Start with the sequence of coins as follows (where you can think of O as TAILS and X as HEADS; there are 14 tails and 15 heads)

XOXOXOXOXOXOXOXOXOXOXOXOXOXOX

Transform it to

XXXXXXXXXXXXXXXOOOOOOOOOOOOOO

using moves of the following sort:

Take two consecutive coins and move them to the end, or the beginning.

If I counted correctly, Charlie's solution took 39 steps. Here is a simpler solution that only takes 20 steps. a) Move the first XO to the end, then the first OX, and continue alternating the first XO and the first OX for a total of 13 moves b) Move the last XX to the start, and repeat 6 more times for a total of 7 moves. c) We are all done in 20 moves. See picture below. Can anybody do better? XOXOXOXOXOXOXOXOXOXOXOXOXOXOX >> XOXOXOXOXOXOXOXOXOXOXOXOXOXXO >> XOXOXOXOXOXOXOXOXOXOXOXOXXOOX >> XOXOXOXOXOXOXOXOXOXOXOXXOOXXO >> XOXOXOXOXOXOXOXOXOXOXXOOXXOOX >> XOXOXOXOXOXOXOXOXOXXOOXXOOXXO >> XOXOXOXOXOXOXOXOXXOOXXOOXXOOX >> XOXOXOXOXOXOXOXXOOXXOOXXOOXXO >> XOXOXOXOXOXOXXOOXXOOXXOOXXOOX >> XOXOXOXOXOXXOOXXOOXXOOXXOOXXO >> XOXOXOXOXXOOXXOOXXOOXXOOXXOOX >> XOXOXOXXOOXXOOXXOOXXOOXXOOXXO >> XOXOXXOOXXOOXXOOXXOOXXOOXXOOX >> XOXXOOXXOOXXOOXXOOXXOOXXOOXXO << << << << << << << XXXXXXXXXXXXXXXOOOOOOOOOOOOOO

*Edited on ***June 20, 2013, 12:02 am**