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- Combinatorial Agriculture 2 answers
Jepetto the toymaker was thinking about a new toy to add to his tiling product line. His new design involved a punctured chessboard: an ordinary $8 \times 8$ chessboard, except with a single square removed.
Now, when he ordered these punctured chessboards, Jepetto was very specific about the missing square; so he was furious when the manufacturer showed up with a chessboard whose hole was in the wrong place. Jepetto yelled at the man:
Don't you see? You've ruined it! How can anyone tile this board with $3\times 1$ rectangular pieces!?
On how many squares could the hole have been misplaced?