Dudeney's Mrs. Perkins's quilt
For Christmas, Mrs. Perkins receives a patchwork quilt made of 169 small squares of silk, all sewn into one large 13-by-13 square. She decides to unpick it and re-cut it into the smallest possible number of whole-number-sized square pieces. What is the fewest square pieces she can manage, and what sizes are they?
Reveal the answer
Eleven squares, with sides 1,1,2,2,2,3,3,4,6,6,7 (their areas sum to 169), fit together into the 13-by-13 square, and it has been proven that ten or fewer is impossible. Henry Dudeney posed this in Amusements in Mathematics (1917) under the invented name 'Mrs. Perkins's Quilt'; puzzle historian David Singmaster notes a very similar problem had already run under Sam Loyd's byline in 1907, a reminder that the two rival puzzle masters often raced each other to the same ideas.
— Henry Ernest Dudeney, Amusements in Mathematics — Puzzle titled 'Mrs. Perkins's Quilt,' 1917; the general problem is now studied as a low-order squared square
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