Задача 21.

* Consider a 50-sided regular polygon. Dr. Faust is standing in one of its vertices. He has three possibilities: 1) to go to a diametrically opposite vertex free of charge; 2) to go to a counterclockwise neighboring vertex by paying \$1.05 to Mephistopheles; 3) to go to a clockwise neighboring vertex and receiving \$1.05 from Mephistopheles. It is known that Dr. Faust has been at each vertex at least once. Show that on some part of the path someone paid to the other at least \$25.