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MMO 356 Moscow MO 1957 polygon made of rigid rods connected by hinges

Source:

August 20, 2019
combinatorial geometrycombinatoricsgeometrypolygon

Problem Statement

A planar polygon A1A2A3...An−1AnA_1A_2A_3 . . .A_{n-1}A_n (n>4n > 4) is made of rigid rods that are connected by hinges. Is it possible to bend the polygon (at hinges only!) into a triangle?
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