Problem #10 HARD
The Infinite Hallway of Lockers
Microsoft Math Pattern Recognition
Problem Statement
A school hallway contains 100 closed lockers, numbered 1 to 100.
A student walks down the hall and opens every locker. A second student walks down and closes every second locker (2, 4, 6, ...). A third student changes the state of every third locker (3, 6, 9, ...), opening it if it was closed, and closing it if it was open. This process continues until 100 students have walked down the hallway.
After the 100th student finishes, which lockers will remain open?
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