Digits from 1 to 9 are written on the board.

A student erases a few of them, and instead writes the digit(s) of their product. (For example if he erases 4, 3 and 7 he would write the digits 8 and 4 since 4 * 3 * 7 = 84.) He also writes a few other random digits on the board.

He repeats this process until only one digit remains on the board. What is this digit and why?

certainly, at some point, there is only a single zero on the board, with no other numbers. But this does not happen at a "check point". The process which he is repeating includes as its last step the addition of a few random numbers, so this looks like an infinite game.

Posted by Cory Taylor on 2002-12-10 04:28:11