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May 2005 Puzzle
Click Here for the Solution
A locker room contains 1000 lockers numbered 1 to 1000
each of which is initially closed.
One at a time,
1000 people enter the locker room:
the first person opens each locker;
the second person then closes all even numbered lockers;
then the third person closes door 3,
opens door 6, closes door 9,
opens door 12, etc…
In general, the nth person changes (either opens or closes)
exactly those lockers whose number is a multiple of n.
After all 1000 people have gone into the locker room and made their changes, which lockers will be open and why?
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