab\u00a0Avant&rsquo;\u00e2ge\u00a0\u00bb, va au cin\u00e9ma. Le prix d\u2019une place est de 4 \u20ac pour les d\u00e9tenteurs de la carte et de 6 \u20ac pour les autres. Pour le groupe, le prix total des places est de 52 \u20ac.<br>Ce m\u00eame groupe assiste quelques jours plus tard \u00e0 un concert. Le prix d\u2019une place est de 18 \u20ac pour ceux qui ont la carte et de 30 \u20ac pour les autres. Pour le groupe, le prix total des places est de 240 \u20ac.<br><br><strong>En d\u00e9taillant pr\u00e9cis\u00e9ment votre d\u00e9marche, trouver la proportion de carte \u00ab\u00a0Avant&rsquo;\u00e2ge\u00a0\u00bb dans le groupe.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large is-style-default\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/23.png\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>24 &#8211; Alignement<\/summary>\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"24\">\n<div class=\"wp-block-column is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>$ABCD$ est un rectangle de longueur 6 et de largeur 4. $M$ est un point du segment $[BD]$, $N$ est le sym\u00e9trique de $C$ par rapport \u00e0 $M$.<br><br>La parall\u00e8le \u00e0 $(AD)$ men\u00e9e par $N$ coupe $(AB)$ en $P$.<br>La parall\u00e8le \u00e0 $(AB)$ men\u00e9e par $N$ coupe $(AD)$ en $Q$.<br><strong><br>En d\u00e9taillant pr\u00e9cis\u00e9ment votre d\u00e9marche, d\u00e9terminer si les points $M$, $P$ et $Q$ sont align\u00e9s.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea251727f17&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea251727f17\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/24.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Cliquer pour agrandir<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>25 &#8211; Histoire d&rsquo;angles<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"25\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Soient huit carr\u00e9s identiques.<br><br><strong>Combien mesure $a+b+c$ ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea251728163&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea251728163\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/25.png\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Cliquer pour agrandir<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>26 &#8211; Engage le jeu que je le gagne<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"26\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<ol class=\"wp-block-list\">\n<li>D\u00e9crire cette pyramide.<\/li>\n\n\n\n<li>Trouver deux nombres premiers palindromes \u00e0 4 chiffres.<\/li>\n\n\n\n<li>Trouver tous les nombres premiers palindromes \u00e0 4 chiffres.<\/li>\n\n\n\n<li><em>(Facultatif)<\/em> \u00c9crire un programme qui g\u00e9n\u00e8re les nombres premiers palindromes \u00e0 $n$ chiffres.<\/li>\n<\/ol>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea2517283f8&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea2517283f8\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/26.png\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Cliquer pour agrandir<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>27 &#8211; Comme nos a\u00efeux<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"27\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Le document suivant est extrait d&rsquo;une table de logarithme (<em>\u00ab\u00a0Nouvelles table de logarithme, \u00e9dition 1911\u00a0\u00bb<\/em>).<br><br>En effectuant <strong>une seule addition<\/strong>, calculez le produit $35 \\times 27$.<br><br>En effectuant <strong>une seule soustraction<\/strong>, calculez le quotient $\\dfrac{779}{19}$<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea251728638&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea251728638\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/27.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Cliquer pour agrandir<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>28 &#8211; Ah toi aussi ?!<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"28\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Dans une classe de 27 \u00e9l\u00e8ves, quelle est la probabilit\u00e9 qu&rsquo;au moins deux d&rsquo;entre eux aient la m\u00eame date d&rsquo;anniversaire ?<br><br><strong>Combien faut-il d&rsquo;\u00e9l\u00e8ves dans la classe pour que cette probabilit\u00e9 d\u00e9passe les 95 % ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image aligncenter size-large is-style-default\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/28.png\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>29 &#8211; Efficacit\u00e9 d&rsquo;un test<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"29\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Une maladie est pr\u00e9sente dans la population, avec la proportion d\u2019une personne malade sur 10 000. Le responsable d\u2019un laboratoire pharmaceutique souhaite faire approuver un nouveau test de d\u00e9pistage qui v\u00e9rifie que, si une personne est malade, alors le test est positif \u00e0 99 %, et que, si une personne n\u2019est pas malade, alors le test est positif \u00e0 0,1 %.<br><br><strong>Pour savoir si le laboratoire peut commercialiser son test,on souhaite conna\u00eetre la probabilit\u00e9 qu\u2019une personne soit malade si le test est positif.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea2517289a1&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea2517289a1\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/29.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Louis Pasteur<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>30 &#8211; Il n&rsquo;y a pas que le bluf dans la vie<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"30\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>On assiste \u00e0 une partie de poker (Texas Hold&#8217;em).<br><br><strong>Observez cette image et discuter les probabilit\u00e9s affich\u00e9es en pourcentages.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image aligncenter size-large is-style-default\"><a href=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/30.jpg\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/30.jpg\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\"><em>Cliquer pour agrandir<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>31 &#8211; Le Chevalier de M\u00e9r\u00e9<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"31\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Le probl\u00e8me suivant, soumis par le Chevalier de M\u00e9r\u00e9 \u00e0 Pascal en 1654, est l&rsquo;un de ceux qui marque le d\u00e9but de l&rsquo;\u00e9tude des probabilit\u00e9s dans l&rsquo;histoire. <br><br>\u00ab Est-il avantageux, lorsqu&rsquo;on joue au d\u00e9, de parier sur l&rsquo;apparition d&rsquo;un 6 en lan\u00e7ant 4 fois le d\u00e9?\u00bb<br><br>\u00abEst-il avantageux de parier sur l&rsquo;apparition d&rsquo;un double-six, quand on lance 24 fois deux d\u00e9s ?\u00bb<br><br><strong>Discutez le sens de ce questionnement et apportez-y votre solution.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea251728edb&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea251728edb\" class=\"wp-block-image aligncenter size-large is-style-rounded wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/image.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Antoine Gombaud, dit le \u00ab chevalier de M\u00e9r\u00e9 \u00bb<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>32 &#8211; Croix et Pile ou Face<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"32\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Probl\u00e8me expos\u00e9 par Blaise Pascal en 1654 \u00e0 Pierre de Fermat.<br><br>\u00abPierre et Blaise misent chacun 32 pistoles et jouent \u00e0 croix et pile (Pile ou Face).<br><br>Pierre mise sur \u00ab\u00a0croix\u00a0\u00bb, Blaise mise sur \u00ab\u00a0pile\u00a0\u00bb. Le jeu s&rsquo;interrompt d\u00e8s qu&rsquo;on a obtenu 3 fois \u00ab\u00a0croix\u00a0\u00bb ou 3 fois \u00ab\u00a0pile\u00a0\u00bb. <br><br>Le gagnant empoche alors les 64 pistoles.<br><br>La pi\u00e8ce a \u00e9t\u00e9 lanc\u00e9e une fois et elle est tomb\u00e9e sur \u00ab\u00a0croix\u00a0\u00bb.<br><br>Pour une raison quelconque, le jeu doit s&rsquo;interrompre brutalement. <br><br><strong>Comment r\u00e9partir \u00e9quitablement les 64 pistoles entre les deux joueurs ?<\/strong>\u00bb<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea2517292d8&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea2517292d8\" class=\"wp-block-image aligncenter size-large is-style-rounded wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/32.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Sch\u00e9ma joint \u00e0 la lettre (cliquer pour agrandir)<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>33 &#8211; Gratter c&rsquo;est gagner<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"33\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>La JdJ (Jurassienne des Jeux) a nou\u00e9 un partenariat avec les Sorciers de la C\u00f4te pour un nouveau jeu \u00e0 gratter.<br><br><strong>L&rsquo;\u00e9quipe commerciale s&rsquo;interroge sur le prix du ticket.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea2517295c1&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea2517295c1\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/33.png\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Cliquer pour agrandir<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>34 &#8211; Phileas Fogg<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"34\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p><strong>Combien de temps mettriez vous en marchant au-dessus de l&rsquo;\u00e9quateur pour faire le tour de la Terre ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/34.png\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>35 &#8211; Plus haut, toujours plus haut\u2026<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"35\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>On imagine poss\u00e9der une feuille de papier que l&rsquo;on peut plier ind\u00e9finiment. Elle a une \u00e9paisseur de 0,5 mm.<br>On l&rsquo;a d\u00e9j\u00e0 pli\u00e9e en deux suffisamment de fois pour atteindre le Mont Blanc.<br><br><strong>Combien de pliures nous reste-t-il a effectuer pour arriver jusqu&rsquo;\u00e0 la Lune ? Jusqu&rsquo;au Soleil ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/35.png\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>36 &#8211; Tour du monde \u00e0 la corde<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"36\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>On imagine poss\u00e9der une corde (non extensible) que l&rsquo;on a tendue tout autour de l&rsquo;\u00e9quateur. <br><strong><br>Quelle serait la longueur du morceau de corde \u00e0 ajouter pour que la corde se retrouve \u00e0 1 m du sol partout autour de la Terre ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large is-style-rounded\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/36.jpeg\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>37 &#8211; C&rsquo;est quoi ce rectangle ?!<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"37\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Un rectangle a un p\u00e9rim\u00e8tre de 17 cm et une aire de 17 cm\u00b2.<br><strong><br>Quelles sont ses dimensions ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image aligncenter size-large\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/37.png\" alt=\"\"\/><figcaption class=\"wp-element-caption\"><em>Tableau de Pierre Mondrian<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>38 &#8211; Boulindrosph\u00e8re<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"38\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>\u00abUn cylindre qui a une base \u00e9gale \u00e0 un grand cercle d&rsquo;une sph\u00e8re, et une hauteur \u00e9gale au diam\u00e8tre de cette sph\u00e8re, est \u00e9gal \u00e0 trois fois la moiti\u00e9 de cette sph\u00e8re, et la surface de ce cylindre est aussi \u00e9gale \u00e0 trois fois la moiti\u00e9 de la surface de cette m\u00eame sph\u00e8re.\u00bb<br><strong><br>Expliquez et d\u00e9montrez cette d\u00e9couverte d&rsquo;Archim\u00e8de vers 220 Av. J.-C.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image aligncenter size-large is-style-rounded\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/38-2.jpg\" alt=\"\"\/><figcaption class=\"wp-element-caption\"><em>Archim\u00e8de<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>39 &#8211; Bain de boule<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"39\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Une boule en acier de rayon 5 cm est plac\u00e9e dans un cylindre de rayon 10 cm et de hauteur 22 cm. On verse du liquide jusqu&rsquo;\u00e0 recouvrir exactement la boule (assez lourde pour rester au fond). On retire la boule tout en conservant le liquide. <br><strong><br>Existe-t-il un autre format de boule qui, plong\u00e9e dans le liquide, serait \u00e0 son tour exactement recouverte par l&rsquo;eau comme la premi\u00e8re ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image aligncenter size-large is-style-default\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/39.jpg\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>40 &#8211; La suite de Fibonacci<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">La suite de Fibonnacci est la suite de nombres dont \u00abchaque terme est la somme des deux pr\u00e9c\u00e9dents\u00bb : <br>0 ; 1 ; 1 ; 2 ; 3 ; 5 ; 8 ; 13 ; 21 &#8230;<br><br>\u00c9crire un programme qui g\u00e9n\u00e8re la suite de Fibonnacci puis qui calcule le quotient de deux termes cons\u00e9cutifs $\\left(\\dfrac{5}{3} ; \\, \\dfrac{8}{5} ; \\, \\dfrac{13}{8} ; \\, \\text{ etc.} \\right)$<br><strong><br>Que remarque-t-on ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image aligncenter size-large is-style-rounded\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/40.jpg\" alt=\"\"\/><figcaption class=\"wp-element-caption\"><em>Leonardo Fibonacci (1170 &#8211; 1250)<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>41 &#8211; Polygone inscrit<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">On consid\u00e8re un triangle ABC isoc\u00e8le et rectangle en A tel que AB=5 cm.<br>Soit F le milieu de [AC] et M un point de [AB]. Soit (d) la perpendiculaire \u00e0 (AB) issue de M, elle coupe (BC) en E.<br>On s\u2019int\u00e9resse \u00e0 l\u2019aire du polygone EFAM.<br><strong><br>Le but de la recherche est de trouver la position du point M sur [AB] pour laquelle l\u2019aire est maximale.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172aa1c&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172aa1c\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/41.png\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>42 &#8211; Code secret<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Dans le coffre de Math Leriche, le code d&rsquo;ouverture est un nombre \u00e0 4 chiffres.<br><br>Si tu diminue le code de 12 % puis doubles le r\u00e9sultat, tu obtiens le m\u00eame nombre que si tu augmentes le code de 28 %, puis ajoute 972.<br><br><strong>Quel est le code d&rsquo;ouverture du coffre ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172ac37&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172ac37\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/42.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>43 &#8211; La guerre des prix<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Sophie veut acheter un ordinateur. Deux magasins vendent le m\u00eame produit, avec un prix de vente identique. Chacun propose une promotion.<br><br>Dans le magasin A, on lui propose une r\u00e9duction de 10 % sur le prix public, mais elle doit payer en plus 2 % du montant de sa facture pour la livraison et l&rsquo;installation. <br><br>Dans le magasin B, on lui propose simplement une r\u00e9duction de 8 %.<br><strong><br>Quelle est la solution la plus avantageuse pour Sophie ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172ae2e&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172ae2e\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/43.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>44 &#8211; Re-bonds<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>On lance une balle comme ci-contre. <br>Elle rebondit en avan\u00e7ant chaque fois d\u2019une longueur \u00e9gale \u00e0 la moiti\u00e9 de la pr\u00e9c\u00e9dente. Son premier rebond l\u2019a fait avancer de 2 m.<br><strong><br>Quelle sera la distance parcourue apr\u00e8s 7 rebonds ? 70 rebonds ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172b01b&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172b01b\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/44.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>45 &#8211; $\\pi=2$<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Sur un segment de longueur 2 cm, on consid\u00e8re la suite de lignes $\\mathscr{L}_n$ suivante : On commence avec $\\mathscr{L}_1$ le demi-cercle de rayon 1 cm, puis on construit $\\mathscr{L}_2$ avec 2 demi-cercles de rayon 0,5 cm, puis $\\mathscr{L}_3$ constitu\u00e9e de 4 demi-cercles de rayon 0,25 cm, et on continue ainsi de suite comme sur la figure ci-contre.<br><strong><br>\u00c9tudier la longueur de $\\mathscr{L}_n$ pour $n$ de plus en plus grand.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172b1fa&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172b1fa\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/45.png\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>46 &#8211; G\u00e9om\u00e9trie du triangle : La relation de Sylvester<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Soit $O$ le centre du cercle circonscrit \u00e0 un triangle $ABC$ et $H$ son orthocentre.<br><br><strong>Alors $\\overrightarrow{OH}=\\overrightarrow{OA}+\\overrightarrow{OB}+\\overrightarrow{OC}$.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image aligncenter size-large is-style-default\"><a href=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/46.png\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/46.png\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\"><em>Cliquer pour agrandir<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>47 &#8211; G\u00e9om\u00e9trie du triangle : Relation vectorielle du centre de gravit\u00e9<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Illustrer et d\u00e9montrer la propri\u00e9t\u00e9 suivante :<br><strong><br>Soit $G$ le centre de gravit\u00e9 d&rsquo;un triangle $ABC$.<br>Alors $\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}=\\overrightarrow{0}$.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image aligncenter size-large is-style-rounded\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/47.jpeg\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>48 &#8211; G\u00e9om\u00e9trie du triangle : La droite d&rsquo;Euler<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Illustrer dans une figure cod\u00e9e puis d\u00e9montrer la propri\u00e9t\u00e9 suivante (on peut utiliser la relation de Sylvester du pb n\u00b046) :<br><br>Soit $O$ le centre du cercle circonscrit \u00e0 un triangle $ABC$, $G$ son centre de gravit\u00e9 et $H$ son orthocentre.<br><br><strong>Alors $O,G$ et $H$ sont sur une droite appel\u00e9e la droite d&rsquo;Euler du triangle.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image aligncenter size-large is-style-default\"><a href=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/46.png\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/48.jpg\" alt=\"\"\/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>49 &#8211; Au moins un<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Environ 42 % des fran\u00e7ais sont du groupe sanguin O (donneur universel). On \u00e9tudie le groupe sanguin de quatre personnes prises au hasard dans la population fran\u00e7aise.<br><strong><br>Quelle est la probabilit\u00e9 qu\u2019au moins l&rsquo;une d&rsquo;entre elles soit du groupe O ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172b950&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172b950\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/49.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>50 &#8211; Optimiser<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Des lyc\u00e9ens r\u00e9alisent un fanzine.<br><br>Lorsque le journal est vendu 1,50 \u20ac, ils vendent 400 exemplaires de chaque num\u00e9ro. Ils ont remarqu\u00e9 que chaque hausse de 10 cts du journal fait perdre en moyenne 8 lecteurs (et inversement, chaque baisse de 10 centimes en fait gagner 8).<br><strong><br>Quel serait le prix de vente optimal du journal ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172bb59&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172bb59\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/50.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><a href=\"https:\/\/www.editions.catalpas.org\/cuizine-un-fanzine-dart-graphique-et-culinaire-15\/\">Fanzine aux \u00e9ditions Catalplas<\/a><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>51 &#8211; Les 3 formes<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p id=\"3-formes\">D\u00e9terminer la <strong>forme d\u00e9velopp\u00e9e, factoris\u00e9e et canonique de la fonction repr\u00e9sent\u00e9e ici. (cliquer pour agrandir)<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172bd50&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172bd50\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/51.png\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>52 &#8211; Somme et produit<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>D\u00e9terminer deux nombres dont la somme vaut 23 et le produit vaut -1200<br><br>D\u00e9terminer deux nombres dont la somme vaut 22 et le produit vaut -1200<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172bf38&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172bf38\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/52.jpeg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>53 &#8211; \u00c9quidistances et courbe<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p>Un bateau arrive \u00e0 proximit\u00e9 de la c\u00f4te en suivant un phare plac\u00e9 sur un rocher en mer.<br><br><strong>D\u00e9crire la trajectoire du navire sachant que le capitaine reste toujours \u00e0 la m\u00eame distance de la terre et du phare.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172c11b&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172c11b\" class=\"wp-block-image aligncenter size-large is-style-default wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/11\/53.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>54 &#8211; Une famille de rectangles<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p><strong>D\u00e9terminer tous les rectangles qui ont une aire en cm\u00b2 \u00e9gale \u00e0 leur p\u00e9rim\u00e8tre en cm.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"585\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/54-1024x585.jpeg\" alt=\"\" class=\"wp-image-3952\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/54-1024x585.jpeg 1024w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/54-300x171.jpeg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/54-768x439.jpeg 768w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/54-1536x878.jpeg 1536w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/54.jpeg 1792w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>55 &#8211; Taille des joueurs<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p><strong>Vous \u00eates journaliste sportif, commentez ce graphique.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172c7da&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172c7da\" class=\"wp-block-image size-full wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"767\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/55.jpg\" alt=\"\" class=\"wp-image-3953\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/55.jpg 1024w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/55-300x225.jpg 300w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/55-768x575.jpg 768w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>56 &#8211; Tremblez, bourgeois !<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p><strong>Expliquez le message tagg\u00e9<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172ca1a&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172ca1a\" class=\"wp-block-image size-large wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/figure.png\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>57 &#8211; Ma ch\u00e8re (?) piscine<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">J&rsquo;ai une petite piscine, hexagonale, juste ce qu&rsquo;il faut pour faire trempette l&rsquo;\u00e9t\u00e9, c&rsquo;est agr\u00e9able. J&rsquo;ai voulu savoir combien \u00e7a me co\u00fbtait de la remplir.<br><br>Alors j&rsquo;ai mesur\u00e9 l&rsquo;int\u00e9rieur d&rsquo;un des c\u00f4t\u00e9s et j&rsquo;ai trouv\u00e9 1m70. La hauteur d&rsquo;eau n\u00e9cessaire : 1m20.<br><br>Puis je suis all\u00e9 chercher sur internet le prix de l&rsquo;eau \u00e0 Lons le Saunier, j&rsquo;ai trouv\u00e9 ce tarif-l\u00e0 :<br><br><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-accent-3-color\"><strong>1,59 \u20ac\/m<sup>3<\/sup><\/strong><\/mark><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/55.jpg\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/57-scaled.jpg\" alt=\"\"\/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>58 &#8211; Les trois phares<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">Sur la c\u00f4te, il y a trois phares:<br><br>Le premier s\u2019allume pendant 3 secondes, puis s\u2019\u00e9teint pendant 3 secondes.<br><br>Le deuxi\u00e8me s\u2019allume pendant 4 secondes, puis s\u2019\u00e9teint pendant 4 secondes.<br><br>Le troisi\u00e8me s\u2019allume pendant 5 secondes, puis s\u2019\u00e9teint pendant 5 secondes.<br><br>Les trois lumi\u00e8res viennent de s\u2019allumer ensemble.<br><br><strong>\u00c0 quel moment peut-on d\u00e9terminer la premi\u00e8re fois que les trois lumi\u00e8res s\u2019\u00e9teignent en m\u00eame temps ?<br><\/strong><br><strong>\u00c0 quel moment peut-on d\u00e9terminer la prochaine fois que les trois lumi\u00e8res s\u2019allumeront en m\u00eame temps ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/58.jpg\" alt=\"\"\/><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>59 &#8211; Cube moyen ou moyenne des cubes ?<\/summary>\n<p class=\"has-text-align-left\">Une entreprise fabrique sur commande des cubes creux de tailles diff\u00e9rentes. En d\u00e9but de processus de fabrication, on d\u00e9termine la longueur des c\u00f4t\u00e9s des cubes \u00e0 fabriquer et en fin de processus, on d\u00e9termine leur capacit\u00e9. Pour avoir une id\u00e9e de la production, la direction a demand\u00e9 de proc\u00e9der \u00e0 plusieurs mesures sur 500 cubes. Ainsi, la moyenne de leurs c\u00f4t\u00e9s est de 10,5 cm et celle de leur volume est 2240 cm<sup>3<\/sup>. Voulant tenir compte de toutes les mesures, la direction a conclu que le cube moyen fabriqu\u00e9 par cette entreprise \u00e9tait un cube de c\u00f4t\u00e9 10,5 cm et de volume 2240<sub><sup> <\/sup><\/sub>cm<sup>3<\/sup> !<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">C\u00f4t\u00e9<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">5<\/td><td class=\"has-text-align-center\" data-align=\"center\">10<\/td><td class=\"has-text-align-center\" data-align=\"center\">15<\/td><td class=\"has-text-align-center\" data-align=\"center\">20<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Volume<\/td><td class=\"has-text-align-center\" data-align=\"center\">1<\/td><td class=\"has-text-align-center\" data-align=\"center\">125<\/td><td class=\"has-text-align-center\" data-align=\"center\">1000<\/td><td class=\"has-text-align-center\" data-align=\"center\">3375<\/td><td class=\"has-text-align-center\" data-align=\"center\">8000<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Effectifs<\/td><td class=\"has-text-align-center\" data-align=\"center\">50<\/td><td class=\"has-text-align-center\" data-align=\"center\">120<\/td><td class=\"has-text-align-center\" data-align=\"center\">140<\/td><td class=\"has-text-align-center\" data-align=\"center\">120<\/td><td class=\"has-text-align-center\" data-align=\"center\">70<\/td><\/tr><\/tbody><\/table><\/figure>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>60 &#8211; Joyeuses P\u00e2ques !<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">A l\u2019approche des f\u00eates de P\u00e2ques, un artisan chocolatier d\u00e9cide de confectionner des \u0153ufs en chocolat. En allant inspecter ses r\u00e9serves, il constate qu\u2019il lui reste 18 kg de cacao, 8 kg de noisettes et 14 litres (kg) de lait. Il a deux sp\u00e9cialit\u00e9s : l\u2019\u0153uf Extra et l\u2019\u0153uf Sublime.<br><br>Un \u0153uf Extra n\u00e9cessite 100 g de cacao, 100 g de noisettes et 200 ml (g) de lait.<br><br>Un \u0153uf Sublime n\u00e9cessite 300 g de cacao, 100 g de noisettes et 100 ml (g) de lait.<br><br>Il fera un profit de 2\u20ac en vendant un \u0153uf Extra, et de 3\u20ac en vendant un \u0153uf Sublime.<br><strong><br>Combien d\u2019\u0153ufs Extra et Sublime doit-il fabriquer pour faire le plus grand b\u00e9n\u00e9fice possible ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172cee0&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172cee0\" class=\"wp-block-image size-large wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/60.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>61 &#8211; \u00c9nigme des balances<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">Les balances A et B sont en \u00e9quilibre.<br><br><strong>Et la balance C ? Sinon, de quel c\u00f4t\u00e9 penche-t-elle ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172d0d3&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172d0d3\" class=\"wp-block-image size-large wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/61.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>62 &#8211; Ah \u00e7a ira, \u00e7a ira\u2026 \u00e0 l&rsquo;heure ?<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">Voici une horloge r\u00e9volutionnaire (1 jour dure 10 heures, une heure dure 100 minutes et 1 minute dure 100 secondes).<br><br><strong>Quelle heure serait indiqu\u00e9e au m\u00eame moment sur une horloge classique ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172d2b8&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172d2b8\" class=\"wp-block-image size-large wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/62.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>63 &#8211; Pyramide et tronc<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\"><strong>\u00c0 quelle hauteur doit-on couper une pyramide r\u00e9guli\u00e8re (la hauteur a la m\u00eame mesure que le c\u00f4t\u00e9 du carr\u00e9 de base) pour obtenir deux morceaux de m\u00eame volume ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172d4b7&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172d4b7\" class=\"wp-block-image size-large wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/image.png\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>64 &#8211; Quatre cercles en un<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">Dans un grand cercle de rayon 10 cm on construit quatre petits cercles identiques tangents entre eux et au grand cercle. <br><strong><br>Quel est le rayon de chacun des quatre petits cercles ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172d698&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172d698\" class=\"wp-block-image size-large wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/64.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>65 &#8211; 4\/4 2 P1\/2<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">Dans l&rsquo;image ci-contre, j&rsquo;ai coup\u00e9 ma tranche de pain de mie grill\u00e9 en quatre parts identiques de deux mani\u00e8re diff\u00e9rentes : des parts carr\u00e9es et des parts triangulaires.<br><strong><br>Quelle part a le plus grand p\u00e9rim\u00e8tre ? La carr\u00e9e ou la triangulaire ?<br><br>Existe-t-il une mani\u00e8re de couper ma tranche en quatre parts identiques pour obtenir un p\u00e9rim\u00e8tre de part maximal ?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172d877&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172d877\" class=\"wp-block-image size-large wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/65.png\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>66 &#8211; Rationnel ?<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172da14&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172da14\" class=\"wp-block-image size-large wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/66.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>67 &#8211; Racine carr\u00e9\u00e9\u00e9\u00e9\u00e9\u00e9\u00e9\u00e9\u2026..<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">Combien vaut $\\sqrt{2+\\sqrt{2+\\sqrt{2+\\sqrt{2+\\dots}}}}$ ?<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172dbee&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172dbee\" class=\"wp-block-image aligncenter size-large wp-lightbox-container\"><img decoding=\"async\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/67.jpg\" alt=\"\"\/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\"><em>Premi\u00e8re trace de la racine carr\u00e9e de 2 dans l&rsquo;histoire<\/em><\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>68 &#8211; No\u00ebl math\u00e9matique<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">Cette ann\u00e9e, Billy a d\u00e9cid\u00e9 d\u2019ouvrir son calendrier de l\u2019Avent de fa\u00e7on originale. Le 1<sup>er<\/sup>&nbsp;d\u00e9cembre, il ouvre la case n\u00b01, puis saute une case tous les jours.<br>Le 2&nbsp;d\u00e9cembre, il saute la case n\u00b0&nbsp;2 et ouvre directement la case n\u00b0&nbsp;3. <br>Le 3&nbsp;d\u00e9cembre, il saute la case n\u00b0&nbsp;4 et ouvre la n\u00b0&nbsp;5, et ainsi de suite jusqu\u2019\u00e0 ce qu\u2019il arrive \u00e0 la fin du calendrier, qui compte 24 cases.<br>Il recommence alors au d\u00e9but en appliquant la m\u00eame proc\u00e9dure avec les cases qu\u2019il n\u2019a pas encore ouvertes. <br>D\u2019abord il ouvre la case n\u00b0&nbsp;2 qu\u2019il avait saut\u00e9e lors de son premier passage, puis, le lendemain, saute la case ferm\u00e9e suivante et ouvre celle d\u2019apr\u00e8s. D\u00e8s qu\u2019il arrive \u00e0 la fin, il reprend au d\u00e9but en appliquant encore et toujours cette m\u00eame proc\u00e9dure avec les cases restantes.<br><br><strong>Pouvez-vous d\u00e9terminer le num\u00e9ro de la derni\u00e8re case qu\u2019il ouvrira, le 24&nbsp;d\u00e9cembre&nbsp;?<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image aligncenter size-large\"><a href=\"https:\/\/www.lemonde.fr\/sciences\/article\/2024\/12\/07\/le-calendrier-de-l-avent-l-enigme-maths-du-monde-n-37_6435082_1650684.html\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2024\/12\/68.jpg\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">Tir\u00e9 du calendrier de l&rsquo;avent math\u00e9matique du Monde<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>69 &#8211; Th\u00e9or\u00e8me de Rolla et alg\u00e8bre de Bolla<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">Le cylindre du rolla bolla mesure 14 cm de diam\u00e8tre et la planche touche le sol \u00e0 40cm du cylindre.<br><br><strong>D\u00e9terminer le point de contact de la planche et du cylindre.<\/strong><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure class=\"wp-block-image aligncenter size-large\"><a href=\"https:\/\/www.lemonde.fr\/sciences\/article\/2024\/12\/07\/le-calendrier-de-l-avent-l-enigme-maths-du-monde-n-37_6435082_1650684.html\"><img decoding=\"async\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2025\/02\/69.png\" alt=\"\"\/><\/a><figcaption class=\"wp-element-caption\">Rolla Bolla<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<details class=\"wp-block-details situation is-layout-flow wp-block-details-is-layout-flow\" style=\"border-style:none;border-width:0px\"><summary>70 &#8211; Une sph\u00e8re dans un c\u00f4ne<\/summary>\n<div class=\"wp-block-columns are-vertically-aligned-center is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\" id=\"40\">\n<div class=\"wp-block-column is-vertically-aligned-center is-style-default is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66%\">\n<p class=\"has-text-align-left\">on cherche \u00e0 d\u00e9terminer la hauteur d\u2019un c\u00f4ne contenant une boule tel que le volume du c\u00f4ne soit minimal.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33%\">\n<figure data-wp-context=\"{&quot;imageId&quot;:&quot;69ea25172e350&quot;}\" data-wp-interactive=\"core\/image\" data-wp-key=\"69ea25172e350\" class=\"wp-block-image aligncenter size-full wp-lightbox-container\"><img loading=\"lazy\" decoding=\"async\" width=\"603\" height=\"542\" data-wp-class--hide=\"state.isContentHidden\" data-wp-class--show=\"state.isContentVisible\" data-wp-init=\"callbacks.setButtonStyles\" data-wp-on--click=\"actions.showLightbox\" data-wp-on--load=\"callbacks.setButtonStyles\" data-wp-on-window--resize=\"callbacks.setButtonStyles\" src=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2025\/12\/cone-et-sphere.png\" alt=\"\" class=\"wp-image-4104\" srcset=\"https:\/\/jhmaths.fr\/wp-content\/uploads\/2025\/12\/cone-et-sphere.png 603w, https:\/\/jhmaths.fr\/wp-content\/uploads\/2025\/12\/cone-et-sphere-300x270.png 300w\" sizes=\"auto, (max-width: 603px) 100vw, 603px\" \/><button\n\t\t\tclass=\"lightbox-trigger\"\n\t\t\ttype=\"button\"\n\t\t\taria-haspopup=\"dialog\"\n\t\t\taria-label=\"Agrandir\"\n\t\t\tdata-wp-init=\"callbacks.initTriggerButton\"\n\t\t\tdata-wp-on--click=\"actions.showLightbox\"\n\t\t\tdata-wp-style--right=\"state.imageButtonRight\"\n\t\t\tdata-wp-style--top=\"state.imageButtonTop\"\n\t\t>\n\t\t\t<svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"12\" height=\"12\" fill=\"none\" viewBox=\"0 0 12 12\">\n\t\t\t\t<path fill=\"#fff\" d=\"M2 0a2 2 0 0 0-2 2v2h1.5V2a.5.5 0 0 1 .5-.5h2V0H2Zm2 10.5H2a.5.5 0 0 1-.5-.5V8H0v2a2 2 0 0 0 2 2h2v-1.5ZM8 12v-1.5h2a.5.5 0 0 0 .5-.5V8H12v2a2 2 0 0 1-2 2H8Zm2-12a2 2 0 0 1 2 2v2h-1.5V2a.5.5 0 0 0-.5-.5H8V0h2Z\" \/>\n\t\t\t<\/svg>\n\t\t<\/button><figcaption class=\"wp-element-caption\">Figure<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/details>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"folder":[],"class_list":["post-3757","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3757","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/comments?post=3757"}],"version-history":[{"count":87,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3757\/revisions"}],"predecessor-version":[{"id":4106,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/pages\/3757\/revisions\/4106"}],"wp:attachment":[{"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/media?parent=3757"}],"wp:term":[{"taxonomy":"folder","embeddable":true,"href":"https:\/\/jhmaths.fr\/index.php\/wp-json\/wp\/v2\/folder?post=3757"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}