In a hallway, 100 closed lockers numbered 1 to 100 undergo 100 passes. On pass 1, every locker is toggled (opened). On pass 2, every 2nd locker is toggled. On pass 3, every 3rd locker is toggled, continuing this pattern until pass 100 where only locker 100 is toggled. After all passes, which lockers remain open?
Lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 (all perfect squares).
A locker ends up open if it is toggled an odd number of times. A locker's number is toggled once for every factor it has. Most numbers have factors in pairs (even count), but perfect square numbers have an odd number of factors because one factor pairs with itself (e.g., 9 has factors 1, 3, 9).
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
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