MathDB

There are

n \ge 3

coins on a circle. Consider a coin and the two coins adjacent to it; if there are an odd number of heads among the three, we call it good. An operation consists of turning over all good coins simultaneously. Initially, exactly one of the

n

coins is a head. The operation is repeatedly performed. (a) Prove that if

n

is odd, the coins will never be all-tails. (b) For which values of

n

is it possible to make the coins all-tails after several operations? Find, in terms of

n

, the number of operations needed for this to occur.

Problem Statement