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| 1 | 3 | 2 | 3 | 1 |
| 3 | 3 | 2 | 3 | 3 |
| 2 | 2 | 3 | 3 | 2 |
| 3 | 3 | 3 | 4 | 4 |
| 1 | 3 | 2 | 4 | 1 |
This 5x5 table has unique properties.
Each number (x) in a cell means:
The cell is surrounded (including diagonal neighbours) by x unique numbers in the squares surrounding it.
Example:
(2,2) cell (red) is 3, so it is surrounded by 3 unique numbers (1,2 and 3)
(4,4) cell (blue) is 4, so it is surrounded by 4 unique numbers (1,2, 3 and 4)
The Question
| 3 | ||||
| 2 | ||||
| 2 | ||||
| 3 |
Fill in the blanks so the table has the same unique properties.
One solution, with
entries at most 4. It was found by basic depth-first search with pruning (checking if the neighbouring condition hold at each cell). This is colloquially called as backtracking.
Here it comes:
3 2 3 3 3 3 4 4 4 2 3 4 1 4 3 2 4 4 4 3 3 3 3 2 3
Other solutions might be possible. Edit: this is the unique solution.
