Fitting all 13 Circles into the Smallest Possible Square!?
113,185
Published 2021-06-01
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All Comments (21)
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Awwwww! Thank you soooo much Mr. Puzzle. I am so excited you picked my comment, really honored. My students next school term are going to go nuts when I show them the video and they get to try the puzzle for real! ❤️ 😃
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"Knowing the solution cannot be undone!" I think you've greatly underestimated my ability to forget things with precision and speed
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If the largest circle has 13 times the area of the smallest circle, then the radius of the largest is sqrt(13) times larger. So if the side of the square is 18.59 times the radius of the small circle, it is 18.59/(2*sqrt(13)) = 2.578 times the diameter of the largest.
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This makes me wonder if squared squares would make hard puzzles. Would be something aesthetically and mathematically pleasing for sure.
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My first strategy for solving this: "Hmmm, maybe we can flip the pieces?" Yeah, I'm not the sharpest tool in the shed...
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13:24 The official sound effect of victory.
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The question that comes to my mind: Is this the only solution? Or, is it by definition, only solvable one way?
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I take advantage of the fact that there is nothing to win this week to send you my sincere congratulations for all your videos! Keep on puzzling!
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Solution to your small exercise: The side length of the frame is 2,577969.. ~ 2,58 times the diameter of the biggest (13) circle.
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I figured you would have to put smaller pieces in the corners to minimize space lost on the 90 degree angle
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Congrats to this week's giveaway winner! Very well deserved. What a heartwarming comment!
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I work in upholstery and one part of my job is to try and fit as much pieces I have to cut into a set amount of fabric material, I guess you could say I do packing puzzles all day at work sometimes 😂 yesterday I didn’t think what I have to cut would fit out of the piece of material I had but after trying 4 times it actually all fit inside the material
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My thought would have been to start with smallest circles in the corners
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I thought the ultimate packing puzzle was fridges and freezers after a grocery shop. And then there's this. There is definitely an algorithm to solve this faster...but I have no time for figuring this out...
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It would be interesting to see Mr. Puzzle return to puzzles like this after a few months to see if he can do them faster or if it's about the same.
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I love it when puzzles like this come out where i can see what is going on!
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This puzzle looks very challenging. So happy to see that you are able to solve it.
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Jigsaw and packing-puzzles are my favorite.
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I think you can calculate the answer instead of trial and error. For example, the sum of the diameters of 10, 8 & 11 = 18.6; 11. 2. 7 & 5 = 19.2; 12, 13 & 5 = 18.6 and 10, 6 & 12 = 18.2. They will not be exactly the same because there will be wastage.
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Awesome puzzle!