MathDB

25

men sit around a circular table. Every hour there is a vote, and each must respond yes or no. Each man behaves as follows: on the

n^{\text{th}}

, vote if his response is the same as the response of at least one of the two people he sits between, then he will respond the same way on the

(n+1)^{\text{th}}

vote as on the

n^{\text{th}}

vote; but if his response is different from that of both his neighbours on the

n^{\text{th}}

vote, then his response on the

(n+1)^{\text{th}}

vote will be different from his response on the

n^{\text{th}}

vote. Prove that, however everybody responded on the first vote, there will be a time after which nobody's response will ever change.

Problem Statement