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 |
+---+---+---+---+---+---+---+---+
It is clear that there are numerous ways to approach this reverse pseudo-sudoku diagram. I observe (looking after my last post) that Daniel also noticed the ostensive problem with the twelve 5's, though I see we both erased five and preserved six, in addition to the one "safe" one at (5,7) -- so our difference of one must be in one of the other digits (or perhaps oversight on my part). I wonder how one (e.g. the proposer) would prove that a given answer was in fact the minimal one. (There have been endless debates whether the 9x9 sudoku can be unique with fewer than 17 givens.)
Those Fives!
