Look at the 8x8 grid below at left. In the rows and columns there are repeated numbers. Erasing 19 of them, we achieve the grid at right, that has no repeated numbers in any row, in any column.
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 5 | 7 | 1 | 2 | 5 | 4 | 4 | 3 | | | 7 | 1 | | 5 | | 4 | 3 |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 4 | 3 | 1 | 2 | 7 | 5 | 6 | 3 | | 4 | 3 | | 2 | 7 | 5 | 6 | |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 5 | 5 | 3 | 4 | 2 | 1 | 7 | 8 | | | 5 | 3 | | 2 | | 7 | 8 |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 6 | 6 | 2 | 7 | 3 | 3 | 3 | 1 | | 6 | | 2 | 7 | | 3 | | 1 |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 3 | 2 | 5 | 6 | 9 | 1 | 8 | 6 | | 3 | 2 | 5 | | 9 | 1 | 8 | 6 |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 2 | 1 | 3 | 4 | 6 | 2 | 5 | 2 | | | 1 | | 4 | 6 | | 5 | 2 |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 9 | 8 | 4 | 1 | 4 | 6 | 2 | 3 | | 9 | 8 | 4 | 1 | | 6 | 2 | |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
| 7 | 5 | 6 | 5 | 8 | 5 | 1 | 4 | | 7 | | 6 | 5 | 8 | | 1 | 4 |
+---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+
Do the same with this 8x8 grid, erasing the minimum number of squares.
+---+---+---+---+---+---+---+---+
| 8 | 4 | 6 | 5 | 3 | 5 | 7 | 4 |
+---+---+---+---+---+---+---+---+
| 6 | 5 | 5 | 4 | 7 | 8 | 3 | 1 |
+---+---+---+---+---+---+---+---+
| 5 | 7 | 2 | 5 | 5 | 4 | 8 | 7 |
+---+---+---+---+---+---+---+---+
| 8 | 6 | 5 | 3 | 2 | 5 | 4 | 4 |
+---+---+---+---+---+---+---+---+
| 3 | 8 | 1 | 4 | 8 | 6 | 5 | 2 |
+---+---+---+---+---+---+---+---+
| 5 | 3 | 7 | 6 | 4 | 2 | 2 | 2 |
+---+---+---+---+---+---+---+---+
| 5 | 8 | 7 | 7 | 6 | 2 | 1 | 3 |
+---+---+---+---+---+---+---+---+
| 1 | 1 | 3 | 7 | 6 | 4 | 6 | 8 |
+---+---+---+---+---+---+---+---+
(In reply to
re(4): ===== so, you beat them? (Spoiler) by pcbouhid)
While pcbouhid is correct that this is a legitimate problem as submitted, it is one which can be solved one digit at a time, using algorithm's such as Daniel's.
The problem becomes much more interesting (and difficult) when using rules such as "no two or more numbers orthogonally adjacent may be erased". The additional restriction means that the puzzle must be solved in its totality, and that no single number can be "solved" without considering its effect on the whole puzzle.
re(5): ===== so, you beat them?
