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Le Monde puzzle [#947]

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Another boardgame in Le Monde mathematical puzzle : Given an 8×8 chequerboard,  consider placing 2×2 tiles over this chequerboard until (a) the entire surface is covered and (b) removing a single 2×2 tile exposes some of the original chequerboard. What is the maximal number of 2×2 tiles one can set according to this scheme? And for a 10×10 chequerboard? This puzzle…
Original Post: Le Monde puzzle [#947]

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