{"id":12800,"date":"2021-11-24T00:05:00","date_gmt":"2021-11-23T23:05:00","guid":{"rendered":"http:\/\/lemotdujour.fr\/?p=12800"},"modified":"2021-11-24T10:35:56","modified_gmt":"2021-11-24T09:35:56","slug":"mercredi-24-novembre-2021","status":"publish","type":"post","link":"https:\/\/lemotdujour.fr\/?p=12800","title":{"rendered":"Mercredi 24 novembre 2021"},"content":{"rendered":"<div class=\"mdjTexte\">\u00ab\u00a0Comment bien poser un probl\u00e8me math\u00e9matique\u00a0?\u00bb<\/div>\n<div class=\"mdjAuteur\">R\u00e9ponse par un exemple<\/div>\n<p><span style=\"color: #777777; font-family: Arial;\">Ma ch\u00e8re belle-s\u0153ur Josiane qui me f\u00e9licite pour la diversit\u00e9 des sujets abord\u00e9s, exprimait sa crainte qu&rsquo;apr\u00e8s avoir simplement vant\u00e9 la beaut\u00e9 d&rsquo;une fleur, je me lance dans un sujet hautement intellectuel, conceptuel et abstrait.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Je note que les avis sont tr\u00e8s partag\u00e9s.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Mon ami Bertrand G. trouve que je parle trop de politique, ce qui serait une perte de temps.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Jean-Philippe ne trouve pas d&rsquo;int\u00e9r\u00eat \u00e0 mes sujets musicaux. D&rsquo;autres lecteurs ont exprim\u00e9 leur distance avec les sujets \u00ab football \u00bb que j&rsquo;avais abord\u00e9s.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Il est vrai que la plupart des blogs sont \u00ab\u00a0mono-th\u00e8me\u00a0\u00bb. Ils parlent exclusivement d&rsquo;art ou de bien \u00eatre ou de politique ou d&rsquo;Histoire ou de Sciences ou de sports ou encore d&rsquo;actualit\u00e9.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Le mot du jour que j&rsquo;\u00e9cris ne se fixe pas ce type de limite.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Il faut simplement que je comprenne un peu de quoi il en retourne, je n&rsquo;ai jamais \u00e9voqu\u00e9 le bitcoin.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Et que j&rsquo;ai le sentiment d&rsquo;avoir \u00e0 dire quelque chose de pertinent ou de surprenant ou de d\u00e9cal\u00e9, je n&rsquo;ai jamais parl\u00e9 d&rsquo;hom\u00e9opathie.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Aujourd&rsquo;hui, je vais parler de math\u00e9matiques, mais pas que \u2026<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">C&rsquo;\u00e9tait en classe de math\u00e9matiques sup\u00e9rieures au Lyc\u00e9e Kl\u00e9ber de Strasbourg, lors de l&rsquo;ann\u00e9e scolaire 1976\/1977, il y a 45 ans donc, et je m&rsquo;en souviens encore.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">C&rsquo;\u00e9tait M Schmidt qui nous a pos\u00e9 cette question\u00a0:<br \/>\n<\/span><\/p>\n<p style=\"margin-left: 28pt;\"><span style=\"color: #c00000; font-family: Arial;\">\u00ab\u00a0Vous devez organiser un tournoi de tennis. Vous avez 100 participants. Chaque match est \u00e0 \u00e9limination directe\u00a0: le joueur qui gagne continue le tournoi, celui qui perd est \u00e9limin\u00e9.<br \/>\n<\/span><span style=\"color: #c00000; font-family: Arial;\">Combien de matchs devez vous organiser pour finir le tournoi et d\u00e9gager suite \u00e0 la finale, un vainqueur ? \u00bb<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Toute la classe qui comptait plusieurs futurs polytechniciens a commenc\u00e9 \u00e0 raisonner\u00a0:<br \/>\n<\/span><\/p>\n<ul>\n<li><span style=\"color: #777777; font-family: Arial;\">Au premier tour je fais 50 matchs, il 50 qualifi\u00e9s et 50 \u00e9limin\u00e9s.<br \/>\n<\/span><\/li>\n<li><span style=\"color: #777777; font-family: Arial;\">Au second tour j&rsquo;en fais 25\u2026<br \/>\n<\/span><\/li>\n<li><span style=\"color: #777777; font-family: Arial;\">Au troisi\u00e8me tour il y a un joueur qui est exempt\u00e9 et je fais 12 matchs\u2026<br \/>\n<\/span><\/li>\n<li><span style=\"color: #777777; font-family: Arial;\">Etc\u2026<br \/>\n<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #777777; font-family: Arial;\">Un autre groupe a abord\u00e9 le sujet autrement. Il est parti de la finale (2 joueurs), puis de la demi-finale (4 joueurs), puis les quarts de finales (8 joueurs) et on arrive ainsi au 32<sup>\u00e8me<\/sup> finale avec 64 joueurs. Et il faut alors trouver le moyen de passer de 100 joueurs \u00e0 64 joueurs dans un premier tour dont on exempte les meilleurs\u2026<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Et pendant que nous cherchions \u00e0 \u00e9laborer des raisonnements savants pour essayer de r\u00e9pondre \u00e0 cette question, Monsieur Schmidt hilare se moquait de nous en nous disant\u00a0:<br \/>\n<\/span><\/p>\n<p style=\"margin-left: 28pt;\"><span style=\"color: #c00000; font-family: Arial;\">\u00ab Alors vous \u00eates en math. Sup. et vous avez besoin de plus de 2 secondes pour r\u00e9pondre \u00e0 une question aussi simple ? \u00bb<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Mais oui, c&rsquo;\u00e9tait une question d&rsquo;une simplicit\u00e9 absolue.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Mais il fallait se poser la bonne question.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Il faut toujours bien poser les questions, m\u00eame si parfois on n&rsquo;a pas la r\u00e9ponse.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">La question est plus importante que la r\u00e9ponse.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Nous vivons au quotidien au milieu de gens qui ont la certitude de poss\u00e9der les bonnes r\u00e9ponses, alors qu&rsquo;ils n&rsquo;ont pas r\u00e9fl\u00e9chi aux bonnes questions \u00e0 se poser.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Ces personnes sont tr\u00e8s dangereuses.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Peut \u00eatre qu&rsquo;Einstein pensait \u00e0 eux quand il disait\u00a0: \u00ab\u00a0<span style=\"color: #c00000;\">Si vous avez un marteau dans le cerveau, tout probl\u00e8me prendra la forme d&rsquo;un clou\u00a0!<span style=\"color: #777777;\"> \u00bb.<br \/>\n<\/span><\/span><\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Alors quelle est la bonne question pour ce tournoi\u00a0?<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Vous avez 100 joueurs. Le tournoi consiste \u00e0 obtenir 1 vainqueur et donc \u00e0 \u00e9liminer 99 joueurs.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">La question qu&rsquo;il faut poser est : <\/span><span style=\"color: #777777; font-family: Arial;\">Combien de matchs sont n\u00e9cessaires pour \u00e9liminer 99 joueurs\u00a0?<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Un enfant de 6 ans sait r\u00e9pondre \u00e0 cette question.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Avec le principe du match \u00e0 \u00e9limination directe<strong>, il faut \u00e9videmment 99 matchs<\/strong> pour \u00e9liminer 99 joueurs et d\u00e9signer un vainqueur.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">M Schmidt \u00e9tait un grand p\u00e9dagogue : <\/span><span style=\"color: #777777; font-family: Arial;\">45 ans apr\u00e8s je m&rsquo;en souviens encore.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Notez que les raisonnements compliqu\u00e9s fonctionnent aussi.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #777777; font-family: Arial;\">Si on reprend le premier raisonnement, gr\u00e2ce \u00e0 ce petit tableau on sait r\u00e9pondre \u00e0 la question\u00a0:<\/span><\/p>\n<table style=\"border-collapse: collapse;\" border=\"0\">\n<colgroup>\n<col style=\"width: 115px;\" \/>\n<col style=\"width: 107px;\" \/>\n<col style=\"width: 107px;\" \/>\n<col style=\"width: 107px;\" \/>\n<col style=\"width: 68px;\" \/><\/colgroup>\n<tbody valign=\"top\">\n<tr style=\"height: 60px;\">\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><\/td>\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: solid 0.5pt; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">Nombre de joueurs avant le tour<\/span><\/p>\n<\/td>\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: solid 0.5pt; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">Nombre de matchs<\/span><\/p>\n<\/td>\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: solid 0.5pt; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">Nombre de qualifi\u00e9s<\/span><\/p>\n<\/td>\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: solid 0.5pt; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">Joueur exempt\u00e9<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">1er tour<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">100<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">50<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">50<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">2\u00e8me tour<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">50<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">25<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">25<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">3\u00e8me tour<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">25<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">12<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">12<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">1<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">4\u00e8me tour<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">13<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">6<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">6<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">1<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">5\u00e8me tour<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">7<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">3<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">3<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">1<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">1\/2 finale<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">4<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">2<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">2<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">Finale<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">2<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">1<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">1<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\"><strong>Total des matchs<\/strong><\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: none;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\"><strong>99<\/strong><\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border: none;\" valign=\"middle\"><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border: none;\" valign=\"middle\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Le second raisonnement fonctionne aussi\u00a0:<\/p>\n<p>Il faut donc qu&rsquo;au premier tour on puisse passer de 100 joueurs \u00e0 64<\/p>\n<p>Pour ce faire, il faut en \u00e9liminer 36<\/p>\n<p>On fait donc un premier tour de 36 matchs<\/p>\n<p>Et le tableau devient celui-ci<\/p>\n<table style=\"border-collapse: collapse;\" border=\"0\">\n<colgroup>\n<col style=\"width: 115px;\" \/>\n<col style=\"width: 107px;\" \/>\n<col style=\"width: 107px;\" \/>\n<col style=\"width: 107px;\" \/>\n<col style=\"width: 68px;\" \/><\/colgroup>\n<tbody valign=\"top\">\n<tr style=\"height: 60px;\">\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><\/td>\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: solid 0.5pt; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">Nombre de joueurs avant le tour<\/span><\/p>\n<\/td>\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: solid 0.5pt; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">Nombre de matchs<\/span><\/p>\n<\/td>\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: solid 0.5pt; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">Nombre de qualifi\u00e9s<\/span><\/p>\n<\/td>\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: solid 0.5pt; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">Joueurs exempt\u00e9<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">1er tour<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">100<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">36<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">36<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">28<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">1\/32 finale<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">64<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">32<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">32<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">1\/16 finale<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">32<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">16<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">16<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">1\/8 finale<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">16<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">8<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">8<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">1\/4 finale<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">8<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">4<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">4<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">1\/2 finale<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">4<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">2<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">2<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\">Finale<\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">2<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">1<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">1<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 20px;\">\n<td style=\"background: #fce4d6; padding-left: 5px; padding-right: 5px; border-top: none; border-left: solid 0.5pt; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\"><span style=\"color: black;\"><strong>Total des matchs<\/strong><\/span><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: none;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\">\u00a0<\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border-top: none; border-left: none; border-bottom: solid 0.5pt; border-right: solid 0.5pt;\" valign=\"middle\">\n<p style=\"text-align: center;\"><span style=\"color: black;\"><strong>99<\/strong><\/span><\/p>\n<\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border: none;\" valign=\"middle\"><\/td>\n<td style=\"padding-left: 5px; padding-right: 5px; border: none;\" valign=\"middle\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>La morale de cette histoire devient alors : on peut arriver au m\u00eame r\u00e9sultat en prenant des chemins diff\u00e9rents, plus ou moins longs&#8230;<\/p>\n<p><span style=\"color: #c00000;\">&lt;1628&gt;<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u00ab\u00a0Comment bien poser un probl\u00e8me math\u00e9matique\u00a0?\u00bb R\u00e9ponse par un exemple Ma ch\u00e8re belle-s\u0153ur Josiane qui me f\u00e9licite pour la diversit\u00e9 des sujets abord\u00e9s, exprimait sa crainte qu&rsquo;apr\u00e8s avoir simplement vant\u00e9 la beaut\u00e9 d&rsquo;une fleur, je me lance dans un sujet<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[63,6],"class_list":["post-12800","post","type-post","status-publish","format-standard","hentry","category-motdujour","tag-mathematiques","tag-philosophie"],"_links":{"self":[{"href":"https:\/\/lemotdujour.fr\/index.php?rest_route=\/wp\/v2\/posts\/12800","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lemotdujour.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lemotdujour.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lemotdujour.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lemotdujour.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=12800"}],"version-history":[{"count":6,"href":"https:\/\/lemotdujour.fr\/index.php?rest_route=\/wp\/v2\/posts\/12800\/revisions"}],"predecessor-version":[{"id":12808,"href":"https:\/\/lemotdujour.fr\/index.php?rest_route=\/wp\/v2\/posts\/12800\/revisions\/12808"}],"wp:attachment":[{"href":"https:\/\/lemotdujour.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=12800"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lemotdujour.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=12800"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lemotdujour.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=12800"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}