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Rabbit Hole: Minimum L-seams

2026-09-17 | original

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Why This Matters

This piece explores a niche but intellectually rich intersection of mathematics and quilting—Mrs. Perkins' Quilt problem, which asks how to divide a square into the fewest integer-sided smaller squares. While not a mainstream tech story, it illustrates how classic combinatorial puzzles can surface unexpectedly in creative/craft domains, and highlights how practical constraints (like sewing seams or paper cutting) can reframe abstract math problems in tangible, computational terms. It's a reminder that algorithmic thinking and optimization problems permeate far beyond typical software or hardware contexts.

Key Takeaways

The article examines Mrs. Perkins' Quilt, a classic math puzzle about dividing a square into the fewest integer-sided smaller squares.
The author draws a parallel between minimizing sewing seams (or paper-cutting corners) and minimizing structural complexity in the mathematical solution.
The piece is part of an ongoing exploratory series, blending recreational mathematics with practical crafting challenges, promising further updates.

Worth a Look

Fiskars Rotary Cutter and Mat Set — If you're inspired to actually piece together a Mrs. Perkins' Quilt with its many precise integer-sided squares, a good rotary cutter and self-healing mat make cutting all those exact square pieces so much easier. It's a staple for any quilter tackling geometric patchwork puzzles like this one.”

See Fiskars Rotary Cutter and Mat Set on Amazon → Affiliate link — we may earn a commission on purchases, at no extra cost to you. Product picked by AI based on this article; it is not a tested recommendation.

I was trying to write a post about art with squarable numbers, and so I thought quilting a Mrs. Perkins' Quilt might be a nice addition to the exploration. With 1500 words almost ready to hit send, I ended up down a rabbit hole. This post is rather long and has a lot of data, so bear with me, or skip it. I will have an artsy post with a quilt in the next week.

Please note, this post will get updated as I work through the problem. The update on the quilt is here.

The quilt:

Ok, first off, Mrs Perkins' quilt is a lovely math problem. The challenge is to slice a square of side n into smaller squares with integer side lengths, use the fewest squares possible.

The website squaring.net has a lot more on the problem, including the original wording, and Wolfram has a demonstration to explore.

"For Christmas, Mrs. Potipher Perkins received a very pretty patchwork quilt constructed of 169 square pieces of silk material. The puzzle is to find the smallest number of square portions of which the quilt could be composed and show how they might be joined together. Or, to put it the reverse way, divide the quilt into as few square portions as possible by merely cutting the stitches."

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Explore topics: mrs perkins quilt henry e dudeney squarable numbers squaring.net quilting technique