A Hundred Lockers
An old puzzle whose answer is easy to find and surprisingly hard to earn.
A school corridor has a hundred lockers in a row, all closed. A hundred kids line up outside.
- The first kid walks the row and opens every locker.
- The second kid goes to every second locker — 2, 4, 6, 8 — and closes each one.
- The third goes to every third locker — 3, 6, 9, 12 — and changes it: open becomes closed, closed becomes open.
- And so on. Kid k visits every kth locker and flips whatever they find, until all hundred kids have gone through.
When the corridor is quiet again, which lockers are open?
It is worth sitting with that for a moment before scrolling. Not to find the answer — the answer is findable — but to notice that there is no obvious place to start.
Try a smaller one
A hundred lockers is too many to hold in your head, and that is usually a signal rather than an obstacle. When a problem is too big to see, shrink it until you can see it, look for a pattern, and only then ask whether the pattern survives going back up.
So: ten lockers, ten kids, all lockers closed and nobody sent yet. Kid 1 touches every locker, kid 2 every second one, kid 3 every third, and so on. Touching a closed locker opens it; touching an open one closes it.
Send them one at a time and watch what each one does. You can also click the lockers yourself — working it by hand is the part that makes the pattern stick.
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