A nice geometry puzzle solved in 3 ways
39K views · Aug 23, 2026 · Science & Technology
Comments · 121
@scmtuk3662 · 1 month ago
I just guessed 1/5, because it just "looked" like the 4 triangles matched up with the other four segments, making 4 squares, making the square in the middle the 5th square.
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@qazsedcft2162 · 1 month ago
I miss the "pause the video to give this problem a try" from your older videos.
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@SanePerson1 · 1 month ago (edited)
As a person familiar with looking at crystals for decades, I recognize that periodic boundary conditions apply: all the black squares are completed by neighboring “unit cells” (or by the matching pieces of those squares on the opposite side of the cell depicted). That’s four total black squares and one blue square - all equal in area. So the blue square is one-fifth of the total. It’s a 10-second question if you’re conditioned by experience to see unit cells or, if you like, repeat units in wallpaper.
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@stoatystoat174 · 1 month ago
I like how the 'Outside the Box' solution is moving Triangles outside of the Square
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@madmurdoch2000 · 1 month ago
as soon as i saw this problem i used method 3 to solve it in about 30 secounds, the simplest solution is always the BEST solution.
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@chemalagos · 1 month ago
I just had an assessment to apply for a job, a math-logic test. 90 minutes, and it was full of questions like "what images fits here provided the others 8" and some language exercises. But, on top of that, there were math exercises that reminded me of MindYourDecisions type of exercise (if you remember, I got the exercise about the mean speed on a trip with two speeds). I felt like, watching these videos, I was prepared. My final results were good, idk yet if I got the job.<br><br><br>Thank you so much, and never stop learning!!
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@ronginzler6600 · 1 month ago
I liked the last solution best. No computation! I solved it a different way. I added up the areas of the 4 biggest triangles, each of which is 1/4 the area of the square, then computed the areas of the 4 smallest triangles and subtracted them from this total because they were counted twice.
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@deerh2o · 1 month ago
The "outside the box" solution literally gives you a net which is the outside of a box!
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@marcusscience23 · 1 month ago
<a href="https://www.youtube.com/watch?v=8xrdVKFCFaA&t=503">8:23</a> Another way to think about it would be to make the square a torus, where the top and bottom sides wrap around, as do the left and right sides. From there, the torus is simply cut up into 5 tessellated congruent squares, so the shaded square is 1/5 the area of the large square, nice and simple.
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@ThePowerfulOne07 · 1 month ago
Love the 3 option. That’s how I visually solved it!
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@KnakuanaRka · 1 month ago
I had heard of the rearranging method before, but I wasn’t sure of the best or simplest way to rigorously prove that everything lines up properly; this helps a lot.
@JLvatron · 1 month ago
Solved in my head!
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