Uploaded July 2026 | Updated September 2026, 2 weeks ago

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An intriguing pattern emerges from a thousand lockers and a thousand people toggling locker doors:

All lockers begin closed.
Pass 1: change the condition of every locker (open them)
Pass 2: change the condition every 2nd locker (close them)
Pass 3: change the condition every 3rd locker (open are closed and closed are opened)
...
Pass m: change the condition of every mth locker (open are closed and closed are opened)
Continue to pass 1000.
Only some lockers are left open: which ones?

#mathvisualproofs #math #visualmath #numbertheory #mathematics #puzzle #lockerproblem