#70 · Puzzles · A surprising pattern

The hundred lockers

100 lockers start closed. Student 1 toggles every locker; student 2 toggles every 2nd; student 3 every 3rd; and so on through student 100. Which lockers end up open?

~10 minWritten answer · compare with the solutionDivisor countingPerfect squares

Stuck? A gentle nudge

Something off?

Workspace

Your working

Check your full solution

Upload photos of your handwritten work or a PDF, and Lemma will read it and tell you whether it's right — and where it first goes wrong if not.