In the book Which way did the bicycle go was given that one can put eleven squares $S_1,\ldots S_{11}$ of side length 1 inside a square of side-length $3.877083$ if any pair of $S_i,S_j$ has no common interior points. It was said that this can be done by making two simultaneous equations and solve them numerically. But I don't see two different methods to make the equations. One is given in Eleven unit squares inside a larger square . But how one can make the second one as it was unsolved in that link? I tried to follow the hint given in the link but I was unable to find the equation nor understand how Filmus got his first equation.
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I didn't know this kind of problems. Very nice and challenging really. – Piquito Nov 27 '15 at 16:57