Great program. I know how you can fix it to solve the 7×7 and most other kenkens. Everything you have done is fine but you need to add another function that checks for consistency within a cage. My following comments relate to your 7×7 unsolved kenken.

For example, take the possible solution of (2, 3, 3) in cage 13. Cells 13b and 13c cannot be 2 because otherwise there would be two 3’s in the same row or column in the cage. Therefore, in this possible solution to the cell, the 2 in cells 13b and 13c would be eliminated, and 3’s in cell 13a would be eliminated.

Simpler is to check for consistency in cage 22 enabling you to solve cage 6 and fully solve the 7×7 kenken. In cage 22, take the (1,3,6,7) possible solution. In cell 22b, 1 is the only choice in this possible solution. Therefore, 1 is not a possible solution in cell 22a (or 22d). This leads to a value of 1 being forced into cell 6b (the only possible 1 in the column) and the kenken can be solved.

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