Blind And Numb

Alright, so I have recently found a more difficult extension to the blind man puzzle:
There are four coins, each with a black side and a white side. The coins are arranged in a 2x2 pattern on a board. A blind man is going to play a game with these coins, he wins the game if at the end of one of his turns every coin has the same side up.

A turn consists of the man selecting any two coins, and he may then flip either or both of them. Coins may not be moved. After his turn he will be told if he has won. If he has not won yet, the board will be randomly rotated before his next turn.

Find a strategy that guarantees he can win within N turns, for some number N.

Its the exact same puzzle, except that you do not get to learn the status of the two holes that you choose. Of course it requires a few more moves, but its really interesting that you can still solve it.


AT said...

To be clear, the action is flipping 1 or 2 coins (i.e. changing state without being told the start/ending state, only if he's won or not), correct? In particular, the action is NOT setting the coins to a specific state (e.g. set both to heads).


kstevens said...

Right, you do not get to say what state the coins end up in, only if you flip them or not.