3 Feb
2018
3 Feb
'18
6:14 p.m.
Puzzle: ------- Suppose there is a school with an infinity of lockers, numbered 1, 2, 3, .... Initially all lockers are closed. Definition: A locker is "switched" if it is changed from shut to open, or vice versa. At 1/2 minute to noon, every 2nd locker 2, 4, 6, ... is switched. at 1/3 minute to noon, every 3rd locker 3, 6, 9, ... is switched. Or in general: For each positive integer n >= 2: * At 1/n of a minute to noon, every nth locker n, 2n, 3n, ... is switched. No other changes are made to the lockers. Question: --------- Which lockers are open at noon? —Dan