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maximum 4-cycles in Cn digraph

Source: Mongolia 1999 Teachers secondary level P2

May 6, 2021
combinatorics

Problem Statement

Any two vertices A,BA,B of a regular nn-gon are connected by an oriented segment (i.e. either A→BA\to B or B→AB\to A). Find the maximum possible number of quadruples (A,B,C,D)(A,B,C,D) of vertices such that A→B→C→D→AA\to B\to C\to D\to A.
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