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All-even board is a medium quant interview question on probability.
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This is a medium-difficulty probability problem that combines counting, linear algebra over finite fields, and constraint propagation. It asks you to find the probability that a randomly filled grid satisfies global parity constraints—a type of reasoning common in combinatorics and coding theory interviews.
The key insight is recognizing that row and column sum constraints are not independent. Once you fix certain entries, the parity requirements on rows and columns force the values of remaining entries. The problem rewards candidates who can count the degrees of freedom rather than enumerate outcomes. You'll need to think carefully about how many entries you can choose freely before all others are determined by the even-sum constraints.