Enigma 1251: Jigsaw of rectangles
4 March 2015
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From New Scientist #2407, 9th August 2003 [link]
It is day 10 of Frances’s holiday and she is cutting rectangles out of cardboard. She is cutting out every rectangle with whole number sides and area at most 10.
When she has finished she has 15 rectangles, which are:
1×1, 1×2, 1×3, 1×4, 2×2, 1×5, 1×6, 2×3, 1×7, 1×8, 2×4, 1×9, 3×3, 1×10, 2×5.
Frances then tries to fit the 15 pieces together to make a square, with no overlapping pieces and no holes. She finds it is impossible. In fact she tried a similar thing on day 2 of her holiday with all rectangles of area at most 2, on day 3 with area at most 3, …, on day 9 with area at most 9; on each day she found it was impossible to make a square.
Frances continues through her holiday, on day 11 with area at most 11, on day 12 with area at most 12, and so on. Each day she finds it impossible to make a square until one memorable day when she finds it is possible.
Which day of the holiday was that memorable day?