medium   Probability

Tic-Tac-Toe Sum

A release-checked medium problem for training Combinations and Permutations.

Question

There is a tic-tac-toe grid in front of you. You permute the integers $1-9$ to the $9$ squares in the grid uniformly at random. Find the probability that the sum of each row and column is odd.

Practice focus

This Probability problem is tagged Combinations and Permutations. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.

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