Given a square grid of size N, where the horizontal rows are numbered 1 to N from top to bottom and the vertical columns are numbered 1 to N from left to right. You must place a number in each cell of the N by N grid such that :-
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Each row is unique.
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Each row is exactly equal to one of the columns, however, it must not be the column with the same index as the row.
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If X is the largest number you place in the grid, then you must also place 1,2,...,X-1, where the condition X <= N is satisfied.
For a 3 x 3 grid, you may have the following matrix
| c1 | c2 | c3 | |
|---|---|---|---|
| r1 | 2 | 1 | 2 |
| r2 | 2 | 2 | 1 |
| r3 | 1 | 2 | 2 |
defined by the following equalities
| c1 = r2 |
| c2 = r3 |
| c3 = r1 |
For a 4 x 4 grid, you may have the following matrix
| c1 | c2 | c3 | c4 | |
|---|---|---|---|---|
| r1 | 1 | 2 | 3 | 1 |
| r2 | 3 | 4 | 4 | 2 |
| r3 | 2 | 4 | 4 | 3 |
| r4 | 1 | 3 | 2 | 1 |
defined by the following equalities
| c1 = r4 |
| c2 = r3 |
| c3 = r2 |
| c4 = r1 |