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I don't think there is a general method for doing this. You can calculate a rough lower bound on the number of squares of a given size that will fit inside a unit circle but it's hard to prove that you can't fit in more somehow by rearranging the squares. See https://mathworld.wolfram.com/SquarePacking.html for the first six square packings.

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This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

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TopNewestI don't think there is a general method for doing this. You can calculate a rough lower bound on the number of squares of a given size that will fit inside a unit circle but it's hard to prove that you can't fit in more somehow by rearranging the squares. See https://mathworld.wolfram.com/SquarePacking.html for the first six square packings.

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Thank you for this.

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