4
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enter image description here

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

enter image description here

3 . . . .
. . . . 2
. . . . .
2 . . . .
. . 3 . .

Fill in the blanks so the table has the same unique properties.

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4
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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.

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  • $\begingroup$ Edit: this is the unique solution. Why? $\endgroup$ – CodeNewbie Sep 22 '16 at 12:47
  • $\begingroup$ @CodeNewbie see edit summary. It is clear that the value in each of the cells is bounded, so this is a finite problem and the only thing you need to do is to check all cases. $\endgroup$ – Matsmath Sep 22 '16 at 12:48

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