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every hour, everyone must vote yes or no. On the nth vote, if your vote is...

every hour, everyone must vote yes or no. On the nth vote, if your vote is the same as the vote of at least one of the people beside you, vote the same on n+1. If your vote is different from both of the people beside you, change your vote on n+1. Prove that regardless of initial voting, there will be a time when no one changes their vote

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Answer #1

suppose n-1th vote be a No and n-2th vote be also NO and nth vote be Yes then n+1 vote will be No; now consider this No as nth vote so n+1 vote will be No; now consider this as nth vote therefore n+1 vote will be No.

similar since the n-1 and n-2 th vote will remain No and all the further votes will be No.

Same will happen for the case of n-1 and n-2 th case to be Yes and n th vote to be No then all the further votes will be yes.

suppose n , n-1 and n-2th vote are same then from 1st condition all the further votes will be same.

hence after a time there will be no change in vote

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