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In this web site there are the solutions of a lot of packing squares problems. I know a very simple method to calculate with pen and paper the solution for the ten squares in a square using the same method than for five squares.

But now I try the eleven squares and the problem seems to be difficult, I try some approximations but they were not very conclusive. So I made a "puzzle" with eleven piece of paper and tried some configurations but they were not really interesting.

So I searched online but I find nothing about Walter Trump's method and I don't want to buy a book for $40 just to know the solution.

Have you got some ideas which can help me ?

Thank you in advance

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  • $\begingroup$ Are you trying to calculate $s$ or to prove $s$ is optimal? $\endgroup$ – nbubis Jun 3 '15 at 12:51
  • $\begingroup$ I'm trying the both ! :) $\endgroup$ – Hexacoordinate-C Jun 3 '15 at 12:55
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It seems like there is no proof$^1$ that this result is actually optimal. There also seems to be an unpublished proof that no $45^\circ$ solution is better than that of Trump, but the actual optimality proof is still out there.

The attached reference also gives a hint to finding the angle ($40.182^\circ$) and configuration:

enter image description here

  1. "Which Way Did the Bicycle Go?: And Other Intriguing Mathematical Mysteries", pp. 105
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  • $\begingroup$ Is it difficult to find these two equations ? :) $\endgroup$ – Hexacoordinate-C Jun 3 '15 at 15:46
  • $\begingroup$ @Shadock - difficult? no. tedious? very. $\endgroup$ – nbubis Jun 3 '15 at 15:52
  • $\begingroup$ OK i will try and if I don't find them you will give me :P Thank you for your help ! $\endgroup$ – Hexacoordinate-C Jun 3 '15 at 15:54

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