Problem #WSP-5522

Problems Discrete Mathematics

Problem

There are some coins in a straight line, all showing heads. You can choose any coin to flip. When you flip one, your friend must flip the coins directly next to it (the ones on its left and right, if there are any). For example: if you flip the first coin, your friend only flips the second coin, and if you flip the second coin, your friend flips the first and third coins.

The question is: no matter how many coins there are, can we always make all of them show tails in the end?