1 8 15 22 29 36 43
2 9 16 23 30 37 44
3 10 17 24 31 38 45
4 11 18 25 32 39 46
5 12 19 26 33 40 47
6 13 20 27 34 41 48
7 14 21 28 35 42 49
In the 7x7 array given above, select six numbers from six cells simultaneously satisfying the following conditions:
 No two numbers chosen should belong to the same row;
 No two numbers chosen should belong to the same column;
 In the set of numbers chosen, each of the ten digits appears once and only once.
For example, if the numbers selected are 7,9,18,26,30 and 45 then this violates the given conditions as 9 and 30 belong to the same row.
(In reply to
One solution by Jyqm)
Perhaps unsurprisingly, this problem has no solution if the same restrictions are applied to a 6x6 matrix.
In this case, no rows or columns could be omitted in the solution. This means that the 1 would have to appear in column 3 (1318). The 2 would then have to appear in column 4 (1924, with 19 ruled out by the previous statement). The only valid number left in column 5 (2530) would be 30, which  moving back to column 4  would rule out 24, as it appears in the same row as 30. At this point, no valid numbers would remain in column 4 (21 includes a 1, which can appear only in column 3; 22 contains two 2s; 20 and 23 contain digits already represented in 30).

Posted by Jyqm
on 20130305 20:21:38 