Three girls, three hollow squares of blocks, one box size
Three children each have a box of identical cubic blocks, with exactly the same number of blocks in every box. The first girl uses all of hers to build a hollow square (a square frame, empty in the middle). The second girl builds a still larger hollow square, using all of hers too. The third girl builds an even larger square, but has exactly four blocks left over, one for each corner. What is the smallest number of blocks each box could hold?
Reveal the answer
1,344 blocks per box. The hollow squares have outer sides of 50, 62 and 72 blocks (around an inner gap of 34), and 50²-34² = 62²-50² = 1,344, while 72²-62² = 1,344-4, leaving exactly four corner blocks spare. Henry Dudeney set this as puzzle no. 161 in his posthumous 1932 collection, 'Puzzles and Curious Problems.'
— Henry Ernest Dudeney, Puzzles and Curious Problems — 1932, puzzle no. 161 (also no. 229 in the 1968 compilation '536 Puzzles & Curious Problems')
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