Brain Teasers & Mental Math
100 lockers, all closed. Student 1 toggles every locker, student 2 every 2nd, student 3 every 3rd, … student 100 toggles locker 100. After all 100 students pass, which lockers are open?
Model answer
The perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 — ten lockers.
Locker n is toggled once for each divisor of n. Divisors pair up (for 12: 1×12, 2×6, 3×4 → six divisors → even toggles → ends…
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