MathDB

There are

n

coins in a row,

n\geq 2

. If one of the coins is head, select an odd number of consecutive coins (or even 1 coin) with the one in head on the leftmost, and then flip all the selected coins upside down simultaneously. This is a

move

. No move is allowed if all

n

coins are tails. Suppose

m-1

coins are heads at the initial stage, determine if there is a way to carry out

\lfloor\frac {2^m}{3}\rfloor

moves

Problem Statement