There is an equilateral pentacontagon (a polygon with 50 sides). In one of its vertex stands Dr. Faust. He has three options 1) walk to the diametrically opposed point free of charge; 2) walk counterclockwise to the neighboring vertex by paying $1.05 to Mephistopheles; 3) walk clockwise to the neighboring vertex by receiving a payment of $1.05 from Mephistopheles. If it is given that Dr. Faust has been everywhere at least once, prove that at some point someone paid no less than $25.
There is an equilateral pentacontagon (a polygon with 50 sides). In one of its vertex stands Dr. Faust. He has three options 1) walk to the diametrically opposed point free of charge; 2) walk counterclockwise to the neighboring vertex by paying $1.05 to Mephistopheles; 3) walk clockwise to the neighboring vertex by receiving a payment of $1.05 from Mephistopheles. If it is given that Dr. Faust has been everywhere at least once, prove that at some point someone paid no less than $25.
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