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His Homework's a Crazy Hard 100 Year Old Puzzle

Wrath of Math

90,322 views

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
Reddit: 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

20 Comments

@WrathofMath Creator 1 year ago (edited) Pinned

There are many subtopics we could branch off to following up this video and introduction of the problems. Perhaps the most interesting is the connection between Mrs. Perkin's quilt and electric circuits, a connection which is even used in one of Conway's proofs in the mentioned paper. I don't know anything about electric circuits though, so have acquired some books to become acquainted!

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@wretchedcats4909 11 months ago

This math problem starting out with how to train your dragon fanfiction is so funny to me.

@kurocksong 1 year ago

Cut my quilt into pieces. This is my last resort.

@nivolord 1 year ago

The sad thing is, this would have been a great problem to just have in a classroom setting, where everyone is having a go at it and trying to find the best solution, without any pressure to get the correct answer. Instead, we got this misleading incoherent word salad of a problem, which turned a genuinely interesting and difficult question into a multiple choice, stripping it of any appeal.

@NestorCustodio 1 year ago

I love the idea of cutting up an n×n quilt into n² unit squares just to transport it. You're fully unmaking the quilt just to move it elsewhere and then making a quilt from scratch again.

@sheep177 1 year ago

they even misspelled square

@Aymelia-colon3 11 months ago

"Powerful warriors" and it's just two teen vikings who have dragons

@corlinfardal 1 year ago

0:52 Hiccup and Astrid are both How to Train Your Dragon characters, and the rest of the text supports that assumption. Hiccup is a boy and Astrid is a girl, the "he" here is Hiccup.

@kingbeauregard 1 year ago

Good lord, it's hard to imagine a worse written description of the problem. "You have a 13x13 square, and you want to cut it up into squares that all have sides of integer length (1, 2, 3, etc). How do you cut it up to make the least number of squares?" I hope Hiccup and Astrid lose.

@sol_x_dier 1 year ago

What I find really interesting about the miserable attempt to rewrite the problem is that it doesn't require integer squares, only squares that "contain at least one patch". It seems any size is permittable as long as it is greater than or equal to 1. In that case, the solution is really just four 6.5x6.5 squares, and we're done!

@ShowersRainwater 11 months ago (edited)

This question reminds me of my favorite economics professor in undergrad. Most of the questions were written this way with tons of useless information. The stories were typically about economics professors at a party where they were smarter than the other professors or about a hypothetical marketplace where beans and weanies were being sold. The in universe lore got pretty complex as the class went on in order for him to fit all the various concepts in.

@prestwig1 1 year ago

I am truly confused. the quilt will not weigh less if it is cut into pieces.

@jeopardy60611 1 year ago

This brings up a problem that I found all too often in school. Teachers assign work that doesn't make sense, and they arbitrarily expect kids to do it, not realizing that there are flaws in the work, and refusing to clarify the work.

@richardfarrer5616 1 year ago (edited)

I have discovered a truly marvellous proof of this which my dragon is too narrow to contain.

@LeongZeJun 1 year ago

How to solve: Don't

@ciCCapROSTi 10 months ago

10:35 Wait how is 11 the optimal solution for 10x10 when you can just chop it in quarters?

@gcewing 1 year ago

Another problem with the wording of the question is that "at least one square of strategy" doesn't limit the cuts to patch boundaries. You could have a 1.5 x 1.5 piece that contains one complete square.