Question 36
There are $n$ ($n \ge 2$) coins in a row. 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 $n$ coins are heads at the initial stage, determine if there is a way to carry out $\lfloor \frac{2^{n+1}}{3} \rfloor$ moves. (posed by Gu Bin)