I'm trying to solve a computer science challenge and have readily been able to validate whether or not the outside dimensions of a sudoku puzzle are valid. However, it doesn't check the validity of the inside squares and will "validate" the following incorrect sudoku puzzle because the 3×3 squares are not unique 1-9:
[1, 2, 3, 4, 5, 6, 7, 8, 9],
[2, 3, 4, 5, 6, 7, 8, 9, 1],
[3, 4, 5, 6, 7, 8, 9, 1, 2],
[4, 5, 6, 7, 8, 9, 1, 2, 3],
[5, 6, 7, 8, 9, 1, 2, 3, 4],
[6, 7, 8, 9, 1, 2, 3, 4, 5],
[7, 8, 9, 1, 2, 3, 4, 5, 6],
[8, 9, 1, 2, 3, 4, 5, 6, 7],
[9, 1, 2, 3, 4, 5, 6, 7, 8]
My question is this: if a sudoku puzzle has all valid columns and rows in the 9×9, is there a way to grab a single other set of values from the puzzle (say, for instance, the first 3×3) and know the whole puzzle to be correct? Or must one check every 3×3 for an otherwise valid whole puzzle square?
Best Answer
Suppose you have valid Soduko. Now swap rows 6 and 7.
The "outside measurements" are still all valid. The 3, $3\times3$ boxes along the top are valid, but the remaining 6 likely are not.