Can a 10 x 10 grid of cells be covered by 25 1 x 4 pieces?
Start by coloring the grid as follows:
No matter how you place a 1×4 piece, it will always cover one A, one B, once C and one D. There are 26 B’s and only 24 D’s. We can place 24 1×4 pieces to cover all the D’, but then we’re left with 1 A, 2 B’s and 1 C. We can’t cover thoe with a ingle 1×4 piece. Therefore the answer i no.
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