Sunday, February 10, 2008

Coins In A Row Puzzle

Coins in a Row Puzzle
Tom has a checkerboard, a pocketful of coins, and some time to pass. He places one coin in each square of the checkerboard. Then he starts turning coins from heads to tails, until only one coin is left showing a head.

He decides to flip them all back to heads, but now he makes a rule. He can only make two kinds of moves: flip all the coins in a row, or flip all the coins in a column of the checkerboard. This suddenly makes his task more interesting, but he finds he can't seem to get all heads. Now he tries getting all tails, but again he can't do it.

* Starting with one head, is there always a way to flip all the coins to heads? Or tails?
* Does the shape of the checkerboard matter?
* Does the position of the single head matter?