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?
i see both points of view, that it would be an infinite game, and also the last unit left standing would be zero. on one hand, once a zero appears, it would make zeros out of all of the other numbers. even if you didn't make a zero with the multiplications, then the random digits would eventually turn up a 0, which is why i belive that levik even added that portion of the problem
well,
