5

Part of 2011 AIME Problems

Problems(2)

Arrangements of vertices of nonagon

Source:

The vertices of a regular nonagon (9-sided polygon) are to be labeled with the digits

1

9

in such a way that the sum of the numbers on every three consecutive vertices is a multiple of

3

. 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.

countingdistinguishabilitygeometrygeometric transformationrotationAMCAIME

Sum of a geometric series [2011.II.5]

Source:

The sum of the first 2011 terms of a geometric series is 200. The sum of the first 4022 terms of the same series is 380. Find the sum of the first 6033 terms of the series.

ratiogeometric seriesAMC