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ways that polyline be segments of n points on circle doesn't cut itself

Source: 1986 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p1

November 21, 2022
combinatoricscombinatorial geometry

Problem Statement

There are nn points on a circle (n>1n > 1). Denote them with P1,P2,P3,...,PnP_1,P_2, P_3, ..., P_n such that the polyline P1P2P3...PnP_1P_2P_3... P_n does not intersect itself. In how many ways is this possible?
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