MathDB
Octagons

Source: 2024 AIME I #11

February 2, 2024
AMCAIMEAIME I

Problem Statement

Each vertex of a regular octagon is coloured either red or blue with equal probability. The probability that the octagon can then be rotated in such a way that all of the blue vertices end up at points that were originally red is mn\tfrac{m}{n}, where mm and nn are relatively prime positive integers. What is m+nm+n?