Différences entre les pages « Tour d'Hanoï » et « Fichier:Grottes humides IMG 20200530 163248.jpg »

 
(Grottes_humides_IMG_20200530_163248)
 
Ligne 1 : Ligne 1 :
{{Tuto Details
+
Grottes_humides_IMG_20200530_163248
|Main_Picture=Tour_d_Hano__IMG_20200504_175352634.jpg
 
|Licences=Attribution (CC-BY)
 
|Description=Le jeu des tours d'Hanoï est un jeu simple qui permet de comprendre la notion d'algorithme.
 
|Disciplines scientifiques=Computing, Mathematics
 
|Difficulty=Easy
 
|Duration=20
 
|Duration-type=minute(s)
 
|Tags=Algorithme, reflexion, deconnecté
 
}}
 
{{Introduction
 
|Introduction=Avant de se lancer dans le jeu, il faut le construire. Rien de plus simple : du carton, des cure-dents, des ciseaux et des feutres, un peu de bricolage et hop, c'est prêt !
 
 
 
 
 
La Tour d'Hanoï est un jeu constitué de disques de différentes tailles empilées sur une tige. Le principe du jeu est de déplacer la pile de disques d'une tige à l'autre.
 
}}
 
{{Materials
 
|ItemList={{ItemList
 
|Item=Carton
 
}}{{ItemList
 
|Item=Ciseaux
 
}}{{ItemList
 
|Item=Scotch
 
}}{{ItemList
 
|Item=Polystyrène
 
}}{{ItemList
 
|Item=Feutre de couleur
 
}}{{ItemList
 
|Item=Compas
 
}}{{ItemList
 
|Item=Cure-dents
 
}}
 
}}
 
{{Tuto Step
 
|Step_Title=Construire les cercles
 
|Step_Content=Sur du carton, tracer 5 cercles de diamètres différents.
 
 
 
Les découper et les décorer.
 
|Step_Picture_00=Tour_d_Hano__IMG_20200504_145111212.jpg
 
|Step_Picture_01=Tour_d_Hano__IMG_20200504_150224387.jpg
 
|Step_Picture_02=Tour_d_Hano__IMG_20200504_152018853.jpg
 
}}
 
{{Tuto Step
 
|Step_Title=Préparer le plateau de jeu
 
|Step_Content=Planter 3 cure-dents dans le bloc de polystyrène.
 
 
 
 
 
Attention, il faut que les 3 cure-dents soient suffisamment éloignés.
 
|Step_Picture_00=Tour_d_Hano__IMG_20200504_152147052.jpg
 
}}
 
{{Tuto Step
 
|Step_Title=Préparer le jeu
 
|Step_Content=Faire un trou dans chacun des disques préparés à l'étape 1.
 
 
 
 
 
Sur le pic numéro 1, empiler les différents disques du plus grand au plus petit.
 
|Step_Picture_00=Tour_d_Hano__IMG_20200504_152158086.jpg
 
}}
 
{{Tuto Step
 
|Step_Title=Jouer
 
|Step_Content=Le but du jeu est de déplacer toute la pile du pic numéro 1 sur un autre pic.
 
 
 
 
 
Les règles du jeu sont les suivantes :
 
 
 
- on ne peut déplacer qu'un seul disque à la fois (toujours un disque qui est sur le haut d'une pile)
 
 
 
- on ne peut pas mettre un grand disque sur un plus petit (comme sur la photo 2)
 
 
 
 
 
Chaque déplacement de disque compte pour un mouvement. Il faut essayer de faire le moins de déplacements possibles.
 
|Step_Picture_00=Tour_d_Hano__IMG_20200504_152306156.jpg
 
|Step_Picture_01=Tour_d_Hano__IMG_20200504_152238000.jpg
 
|Step_Picture_01_annotation={"version":"3.5.0","objects":[{"type":"image","version":"3.5.0","originX":"left","originY":"top","left":-3,"top":0,"width":2976,"height":3968,"fill":"rgb(0,0,0)","stroke":null,"strokeWidth":0,"strokeDashArray":null,"strokeLineCap":"butt","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":0.2,"scaleY":0.2,"angle":0,"flipX":false,"flipY":false,"opacity":1,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"crossOrigin":"","cropX":0,"cropY":0,"src":"https://www.wikidebrouillard.org/images/9/9d/Tour_d_Hano_IMG_20200504_152238000.jpg","filters":[]},{"type":"textbox","version":"3.5.0","originX":"center","originY":"center","left":534.99,"top":291,"width":120,"height":22.6,"fill":"#0054FF","stroke":"#0054FF","strokeWidth":1,"strokeDashArray":null,"strokeLineCap":"butt","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":1,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"text":"Petit disque","fontSize":20,"fontWeight":"normal","fontFamily":"sans-serif","fontStyle":"normal","lineHeight":1.16,"underline":false,"overline":false,"linethrough":false,"textAlign":"left","textBackgroundColor":"","charSpacing":0,"minWidth":20,"splitByGrapheme":false,"styles":{} },{"type":"textbox","version":"3.5.0","originX":"center","originY":"center","left":108.27,"top":268,"width":137.47,"height":22.6,"fill":"#000000","stroke":"#000000","strokeWidth":1,"strokeDashArray":null,"strokeLineCap":"butt","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":1,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"text":"Grand disque","fontSize":20,"fontWeight":"normal","fontFamily":"sans-serif","fontStyle":"normal","lineHeight":1.16,"underline":false,"overline":false,"linethrough":false,"textAlign":"left","textBackgroundColor":"","charSpacing":0,"minWidth":20,"splitByGrapheme":false,"styles":{} },{"type":"wfarrow2line","version":"3.5.0","originX":"center","originY":"center","left":443.5,"top":265,"width":53,"height":32,"fill":"rgba(255,0,0,0)","stroke":"#0054FF","strokeWidth":4,"strokeDashArray":null,"strokeLineCap":"round","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":1,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"x1":26.5,"x2":-26.5,"y1":16,"y2":-16,"x2a":-13.513663886772822,"y2a":1.1858975428777558,"x2b":-5.243758302230144,"y2b":-12.511133581521056},{"type":"wfarrow2circle","version":"3.5.0","originX":"center","originY":"center","left":470,"top":281,"width":16,"height":16,"fill":"#aaa","stroke":"#666","strokeWidth":0,"strokeDashArray":null,"strokeLineCap":"butt","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":0.5,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"radius":8,"startAngle":0,"endAngle":6.283185307179586},{"type":"wfarrow2circle","version":"3.5.0","originX":"center","originY":"center","left":417,"top":249,"width":16,"height":16,"fill":"#aaa","stroke":"#666","strokeWidth":0,"strokeDashArray":null,"strokeLineCap":"butt","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":0.5,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"radius":8,"startAngle":0,"endAngle":6.283185307179586},{"type":"wfarrow2line","version":"3.5.0","originX":"center","originY":"center","left":145,"top":208,"width":98,"height":78,"fill":"rgba(255,0,0,0)","stroke":"#000000","strokeWidth":4,"strokeDashArray":null,"strokeLineCap":"round","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":1,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"x1":-49,"x2":49,"y1":39,"y2":-39,"x2a":38.3334820680096,"y2a":-20.28569009537014,"x2b":28.369549149503598,"y2b":-32.804477608364856},{"type":"wfarrow2circle","version":"3.5.0","originX":"center","originY":"center","left":96,"top":247,"width":16,"height":16,"fill":"#aaa","stroke":"#666","strokeWidth":0,"strokeDashArray":null,"strokeLineCap":"butt","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":0.5,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"radius":8,"startAngle":0,"endAngle":6.283185307179586},{"type":"wfarrow2circle","version":"3.5.0","originX":"center","originY":"center","left":194,"top":169,"width":16,"height":16,"fill":"#aaa","stroke":"#666","strokeWidth":0,"strokeDashArray":null,"strokeLineCap":"butt","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":0.5,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"radius":8,"startAngle":0,"endAngle":6.283185307179586},{"type":"wfline","version":"3.5.0","originX":"center","originY":"center","left":311,"top":157.5,"width":522,"height":215,"fill":"rgba(255,0,0,0)","stroke":"#FF0000","strokeWidth":4,"strokeDashArray":null,"strokeLineCap":"round","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":1,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"x1":-261,"x2":261,"y1":-107.5,"y2":107.5},{"type":"wfarrow2circle","version":"3.5.0","originX":"center","originY":"center","left":50,"top":50,"width":16,"height":16,"fill":"#aaa","stroke":"#666","strokeWidth":0,"strokeDashArray":null,"strokeLineCap":"butt","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":0.5,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"radius":8,"startAngle":0,"endAngle":6.283185307179586},{"type":"wfarrow2circle","version":"3.5.0","originX":"center","originY":"center","left":572,"top":265,"width":16,"height":16,"fill":"#aaa","stroke":"#666","strokeWidth":0,"strokeDashArray":null,"strokeLineCap":"butt","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":0.5,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"radius":8,"startAngle":0,"endAngle":6.283185307179586},{"type":"wfline","version":"3.5.0","originX":"center","originY":"center","left":308,"top":163.5,"width":518,"height":259,"fill":"rgba(255,0,0,0)","stroke":"#FF0000","strokeWidth":4,"strokeDashArray":null,"strokeLineCap":"round","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":1,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"x1":-259,"x2":259,"y1":129.5,"y2":-129.5},{"type":"wfarrow2circle","version":"3.5.0","originX":"center","originY":"center","left":49,"top":293,"width":16,"height":16,"fill":"#aaa","stroke":"#666","strokeWidth":0,"strokeDashArray":null,"strokeLineCap":"butt","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":0.5,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"radius":8,"startAngle":0,"endAngle":6.283185307179586},{"type":"wfarrow2circle","version":"3.5.0","originX":"center","originY":"center","left":567,"top":34,"width":16,"height":16,"fill":"#aaa","stroke":"#666","strokeWidth":0,"strokeDashArray":null,"strokeLineCap":"butt","strokeDashOffset":0,"strokeLineJoin":"miter","strokeMiterLimit":4,"scaleX":1,"scaleY":1,"angle":0,"flipX":false,"flipY":false,"opacity":0.5,"shadow":null,"visible":true,"clipTo":null,"backgroundColor":"","fillRule":"nonzero","paintFirst":"fill","globalCompositeOperation":"source-over","transformMatrix":null,"skewX":0,"skewY":0,"radius":8,"startAngle":0,"endAngle":6.283185307179586}],"height":450,"width":600}
 
}}
 
{{Notes
 
|Observations=Il faut tester plusieurs combinaisons pour réussir ce défi.
 
 
 
<br />
 
|Avertissement=Attention à bien respecter les règles du jeu :
 
 
 
- jamais un grand disque sur un petit
 
 
 
- toujours 1 seul disque déplacé à la fois.
 
|Explanations=La Tour d'Hanoï permet de comprendre la notion d'algorithme : on refait plusieurs fois la même séquence d'actions qui visent  reformer une pile de disques de plus en plus grands sur une autre tige.
 
 
 
 
 
Pour déplacer une tour de n disques, il faut au minimum (2^n)-1 déplacements (lire : "2 puissance n, moins 1")
 
|Applications=Les programmes informatiques intègrent des algorithmes, qui permettent d'augmenter la vitesse de calcul.
 
|Animation=Pour prendre en main plus facilement le jeu et éviter que le participant se décourage trop vite, on peut commencer à lancer le défi avec seulement 3 disques, à déplacer d'une tige  à l'autre.  Cela permet de comprendre la base de l'algorithme :
 
 
 
# Déplacer le petit disque sur une tige, puis le moyen sur un autre.
 
# Mettre le petit disque sur le moyen pour libérer une tige.
 
# Déplacer le grand disque sur la tige ainsi libérée.
 
# Déplacer le petit disque pour libérer le moyen.
 
# Déplacer le moyen sur le grand
 
# Et enfin remettre le petit sur le haut de la pile !
 
 
 
 
 
Une fois que ce mécanisme est compris, on peut introduire un disque supplémentaire, puis un autre.
 
 
 
Avec 5 disques, il faut faire au minimum 31 mouvements.
 
|Notes=Pour tester en ligne la Tour d'Hanoï et lire la légende qui s'y rapporte : http://sorciersdesalem.math.cnrs.fr/Vulgarisation/Hanoi/hanoi.html
 
 
 
Explication du lien entre les tours d'Hanoï et le code binaire, pour les plus initiés : https://www.nagwa.com/fr/videos/323158594734/
 
 
 
 
 
 
 
<br />
 
}}
 
{{Tuto Status
 
|Complete=Draft
 
}}
 

Version actuelle datée du 1 juin 2020 à 11:52

Grottes_humides_IMG_20200530_163248