2021 JMPSC Invitationals Problems/Problem 7

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Problem

In a $3 \times 3$ grid with nine square cells, how many ways can Jacob shade in some nonzero number of cells such that each row, column, and diagonal contains at most one shaded cell? (A diagonal is a set of squares such that their centers lie on a line that makes a $45^\circ$ angle with the sides of the grid. Note that there are more than two diagonals.)

Solution

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