Solution 1. The column player replaces A by 2. This forces the row player to play in the same row and therefore to replace B by 6 to satisfy the row constraint, yielding:

8 1 5 3 4 9 2 6 7
7 2 4 6 5 1 8 9 3
3 9 6 8 7 2 4 1 5
1 4 7 5 2 8 6 3 9
C 8 2 9 3 6 D E 1
9 6 3 F 1 7 G H I
2 3 1 J 8 K 9 5 6
6 7 8 1 9 5 3 2 4
L 5 9 2 M 3 1 7 N

Now, the column player replaces J by 4, yielding:

8 1 5 3 4 9 2 6 7
7 2 4 6 5 1 8 9 3
3 9 6 8 7 2 4 1 5
1 4 7 5 2 8 6 3 9
C 8 2 9 3 6 D E 1
9 6 3 F 1 7 G H I
2 3 1 4 8 K 9 5 6
6 7 8 1 9 5 3 2 4
L 5 9 2 M 3 1 7 N

That forces the row player to replace K by something. In that box, the only possibility is 7, but it is precluded by the column constraint on K's column. Thus, the column player forces a win.

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