Arrangements of vertices of nonagon
Source:
March 18, 2011
countingdistinguishabilitygeometrygeometric transformationrotationAMCAIME
Problem Statement
The vertices of a regular nonagon (9-sided polygon) are to be labeled with the digits through in such a way that the sum of the numbers on every three consecutive vertices is a multiple of . Two acceptable arrangements are considered to be indistinguishable if one can be obtained from the other by rotating the nonagon in the plane. Find the number of distinguishable acceptable arrangements.