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
Simpler Shorter Solution (20 moves)
