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There are 1000 mailboxes at a post office, numbered 1, 2, 3, …, 1000. There are...

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Advance Math

There are 1000 mailboxes at a post office, numbered 1, 2, 3, …,1000. There are also 1000 mailbox owners, one for each mailbox. Atthe start of the Mailbox Challenge, all mailboxes are closed andthe owners open and close the mailboxes according to the followingrules:

Owner 1 opens every mailbox.

Owner 2 closes every second mailbox; that is, lockers 2, 4, 6,8, …, 1000.

Owner 3 changes the state of every third locker, closing it ifit is open and

opening it if it is closed.

Owner n changes the state of every nth mailbox, etc.

When all the owners have taken their turns, how many mailboxesare open?

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