Possible Checker Placements

Discrete Mathematics Level 4

On a 40 by 40 square grid, Victor covers a 1 by 1 square with a checker piece. He is then able to cover the rest of the squares with 533 \( 1 \times 3 \) triminos.

What is the total number of squares on which the checker piece could be placed?

Details and assumptions

The \( 1 \times 3\) trimino consists of 3 squares arranged in a straight row (or column).


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