Odd sums on a 3×3 grid
The integers through are placed uniformly at random (one per cell) on a grid. What is the probability that every row, every column, and both main diagonals have an odd sum? The probability is for an integer ; find .
Show hints (2)+
- Reduce to parities: odd, even numbers. A line sums odd iff it holds an even number of evens ( or ).
- Count valid placements of the evens (constrained), times the arrangements of odds/evens; you get .
Answer
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