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We've all been there: it's puzzle time, but once you dump out the pieces and start laying them flat, you realize you don't have enough space on your table. Join me as we use physics to find out ✨HOW BIG A TABLE YOU NEED FOR YOUR JIGSAW PUZZLE ✨

https://doi.org/10.48550/arXiv.2312.04588
#SciComm


How big a table do you need for your jigsaw puzzle?

Jigsaw puzzles are typically labeled with their finished area and number of pieces. With this information, is it possible to estimate the area required to lay each piece flat before assembly? We derive a simple formula based on two-dimensional circul…
arXiv.org
#scicomm

Hubert Chathi reshared this.

Madeleine Bonsma-Fisher, PhD
Madeleine Bonsma-Fisher, PhD  
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This work was a pandemic collaboration between me and the brilliant Kent Bonsma-Fisher, with assistance from our toddler and cat. The result, in his words, was "the cleanest dataset I have ever collected." Today our results are public on #arXiv!
A black cat standing on a dining room table with an unassembled puzzle laying on it
#arxiv
Madeleine Bonsma-Fisher, PhD
Madeleine Bonsma-Fisher, PhD  
•
TL;DR: an unassembled jigsaw puzzle takes up an area that is the square root of 3 times the area of the assembled puzzle, or about 1.7 times the assembled area. This is *independent of the number of pieces*.
Madeleine Bonsma-Fisher, PhD
Madeleine Bonsma-Fisher, PhD  
•
We derived a theory with a "spherical cow in a vacuum" approach: we approximated each puzzle piece area as a circle, then calculated the area of the circles packed together. Our prediction: the unassembled area is sqrt(3) times the assembled area. Then we took data.
A cartoon puzzle piece with a dotted circle drawn around it
A graphic showing how circles pack on a 2D surface in a hexagonal lattice
Madeleine Bonsma-Fisher, PhD
Madeleine Bonsma-Fisher, PhD  
•
We built 9 puzzles across a variety of total sizes and with piece numbers ranging from 9 to 2000. We laid out all the pieces flat, trying to be realistic by not paying much attention to how they were arranged and not spending time trying to get them closer together.
Me and my toddler building a puzzle at our dining room table.
A small unassembled puzzle arranged with the pieces in a flat layer in an approximate circle
Madeleine Bonsma-Fisher, PhD
Madeleine Bonsma-Fisher, PhD  
•
The results were the most incredible agreement between theory and data I've ever seen in over a decade of being a physicist. I think I gasped when I saw this plot. Without any fitting, our simple theory *very accurately* predicted the unassembled area of all these puzzles.
A plot showing the assembled area vs. unassembled area of 9 puzzles with a dashed line indicating the square root of 3. All the data points are very close to or touching the dashed line.
Madeleine Bonsma-Fisher, PhD
Madeleine Bonsma-Fisher, PhD  
•
We were surprised that the unassembled area didn't depend on the number of puzzle pieces. The intuition is this: if you have a small number of large pieces, the gaps between pieces are big, but this is multiplied by a small total number of pieces, and vice versa for small pieces.
Two unassembled puzzles on a table, one with a few very large pieces and one with many small pieces.
Madeleine Bonsma-Fisher, PhD
Madeleine Bonsma-Fisher, PhD  
•
So there you have it: you'll need a puzzle table just under twice as big as your assembled puzzle in order to not resort to the box lid or that random side table. Grab a puzzle and impress your relatives this holiday season with your predictive powers!
Nicd
Nicd  
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Now this is the content I wish to see online. And useful as my wife and mother-in-law are puzzle fanatics. :)
Shawn Platkus
Shawn Platkus  
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This, as stated, is obviously incorrect. Otherwise the boxes that the puzzles come in would be larger in area than the assembled puzzle. However they are always smaller in area than the assembled puzzle.
Madeleine Bonsma-Fisher, PhD
Madeleine Bonsma-Fisher, PhD  
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@platkus we and you are making different assumptions about what constitutes the area of a puzzle. Our question was "how much area does it take to lay out all the pieces in a single layer", while of course in the box they don't need to be in a single layer. In the extreme case, you could stack every piece on top of the others and say the area of an unassembled puzzle is 1 piece. That's fine! Just not what we were trying to figure out.
@Shawn Platkus
Shawn Platkus
Shawn Platkus  
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Right. I was just pointing out that your post didn’t make the parameters clear. That’s why I said “as stated” it was incorrect.
Madeleine Bonsma-Fisher, PhD
Madeleine Bonsma-Fisher, PhD  
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@platkus this is a weird hill to die on, the parameters are very clear both in the paper and later in this thread
https://mastodon.social/@mbonsma/111564845145935604

Madeleine Bonsma-Fisher, PhD

2023-12-12 01:27:18


We built 9 puzzles across a variety of total sizes and with piece numbers ranging from 9 to 2000. We laid out all the pieces flat, trying to be realistic by not paying much attention to how they were arranged and not spending time trying to get them closer together.
Me and my toddler building a puzzle at our dining room table.
A small unassembled puzzle arranged with the pieces in a flat layer in an approximate circle

@Shawn Platkus
Shawn Platkus
Shawn Platkus  
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Sure, but not everyone is going to read the paper or the thread. I don’t see any reason the parameters couldn’t have been stated in this initial post. Not a big deal, but just pointing out that it could have been made clearer.
Nicd
Nicd  
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If you didn't read the research or even the thread, you shouldn't critique the research or the thread.
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