{"id":689,"date":"2019-03-15T21:18:00","date_gmt":"2019-03-15T17:18:00","guid":{"rendered":"https:\/\/iremi.univ-reunion.fr\/?p=689"},"modified":"2025-08-06T20:38:14","modified_gmt":"2025-08-06T16:38:14","slug":"sowing","status":"publish","type":"post","link":"https:\/\/iremi.univ-reunion.fr\/?p=689","title":{"rendered":"Sowing"},"content":{"rendered":"\n<p>Sowing est un jeu de semailles, cr\u00e9\u00e9 par John Conway en 1996. Tr\u00e8s simple, il est jouable d\u00e8s le CP. Mais c&rsquo;est au congr\u00e8s MATh.en.JEANS de 2019 qu&rsquo;il a fait l&rsquo;objet<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>d&rsquo;une s\u00e9ance de jeu par les participants<\/li>\n\n\n\n<li>d&rsquo;un expos\u00e9, que voici :<\/li>\n<\/ul>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/Sowing2020.pdf\" type=\"application\/pdf\" style=\"width:100%;height:440px\" aria-label=\"Contenu embarqu\u00e9 Sowing2020.\"><\/object><a id=\"wp-block-file--media-5815eb73-69d0-4099-bc53-23dc3bc03557\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/Sowing2020.pdf\">Sowing2020<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/Sowing2020.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-5815eb73-69d0-4099-bc53-23dc3bc03557\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>La r\u00e8gle du jeu est suffisamment simple pour que des \u00e9l\u00e8ves de CP puissent apprendre \u00e0 y jouer en quelques minutes. On s\u00e8me des graines sur un plateau \u00e0 une seule rang\u00e9e comme celui-ci :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"179\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/DSC_0969.jpg\" alt=\"\" class=\"wp-image-710\" srcset=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/DSC_0969.jpg 720w, https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/DSC_0969-300x75.jpg 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<p>Chaque tour de jeu consiste \u00e0<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>choisir une case non vide du plateau<\/li>\n\n\n\n<li>mettre dans sa main toutes les graines qu&rsquo;elle contient<\/li>\n\n\n\n<li>semer ces graines, une par une, vers la droite, en commen\u00e7ant par la case voisine (apr\u00e8s le tour de jeu, la case choisie est vide).<\/li>\n<\/ul>\n\n\n\n<p>Et c&rsquo;est tout ! Il faut juste que la derni\u00e8re graine soit sem\u00e9e dans une case contenant d\u00e9j\u00e0 au moins une graine. Par exemple, ci-dessous, la case contenant 4 graines ne peut pas \u00eatre jou\u00e9e par Sud (par contre elle est jouable par Nord) parce que le semis sortirait du plateau, et la case tout \u00e0 gauche non plus, ne peut \u00eatre jou\u00e9e : la derni\u00e8re des 3 graines qu&rsquo;elle contient tomberait dans une case vide. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"502\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowingavant.jpg\" alt=\"\" class=\"wp-image-712\" srcset=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowingavant.jpg 720w, https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowingavant-300x209.jpg 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<p>Sud peut jouer une case contenant une graine, en d\u00e9posant cette graine dans la voisine de droite, mais elle choisit de semer les 3 graines :<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"720\" height=\"486\" src=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowingapres.jpg\" alt=\"\" class=\"wp-image-713\" srcset=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowingapres.jpg 720w, https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowingapres-300x203.jpg 300w\" sizes=\"auto, (max-width: 720px) 100vw, 720px\" \/><\/figure>\n\n\n\n<p>La case jou\u00e9e est maintenant vide, la case qui \u00e9tait vide contient une graine, la case qui contenait une graine en contient maintenant 2, et la case de droite contient maintenant 5 graines. Nord peut semer, ou bien la graine unique \u00e0 gauche (vers sa voisine qui contiendrait alors 4 graines), ou bien les 5 graines (la derni\u00e8re tomberait dans la case \u00e0 3 graines).<\/p>\n\n\n\n<p>Sowing est jouable d\u00e8s le CP (du moment que les \u00e9l\u00e8ves sont lat\u00e9ralis\u00e9s) et <a href=\"https:\/\/alainbusser.github.io\/Jeux_maths_OI\/sowing.html\">on peut y jouer en ligne<\/a>. Voici une fiche d&rsquo;exercices sur Sowing, couvrant toute l&rsquo;\u00e9cole \u00e9l\u00e9mentaire :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/fiche_sowing.pdf\" type=\"application\/pdf\" style=\"width:100%;height:430px\" aria-label=\"Contenu embarqu\u00e9 fiche_sowing.\"><\/object><a id=\"wp-block-file--media-c8380e80-2c3a-49ae-962a-7fcab197409e\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/fiche_sowing.pdf\">fiche_sowing<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/fiche_sowing.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-c8380e80-2c3a-49ae-962a-7fcab197409e\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\" \/>\n\n\n\n<h2 class=\"wp-block-heading\">Sowing en informatique<\/h2>\n\n\n\n<p>Le jeu Sowing est suffisamment simple pour \u00eatre abordable en NSI (voire SNT) :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowingNSI.pdf\" type=\"application\/pdf\" style=\"width:100%;height:430px\" aria-label=\"Contenu embarqu\u00e9 sowingNSI.\"><\/object><a id=\"wp-block-file--media-21e338f7-8e69-4732-8ed6-4d99e31774c4\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowingNSI.pdf\">sowingNSI<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowingNSI.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-21e338f7-8e69-4732-8ed6-4d99e31774c4\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>Voici comment on mod\u00e9lise Sowing en Python :;<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>SUD = 1\nNORD = -1\ndef jouer(p,i,j):\n        q = &#091;x for x in p]\n        graines = q&#091;i]\n        q&#091;i] = 0\n        while graines&gt;0:\n            i += j\n            graines -= 1\n            q&#091;i] += 1\n    return q\n<\/code><\/pre>\n\n\n\n<p>Pour trouver une strat\u00e9gie gagnante, on peut calculer l&rsquo;arbre du jeu :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowing4a.pdf\" type=\"application\/pdf\" style=\"width:100%;height:510px\" aria-label=\"Contenu embarqu\u00e9 sowing4a.\"><\/object><a id=\"wp-block-file--media-ac3dd2e1-9514-40b2-95bc-b1fda78de0e4\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowing4a.pdf\">sowing4a<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowing4a.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-ac3dd2e1-9514-40b2-95bc-b1fda78de0e4\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p>arbre qui est plus complexe lorsqu&rsquo;on joue avec 10 graines dans 5 cases :<\/p>\n\n\n\n<div data-wp-interactive=\"core\/file\" class=\"wp-block-file\"><object data-wp-bind--hidden=\"!state.hasPdfPreview\" hidden class=\"wp-block-file__embed\" data=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowing5a.pdf\" type=\"application\/pdf\" style=\"width:100%;height:420px\" aria-label=\"Contenu embarqu\u00e9 sowing5a.\"><\/object><a id=\"wp-block-file--media-fd64ed50-623c-4129-b941-75420726de5d\" href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowing5a.pdf\">sowing5a<\/a><a href=\"https:\/\/iremi.univ-reunion.fr\/wp-content\/uploads\/2019\/03\/sowing5a.pdf\" class=\"wp-block-file__button wp-element-button\" download aria-describedby=\"wp-block-file--media-fd64ed50-623c-4129-b941-75420726de5d\">T\u00e9l\u00e9charger<\/a><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Sowing est un jeu de semailles, cr\u00e9\u00e9 par John Conway en 1996. Tr\u00e8s simple, il est jouable d\u00e8s le CP. Mais c&rsquo;est au congr\u00e8s MATh.en.JEANS de 2019 qu&rsquo;il a fait l&rsquo;objet La r\u00e8gle du jeu est suffisamment simple pour que des \u00e9l\u00e8ves de CP puissent apprendre \u00e0 y jouer en quelques minutes. On s\u00e8me des [&hellip;]<\/p>\n","protected":false},"author":6,"featured_media":712,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3,12,10],"tags":[18,34,79,32,35],"coauthors":[54],"class_list":["post-689","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-arithmetique-et-algebre","category-jeux-mathematiques","category-machines-information-codage","tag-algorithmique","tag-construction-du-nombre","tag-graphes","tag-lycee","tag-nsi"],"_links":{"self":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/689","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/users\/6"}],"replies":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=689"}],"version-history":[{"count":11,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/689\/revisions"}],"predecessor-version":[{"id":1304,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/posts\/689\/revisions\/1304"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=\/wp\/v2\/media\/712"}],"wp:attachment":[{"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=689"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=689"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=689"},{"taxonomy":"author","embeddable":true,"href":"https:\/\/iremi.univ-reunion.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcoauthors&post=689"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}