August 28, 2024

P97 - Sudoku.

Sudoku puzzles go like this:

Problem statement                Solution

.  .  4 | 8  .  . | .  1  7      9  3  4 | 8  2  5 | 6  1  7
        |         |                      |         |
6  7  . | 9  .  . | .  .  .      6  7  2 | 9  1  4 | 8  5  3
        |         |                      |         |
5  .  8 | .  3  . | .  .  4      5  1  8 | 6  3  7 | 9  2  4
--------+---------+--------      --------+---------+--------
3  .  . | 7  4  . | 1  .  .      3  2  5 | 7  4  8 | 1  6  9
        |         |                      |         |
.  6  9 | .  .  . | 7  8  .      4  6  9 | 1  5  3 | 7  8  2
        |         |                      |         |
.  .  1 | .  6  9 | .  .  5      7  8  1 | 2  6  9 | 4  3  5
--------+---------+--------      --------+---------+--------
1  .  . | .  8  . | 3  .  6      1  9  7 | 5  8  2 | 3  4  6
        |         |                      |         |
.  .  . | .  .  6 | .  9  1      8  5  3 | 4  7  6 | 2  9  1
        |         |                      |         |
2  4  . | .  .  1 | 5  .  .      2  4  6 | 3  9  1 | 5  7  8

Every spot in the puzzle belongs to a (horizontal) row and a (vertical) column, as well as to one single 3×3 square (which we call “square” for short).  At the beginning, some of the spots carry a single-digit number between 1 and 9. 

The problem is to fill the missing spots with digits in such a way that every number between 1 and 9 appears exactly once in each row, in each column, and in each square.

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