H119 Les colliers de perles [***** à la main]
Solution d’Alain Esculier
Pour toute suite solution, on a la solution obtenue en écrivant la suite dans l’ordre inverse.
Dans la suite, je n’ai mis que les solutions dont le premier terme est inférieur au dernier : il faut donc associer à chacune la suite renversée.
Solutions pour les colliers ouverts
Le nombre minimum de perles est 15, valeur pour laquelle on trouve 2 solutions.
( à chaque solution, associer la suite renversée )
N=15, 2 solutions
[8,1,15,10,6,3,13,12,4,5,11,14,2,7,9]
N=16, 2 solutions
[8,1,15,10,6,3,13,12,4,5,11,14,2,7,9,16]
N=17, 2 solutions
[16,9,7,2,14,11,5,4,12,13,3,6,10,15,1,8,17]
N=23, 6 solutions
[2,23,13,12,4,21,15,10,6,19,17,8,1,3,22,14,11,5,20,16,9,7,18], [9,16,20,5,11,14,22,3,1,8,17,19,6,10,15,21,4,12,13,23,2,7,18], [18,7,9,16,20,5,11,14,2,23,13,12,4,21,15,10,6,19,17,8,1,3,22],
N=25, 20 solutions
[[2,23,13,12,24,25,11,14,22,3,1,8,17,19,6,10,15,21,4,5,20,16,9,7,18], [3,22,14,2,23,13,12,4,21,15,10,6,19,17,8,1,24,25,11,5,20,16,9,7,18], [4,21,15,10,6,19,17,8,1,3,22,14,2,23,13,12,24,25,11,5,20,16,9,7,18], [8,17,19,6,10,15,21,4,12,13,23,2,14,22,3,1,24,25,11,5,20,16,9,7,18], [9,16,20,5,4,21,15,10,6,19,17,8,1,3,22,14,11,25,24,12,13,23,2,7,18], [10,15,21,4,12,13,23,2,14,22,3,6,19,17,8,1,24,25,11,5,20,16,9,7,18], [11,25,24,12,13,23,2,14,22,3,1,8,17,19,6,10,15,21,4,5,20,16,9,7,18], [13,23,2,14,22,3,1,8,17,19,6,10,15,21,4,12,24,25,11,5,20,16,9,7,18], [18,7,9,16,20,5,11,25,24,1,8,17,19,6,10,15,21,4,12,13,3,22,14,2,23], [18,7,9,16,20,5,11,25,24,12,4,21,15,10,6,19,17,8,1,3,13,23,2,14,22],
Solutions pour les colliers fermés
Le nombre minimum de perles est 32, valeur pour laquelle on trouve 44 solutions.
( à chaque solution, associer la suite renversée )
[1,8,28,21,4,32,17,19,30,6,3,13,12,24,25,11,5,31,18,7,29,20,16,9,27,22,14,2,23,26,10,15], 16 [1,15,10,26,23,2,14,22,27,9,16,20,29,7,18,31,5,11,25,24,12,13,3,6,30,19,17,32,4,21,28,8], 9 [2,14,22,27,9,16,20,29,7,18,31,5,11,25,24,12,13,3,6,30,19,17,32,4,21,28,8,1,15,10,26,23], 25 [2,23,26,10,15,1,8,28,21,4,32,17,19,30,6,3,13,12,24,25,11,5,31,18,7,29,20,16,9,27,22,14], 16 [3,6,30,19,17,32,4,21,28,8,1,15,10,26,23,2,14,22,27,9,16,20,29,7,18,31,5,11,25,24,12,13], 16 [3,13,12,24,25,11,5,31,18,7,29,20,16,9,27,22,14,2,23,26,10,15,1,8,28,21,4,32,17,19,30,6], 9 [4,21,28,8,1,15,10,26,23,2,14,22,27,9,16,20,29,7,18,31,5,11,25,24,12,13,3,6,30,19,17,32], 36 [4,32,17,19,30,6,3,13,12,24,25,11,5,31,18,7,29,20,16,9,27,22,14,2,23,26,10,15,1,8,28,21], 25 [5,11,25,24,12,13,3,6,30,19,17,32,4,21,28,8,1,15,10,26,23,2,14,22,27,9,16,20,29,7,18,31], 36 [5,31,18,7,29,20,16,9,27,22,14,2,23,26,10,15,1,8,28,21,4,32,17,19,30,6,3,13,12,24,25,11], 16 [6,3,13,12,24,25,11,5,31,18,7,29,20,16,9,27,22,14,2,23,26,10,15,1,8,28,21,4,32,17,19,30], 36 [7,18,31,5,11,25,24,12,13,3,6,30,19,17,32,4,21,28,8,1,15,10,26,23,2,14,22,27,9,16,20,29], 36 [7,29,20,16,9,27,22,14,2,23,26,10,15,1,8,28,21,4,32,17,19,30,6,3,13,12,24,25,11,5,31,18], 25 [8,1,15,10,26,23,2,14,22,27,9,16,20,29,7,18,31,5,11,25,24,12,13,3,6,30,19,17,32,4,21,28], 36 [9,16,20,29,7,18,31,5,11,25,24,12,13,3,6,30,19,17,32,4,21,28,8,1,15,10,26,23,2,14,22,27], 36 [9,27,22,14,2,23,26,10,15,1,8,28,21,4,32,17,19,30,6,3,13,12,24,25,11,5,31,18,7,29,20,16], 25 [10,15,1,8,28,21,4,32,17,19,30,6,3,13,12,24,25,11,5,31,18,7,29,20,16,9,27,22,14,2,23,26], 36 [10,26,23,2,14,22,27,9,16,20,29,7,18,31,5,11,25,24,12,13,3,6,30,19,17,32,4,21,28,8,1,15], 25 [11,5,31,18,7,29,20,16,9,27,22,14,2,23,26,10,15,1,8,28,21,4,32,17,19,30,6,3,13,12,24,25], 36 [12,13,3,6,30,19,17,32,4,21,28,8,1,15,10,26,23,2,14,22,27,9,16,20,29,7,18,31,5,11,25,24], 36 [12,24,25,11,5,31,18,7,29,20,16,9,27,22,14,2,23,26,10,15,1,8,28,21,4,32,17,19,30,6,3,13], 25 [14,2,23,26,10,15,1,8,28,21,4,32,17,19,30,6,3,13,12,24,25,11,5,31,18,7,29,20,16,9,27,22], 36 [16,9,27,22,14,2,23,26,10,15,1,8,28,21,4,32,17,19,30,6,3,13,12,24,25,11,5,31,18,7,29,20], 36 [17,19,30,6,3,13,12,24,25,11,5,31,18,7,29,20,16,9,27,22,14,2,23,26,10,15,1,8,28,21,4,32], 49 [17,32,4,21,28,8,1,15,10,26,23,2,14,22,27,9,16,20,29,7,18,31,5,11,25,24,12,13,3,6,30,19], 36 [18,7,29,20,16,9,27,22,14,2,23,26,10,15,1,8,28,21,4,32,17,19,30,6,3,13,12,24,25,11,5,31], 49 [19,17,32,4,21,28,8,1,15,10,26,23,2,14,22,27,9,16,20,29,7,18,31,5,11,25,24,12,13,3,6,30], 49 [20,16,9,27,22,14,2,23,26,10,15,1,8,28,21,4,32,17,19,30,6,3,13,12,24,25,11,5,31,18,7,29], 49 [21,4,32,17,19,30,6,3,13,12,24,25,11,5,31,18,7,29,20,16,9,27,22,14,2,23,26,10,15,1,8,28], 49 [22,14,2,23,26,10,15,1,8,28,21,4,32,17,19,30,6,3,13,12,24,25,11,5,31,18,7,29,20,16,9,27], 49 [23,2,14,22,27,9,16,20,29,7,18,31,5,11,25,24,12,13,3,6,30,19,17,32,4,21,28,8,1,15,10,26], 49 [24,12,13,3,6,30,19,17,32,4,21,28,8,1,15,10,26,23,2,14,22,27,9,16,20,29,7,18,31,5,11,25], 49
