olymmath

RU-ALLRUSSIAN 1971 Problem 8

    An integer is written at each vertex of a regular n- gon. A move is to find four adjacent vertices with numbers a, b, c, d (in that order), so that (a−d)(b−c)<0(\mathrm{a} - \mathrm{d})(\mathrm{b} - \mathrm{c})< 0 , and then to interchange b and c. Show that only finitely many moves are possible. For example, a possible sequence of moves is shown below:

    Dataset text NuminaMath olympiads. Quoted with source.

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    Locator ru-allrussian/1971/p8 · Tag HS0704CA4F · Edit this page on GitHub · Keys: j next, k previous