Suite de la découverte du Kakuro avec un outil très pratique, publié dans notre ouvrage paru chez Pearson en 2006 : la table des ensembles.
Au Kakuro, retrouver pour chaque indice tous les ensembles possibles sans répétition possibles pourrait apparaitre un peu fastidieux.
Bien sûr, pour un indice « 5 » en deux cases, pas de problèmes. Seuls les ensembles {1,4} et {2,3} sont possibles. Par contre pour trouver « 21 » en 5 cases, 8 différents ensembles sont possibles, donc 85 possibilités de combinaisons !
Mais ne vous en faites pas, nous avons pensé à tout… et à vous !
Vous trouverez ci-dessous un document très précieux : la table des ensembles. Elle vous indique, en fonction du nombre de cases vierges, tous les ensembles pour un indice donné.
Vous vous y référerez très souvent.
Bloc de 2 cases
3: 1,2;
4: 1,3;
5: 1,4; 2,3;
6: 1,5; 2,4;
7: 1,6; 2,5; 3,4;
8: 1,7; 2,6; 3,5;
9: 1,8; 2,7; 3,6; 4,5;
10: 1,9; 2,8; 3,7; 4,6;
11: 2,9; 3,8; 4,7; 5,6;
12: 3,9; 4,8; 5,7;
13: 4,9; 5,8; 6,7;
14: 5,9; 6,8;
15: 6,9; 7,8;
16: 7,9;
17: 8,9;
Bloc de 3 cases
6: 1,2,3;
7: 1,2,4;
8: 1,2,5; 1,3,4;
9: 1,2,6; 1,3,5; 2,3,4;
10: 1,2,7; 1,3,6; 1,4,5; 2,3,5;
11: 1,2,8; 1,3,7; 1,4,6; 2,3,6; 2,4,5;
12: 1,2,9; 1,3,8; 1,4,7; 1,5,6; 2,3,7; 2,4,6; 3,4,5;
13: 1,3,9; 1,4,8; 1,5,7; 2,3,8; 2,4,7; 2,5,6; 3,4,6;
14: 1,4,9; 1,5,8; 1,6,7; 2,3,9; 2,4,8; 2,5,7; 3,4,7; 3,5,6;
15: 1,5,9; 1,6,8; 2,4,9; 2,5,8; 2,6,7; 3,4,8; 3,5,7; 4,5,6;
16: 1,6,9; 1,7,8; 2,5,9; 2,6,8; 3,4,9; 3,5,8; 3,6,7; 4,5,7;
17: 1,7,9; 2,6,9; 2,7,8; 3,5,9; 3,6,8; 4,5,8; 4,6,7;
18: 1,8,9; 2,7,9; 3,6,9; 3,7,8; 4,5,9; 4,6,8; 5,6,7;
19: 2,8,9; 3,7,9; 4,6,9; 4,7,8; 5,6,8;
20: 3,8,9; 4,7,9; 5,6,9; 5,7,8;
21: 4,8,9; 5,7,9; 6,7,8;
22: 5,8,9; 6,7,9;
23: 6,8,9;
24: 7,8,9;
Bloc de 4 cases
10: 1,2,3,4;
11: 1,2,3,5;
12: 1,2,3,6; 1,2,4,5;
13: 1,2,3,7; 1,2,4,6; 1,3,4,5;
14: 1,2,3,8; 1,2,4,7; 1,2,5,6; 1,3,4,6; 2,3,4,5;
15: 1,2,3,9; 1,2,4,8; 1,2,5,7; 1,3,4,7; 1,3,5,6; 2,3,4,6;
16: 1,2,4,9; 1,2,5,8; 1,2,6,7; 1,3,4,8; 1,3,5,7; 1,4,5,6; 2,3,4,7; 2,3,5,6;
17: 1,2,5,9; 1,2,6,8; 1,3,4,9; 1,3,5,8; 1,3,6,7; 1,4,5,7; 2,3,4,8; 2,3,5,7; 2,4,5,6;
18: 1,2,6,9; 1,2,7,8; 1,3,5,9; 1,3,6,8; 1,4,5,8; 1,4,6,7; 2,3,4,9; 2,3,5,8; 2,3,6,7; 2,4,5,7; 3,4,5,6;
19: 1,2,7,9; 1,3,6,9; 1,3,7,8; 1,4,5,9; 1,4,6,8; 1,5,6,7; 2,3,5,9; 2,3,6,8; 2,4,5,8; 2,4,6,7; 3,4,5,7;
20: 1,2,8,9; 1,3,7,9; 1,4,6,9; 1,4,7,8; 1,5,6,8; 2,3,6,9; 2,3,7,8; 2,4,5,9; 2,4,6,8; 2,5,6,7; 3,4,5,8; 3,4,6,7;
21: 1,3,8,9; 1,4,7,9; 1,5,6,9; 1,5,7,8; 2,3,7,9; 2,4,6,9; 2,4,7,8; 2,5,6,8; 3,4,5,9; 3,4,6,8; 3,5,6,7;
22: 1,4,8,9; 1,5,7,9; 1,6,7,8; 2,3,8,9; 2,4,7,9; 2,5,6,9; 2,5,7,8; 3,4,6,9; 3,4,7,8; 3,5,6,8; 4,5,6,7;
23: 1,5,8,9; 1,6,7,9; 2,4,8,9; 2,5,7,9; 2,6,7,8; 3,4,7,9; 3,5,6,9; 3,5,7,8; 4,5,6,8;
24: 1,6,8,9; 2,5,8,9; 2,6,7,9; 3,4,8,9; 3,5,7,9; 3,6,7,8; 4,5,6,9; 4,5,7,8;
25: 1,7,8,9; 2,6,8,9; 3,5,8,9; 3,6,7,9; 4,5,7,9; 4,6,7,8;
26: 2,7,8,9; 3,6,8,9; 4,5,8,9; 4,6,7,9; 5,6,7,8;
27: 3,7,8,9; 4,6,8,9; 5,6,7,9;
28: 4,7,8,9; 5,6,8,9;
29: 5,7,8,9;
30: 6,7,8,9;
Bloc de 5 cases
15: 1,2,3,4,5;
16: 1,2,3,4,6;
17: 1,2,3,4,7; 1,2,3,5,6;
18: 1,2,3,4,8; 1,2,3,5,7; 1,2,4,5,6;
19: 1,2,3,4,9; 1,2,3,5,8; 1,2,3,6,7; 1,2,4,5,7; 1,3,4,5,6;
20: 1,2,3,5,9; 1,2,3,6,8; 1,2,4,5,8; 1,2,4,6,7; 1,3,4,5,7; 2,3,4,5,6;
21: 1,2,3,6,9; 1,2,3,7,8; 1,2,4,5,9; 1,2,4,6,8; 1,2,5,6,7; 1,3,4,5,8; 1,3,4,6,7; 2,3,4,5,7;
22: 1,2,3,7,9; 1,2,4,6,9; 1,2,4,7,8; 1,2,5,6,8; 1,3,4,5,9; 1,3,4,6,8; 1,3,5,6,7; 2,3,4,5,8; 2,3,4,6,7;
23: 1,2,3,8,9; 1,2,4,7,9; 1,2,5,6,9; 1,2,5,7,8; 1,3,4,6,9; 1,3,4,7,8; 1,3,5,6,8; 1,4,5,6,7; 2,3,4,5,9; 2,3,4,6,8; 2,3,5,6,7;
24: 1,2,4,8,9; 1,2,5,7,9; 1,2,6,7,8; 1,3,4,7,9; 1,3,5,6,9; 1,3,5,7,8; 1,4,5,6,8; 2,3,4,6,9; 2,3,4,7,8; 2,3,5,6,8; 2,4,5,6,7;
25: 1,2,5,8,9; 1,2,6,7,9; 1,3,4,9,8; 1,3,5,7,9; 1,3,6,7,8; 1,4,5,6,9; 1,4,5,7,8; 2,3,4,7,9; 2,3,5,6,9; 2,3,5,7,8; 2,4,5,6,8; 3,4,5,6,7;
26: 1,2,6,8,9; 1,3,5,8,9; 1,3,6,7,9; 1,4,5,7,9; 1,4,6,7,8; 2,3,4,8,9; 2,3,5,7,9; 2,3,6,7,8; 2,4,5,6,9; 2,4,5,7,8; 3,4,5,6,8;
27: 1,2,7,8,9; 1,3,6,8,9; 1,4,5,8,9; 1,4,6,7,9; 1,5,6,7,8; 2,3,5,8,9; 2,3,6,7,9; 2,4,5,7,9; 2,4,6,7,8; 3,4,5,6,9; 3,4,5,7,8;
28: 1,3,7,8,9; 1,4,6,8,9; 1,5,6,7,9; 2,3,6,8,9; 2,4,5,8,9; 2,4,6,7,9; 2,5,6,7,8; 3,4,5,7,9; 3,4,6,7,8;
29: 1,4,7,8,9; 1,5,6,8,9; 2,3,7,8,9; 2,4,6,8,9; 2,5,6,7,9; 3,4,5,8,9; 3,4,6,7,9; 3,5,6,7,8;
30: 1,5,7,8,9; 2,4,7,8,9; 2,5,6,8,9; 3,4,6,8,9; 3,5,6,7,9; 4,5,6,7,8;
31: 1,6,7,8,9; 2,5,7,8,9; 3,4,7,8,9; 3,5,6,8,9; 4,5,6,7,9;
32: 2,6,7,8,9; 3,5,7,8,9; 4,5,6,8,9;
33: 3,6,7,8,9; 4,5,7,8,9;
34: 4,6,7,8,9;
35: 5,6,7,8,9;
Bloc de 6 cases
21: 1,2,3,4,5,6;
22: 1,2,3,4,5,7;
23: 1,2,3,4,5,8; 1,2,3,4,6,7;
24: 1,2,3,4,5,9; 1,2,3,4,6,8; 1,2,3,5,6,7;
25: 1,2,3,4,6,9; 1,2,3,4,7,8; 1,2,3,5,6,8; 1,2,4,5,6,7;
26: 1,2,3,4,7,9; 1,2,3,5,6,9; 1,2,3,5,7,8; 1,2,4,5,6,8; 1,3,4,5,6,7;
27: 1,2,3,4,8,9; 1,2,3,5,7,9; 1,2,3,6,7,8; 1,2,4,5,6,9; 1,2,4,5,7,8; 1,3,4,5,6,8; 2,3,4,5,6,7;
28: 1,2,3,5,8,9; 1,2,3,6,7,9; 1,2,4,5,7,9; 1,2,4,6,7,8; 1,3,4,5,6,9; 1,3,4,5,7,8; 2,3,4,5,6,8;
29: 1,2,3,6,8,9; 1,2,4,5,8,9; 1,2,4,6,7,9; 1,2,5,6,7,8; 1,3,4,5,7,9; 1,3,4,6,7,8; 2,3,4,5,6,9; 2,3,4,5,7,8;
30: 1,2,3,7,8,9; 1,2,4,6,8,9; 1,2,5,6,7,9; 1,3,4,5,8,9; 1,3,4,6,7,9; 1,3,5,6,7,8; 2,3,4,5,7,9; 2,3,4,6,7,8;
31: 1,2,4,7,8,9; 1,2,5,6,8,9; 1,3,4,6,8,9; 1,3,5,6,7,9; 1,4,5,6,7,8; 2,3,4,5,8,9; 2,3,4,6,7,9; 2,3,5,6,7,8;
32: 1,2,5,7,8,9; 1,3,4,7,8,9; 1,3,5,6,8,9; 1,4,5,6,7,9; 2,3,4,6,8,9; 2,3,5,6,7,9; 2,4,5,6,7,8;
33: 1,2,6,7,8,9; 1,3,5,7,8,9; 1,4,5,6,8,9; 2,3,4,7,8,9; 2,3,5,6,8,9; 2,4,5,6,7,9; 3,4,5,6,7,8;
34: 1,3,6,7,8,9; 1,4,5,7,8,9; 2,3,5,7,8,9; 2,4,5,6,8,9; 3,4,5,6,7,9;
35: 1,4,6,7,8,9; 2,3,6,7,8,9; 2,4,5,7,8,9; 3,4,5,6,8,9;
36: 1,5,6,7,8,9; 2,4,6,7,8,9; 3,4,5,7,8,9;
37: 2,5,6,7,8,9; 3,4,6,7,8,9;
38: 3,5,6,7,8,9;
39: 4,5,6,7,8,9;
Bloc de 7 cases
28 : 1,2,3,4,5,6,7 ;
29 : 1,2,3,4,5,6,8 ;
30 : 1,2,3,4,5,6,9 ; 1,2,3,4,5,7,8
31 : 1,2,3,4,5,7,9 ; 1,2,3,4,6,7,8 ;
32 : 1,2,3,4,5,8,9 ; 1,2,3,4,6,7,9 ;
33 : 1,2,3,4,6,8,9 ; 1,2,3,5,6,7,9
34 : 1,2,3,5,6,8,9 ; 1,2,3,4,7,8,9 ;
35 : 1,2,4,5,6,8,9 ; 1,3,4,5,6,7,9 ; 2,3,4,5,6,7,9
36 : 1,3,4,5,6,8,9 ; 2,3,4,5,6,7,9
37 : 1,2,4,6,7,8,9 ; 1,3,4,5,7,8,9
38 : 1,3,4,6,7,8,9 ; 2,3,4,5,7,8,9 ;
39 : 1,3,5,6,7,8,9 ; 2,3,4,6,7,8,9
40 : 1,4,5,6,7,8,9 ; 2,3,5,6,7,8,9
41 : 2,4,5,6,7,8,9
42 : 3,4,5,6,7,8,9
Bloc de 8 cases
36 : 1,2,3,4,5,6,7,8
37 : 1,2,3,4,5,6,7,9
38 : 1,2,3,4,5,6,8,9
39 : 1,2,3,4,5,7,8,9
40 : 1,2,3,4,6,7,8,9
41 : 1,2,3,5,6,7,8,9
42 : 1,2,4,5,6,7,8,9
43 : 1,3,4,5,6,7,8,9
44 : 2,3,4,5,6,7,8,9
Bloc de 9 cases
45 : 1,2,3,4,5,6,7,8,9