J’ai pris un petit peu de temps pour tenter deux-trois trucs.
Les pièces sont numérotées de 1 à 8 et 9 c’est l’extérieur.
Si je pars du principe que Gros Totoro va se promener dans chaque endroit, en n’y passant qu’une seule fois, en prenant la pièce 1 comme point de départ, cela me donne 42 possibilités
Détail
Source = 1
Counter = 1
Hamiltonian Path :
1, 9, 7, 6, 8, 5, 3, 4, 2.
Weight of the current Hamiltonian Path = 8
Counter = 2
Hamiltonian Path :
1, 9, 2, 4, 3, 5, 8, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 3
Hamiltonian Path :
1, 2, 9, 8, 5, 4, 3, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 4
Hamiltonian Path :
1, 2, 9, 8, 5, 3, 4, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 5
Hamiltonian Path :
1, 2, 9, 7, 6, 8, 5, 4, 3.
Weight of the current Hamiltonian Path = 8
Counter = 6
Hamiltonian Path :
1, 2, 9, 7, 6, 8, 5, 3, 4.
Weight of the current Hamiltonian Path = 8
Counter = 7
Hamiltonian Path :
1, 2, 9, 7, 6, 4, 3, 5, 8.
Weight of the current Hamiltonian Path = 8
Counter = 8
Hamiltonian Path :
1, 2, 9, 7, 6, 3, 4, 5, 8.
Weight of the current Hamiltonian Path = 8
Counter = 9
Hamiltonian Path :
1, 2, 9, 4, 3, 5, 8, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 10
Hamiltonian Path :
1, 2, 9, 3, 4, 5, 8, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 11
Hamiltonian Path :
1, 2, 4, 9, 8, 5, 3, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 12
Hamiltonian Path :
1, 2, 4, 9, 7, 6, 8, 5, 3.
Weight of the current Hamiltonian Path = 8
Counter = 13
Hamiltonian Path :
1, 2, 4, 9, 7, 6, 3, 5, 8.
Weight of the current Hamiltonian Path = 8
Counter = 14
Hamiltonian Path :
1, 2, 4, 9, 3, 5, 8, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 15
Hamiltonian Path :
1, 2, 4, 6, 8, 5, 3, 9, 7.
Weight of the current Hamiltonian Path = 8
Counter = 16
Hamiltonian Path :
1, 2, 4, 6, 7, 9, 8, 5, 3.
Weight of the current Hamiltonian Path = 8
Counter = 17
Hamiltonian Path :
1, 2, 4, 6, 7, 9, 3, 5, 8.
Weight of the current Hamiltonian Path = 8
Counter = 18
Hamiltonian Path :
1, 2, 4, 6, 3, 5, 8, 9, 7.
Weight of the current Hamiltonian Path = 8
Counter = 19
Hamiltonian Path :
1, 2, 4, 5, 8, 9, 7, 6, 3.
Weight of the current Hamiltonian Path = 8
Counter = 20
Hamiltonian Path :
1, 2, 4, 5, 8, 9, 3, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 21
Hamiltonian Path :
1, 2, 4, 5, 8, 6, 7, 9, 3.
Weight of the current Hamiltonian Path = 8
Counter = 22
Hamiltonian Path :
1, 2, 4, 5, 8, 6, 3, 9, 7.
Weight of the current Hamiltonian Path = 8
Counter = 23
Hamiltonian Path :
1, 2, 4, 5, 3, 9, 8, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 24
Hamiltonian Path :
1, 2, 4, 5, 3, 9, 7, 6, 8.
Weight of the current Hamiltonian Path = 8
Counter = 25
Hamiltonian Path :
1, 2, 4, 5, 3, 6, 8, 9, 7.
Weight of the current Hamiltonian Path = 8
Counter = 26
Hamiltonian Path :
1, 2, 4, 5, 3, 6, 7, 9, 8.
Weight of the current Hamiltonian Path = 8
Counter = 27
Hamiltonian Path :
1, 2, 4, 3, 9, 8, 5, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 28
Hamiltonian Path :
1, 2, 4, 3, 9, 7, 6, 8, 5.
Weight of the current Hamiltonian Path = 8
Counter = 29
Hamiltonian Path :
1, 2, 4, 3, 9, 7, 6, 5, 8.
Weight of the current Hamiltonian Path = 8
Counter = 30
Hamiltonian Path :
1, 2, 4, 3, 9, 5, 8, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 31
Hamiltonian Path :
1, 2, 4, 3, 6, 8, 5, 9, 7.
Weight of the current Hamiltonian Path = 8
Counter = 32
Hamiltonian Path :
1, 2, 4, 3, 6, 7, 9, 8, 5.
Weight of the current Hamiltonian Path = 8
Counter = 33
Hamiltonian Path :
1, 2, 4, 3, 6, 7, 9, 5, 8.
Weight of the current Hamiltonian Path = 8
Counter = 34
Hamiltonian Path :
1, 2, 4, 3, 6, 5, 8, 9, 7.
Weight of the current Hamiltonian Path = 8
Counter = 35
Hamiltonian Path :
1, 2, 4, 3, 5, 9, 8, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 36
Hamiltonian Path :
1, 2, 4, 3, 5, 9, 7, 6, 8.
Weight of the current Hamiltonian Path = 8
Counter = 37
Hamiltonian Path :
1, 2, 4, 3, 5, 8, 9, 7, 6.
Weight of the current Hamiltonian Path = 8
Counter = 38
Hamiltonian Path :
1, 2, 4, 3, 5, 8, 9, 6, 7.
Weight of the current Hamiltonian Path = 8
Counter = 39
Hamiltonian Path :
1, 2, 4, 3, 5, 8, 6, 9, 7.
Weight of the current Hamiltonian Path = 8
Counter = 40
Hamiltonian Path :
1, 2, 4, 3, 5, 8, 6, 7, 9.
Weight of the current Hamiltonian Path = 8
Counter = 41
Hamiltonian Path :
1, 2, 4, 3, 5, 6, 8, 9, 7.
Weight of the current Hamiltonian Path = 8
Counter = 42
Hamiltonian Path :
1, 2, 4, 3, 5, 6, 7, 9, 8.
Weight of the current Hamiltonian Path = 8
Procedure complete.
Mais ça reste assez linéraire, 1, 2, 4, etc.
Ce qui change, finalement, c’est le moment où il va sortir et l’endroit par lequel il va entrer dans la maison ensuite.
À titre de comparaison, en gardant le même principe de ne passer à un endroit qu’une seule fois, en partant de 6 il n’y a que 3 parcours possibles.
Je n’ai pas tout testé, mais on a aussi 18 parcours depuis 3, 6 parcours depuis 4, 2 parcours depuis 9.
Rien qu’avec ces cinq points de départ, ça nous donne 71 chemins possibles. La rejouabilité sera au rendez-vous
(Surtout que là je vous parle de A vers B, mais qu’on peut aussi utiliser B vers A.)
Pour la blague, j’ai essayé de ne pas considérer un extérieur unique mais, grossièrement, un espace « devant la maison » et un autre « derrière la maison ».