His Homework's a Crazy Hard 100 Year Old Puzzle

This problem showed up on r/askmath last week, a problem from what appears to be a sort of primary school math packet. The problem takes us through a long-winded fantasy narrative to poorly describe a problem, with the addition of a figure that only adds to the confusion. We'll get to the bottom of this problem which will us back to 1917, when Henry Dudeney published Amusements in Mathematics, a book that featured a puzzle called Mrs. Perkin's Quilt, which would go onto inspire a lot of research and variations such as squaring the square. #askreddit #mathematics

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SOURCES
  / is_my_answer_correct_or_wrong  
Amusements in Mathematics by Henry Ernest Dudeney
Mrs. Perkin's Electric Quilt by Paul J. Nahin
https://demonstrations.wolfram.com/Mr...
https://www.alaricstephen.com/main-fe...
https://mathworld.wolfram.com/MrsPerk...
http://www.squaring.net/quilts/mrs-pe...
https://oeis.org/A005670
Conway JH. Mrs Perkins’s quilt. Mathematical Proceedings of the Cambridge Philosophical Society. 1964;60(3):363-368. doi:10.1017/S0305004100037877 (https://www.cambridge.org/core/journa...)

0:00 Intro
1:36 Possible Answers
3:49 Reddit's Thoughts
5:37 The Origins
9:37 Optimal Solution
11:51 General Problem
13:38 Squaring the Square
15:31 Conway's Bounds
17:08 Conclusion