Recordeu que un Sudoku és un joc que consisteix a completar una graella

9 \times 9

amb números entre 1 i 9 de manera que el resultat final no tingui números repetits a la mateixa fila, columna o submatriu

3 \times 3

. Per exemple, aquest és un Sudoku i la seva solució:

(9,9) (0,0)(0,9) (1,0)(1,9) (2,0)(2,9) (3,0)(3,9) (4,0)(4,9) (5,0)(5,9) (6,0)(6,9) (7,0)(7,9) (8,0)(8,9) (9,0)(9,9)

(0,0)(9,0) (0,1)(9,1) (0,2)(9,2) (0,3)(9,3) (0,4)(9,4) (0,5)(9,5) (0,6)(9,6) (0,7)(9,7) (0,8)(9,8) (0,9)(9,9)

(0.5,0.5)4 (2.5,0.5)5 (3.5,0.5)6

(1.5,1.5)2 (2.5,1.5)9 (3.5,1.5)1

(4.5,2.5)7 (5.5,2.5)5 (8.5,2.5)8

(2.5,3.5)6 (3.5,3.5)4 (4.5,3.5)2

(1.5,4.5)4 (2.5,4.5)8 (6.5,4.5)5 (7.5,4.5)6

(4.5,5.5)6 (5.5,5.5)1 (6.5,5.5)8

(0.5,6.5)1 (3.5,6.5)9 (4.5,6.5)3

(5.5,7.5)6 (6.5,7.5)4 (7.5,7.5)5

(5.5,8.5)2 (6.5,8.5)3 (8.5,8.5)7

(9,9) (0,0)(0,9) (1,0)(1,9) (2,0)(2,9) (3,0)(3,9) (4,0)(4,9) (5,0)(5,9) (6,0)(6,9) (7,0)(7,9) (8,0)(8,9) (9,0)(9,9)

(0,0)(9,0) (0,1)(9,1) (0,2)(9,2) (0,3)(9,3) (0,4)(9,4) (0,5)(9,5) (0,6)(9,6) (0,7)(9,7) (0,8)(9,8) (0,9)(9,9)

(0.5,0.5)4 (1.5,0.5)7 (2.5,0.5)5 (3.5,0.5)6 (4.5,0.5)8 (5.5,0.5)9 (6.5,0.5)1 (7.5,0.5)3 (8.5,0.5)2

(0,1) (0.5,0.5)9 (1.5,0.5)2 (2.5,0.5)9 (3.5,0.5)1 (4.5,0.5)4 (5.5,0.5)3 (6.5,0.5)6 (7.5,0.5)7 (8.5,0.5)5

(0,2) (0.5,0.5)6 (1.5,0.5)3 (2.5,0.5)1 (3.5,0.5)2 (4.5,0.5)7 (5.5,0.5)5 (6.5,0.5)9 (7.5,0.5)4 (8.5,0.5)8

(0,3) (0.5,0.5)5 (1.5,0.5)1 (2.5,0.5)6 (3.5,0.5)4 (4.5,0.5)2 (5.5,0.5)8 (6.5,0.5)7 (7.5,0.5)9 (8.5,0.5)3

(0,4) (0.5,0.5)2 (1.5,0.5)4 (2.5,0.5)8 (3.5,0.5)3 (4.5,0.5)9 (5.5,0.5)7 (6.5,0.5)5 (7.5,0.5)6 (8.5,0.5)1

(0,5) (0.5,0.5)7 (1.5,0.5)9 (2.5,0.5)3 (3.5,0.5)5 (4.5,0.5)6 (5.5,0.5)1 (6.5,0.5)8 (7.5,0.5)2 (8.5,0.5)4

(0,6) (0.5,0.5)1 (1.5,0.5)5 (2.5,0.5)7 (3.5,0.5)9 (4.5,0.5)3 (5.5,0.5)4 (6.5,0.5)2 (7.5,0.5)8 (8.5,0.5)6

(0,7) (0.5,0.5)3 (1.5,0.5)8 (2.5,0.5)2 (3.5,0.5)7 (4.5,0.5)1 (5.5,0.5)6 (6.5,0.5)4 (7.5,0.5)5 (8.5,0.5)9

(0,8) (0.5,0.5)9 (1.5,0.5)6 (2.5,0.5)4 (3.5,0.5)8 (4.5,0.5)5 (5.5,0.5)2 (6.5,0.5)3 (7.5,0.5)1 (8.5,0.5)7

En aquest problema no us demanem que resolgueu cap Sudoku, només que comproveu que cada matriu donada pot ser la solució d’un Sudoku.

Entrada

L’entrada consisteix en un nombre

n

, seguit de

n

casos. Cada cas té 9 files, cadascuna amb 9 números entre 1 i 9.

Sortida

Per a cada cas, escriviu “si” o “no” depenent de si la matriu donada compleix les regles de les solucions dels Sudokus.

És la solució d’un Sudoku?

Entrada