SMT 2010 Algebra Problem 5
Source:
July 27, 2011
Problem Statement
A series of lockers, numbered 1 through 100, are all initially closed. Student 1 goes through and opens every locker. Student 3 goes through and "flips" every 3rd locker ("fipping") a locker means changing its state: if the locker is open he closes it, and if the locker is closed he opens it. Student 5 then goes through and "flips" every 5th locker. This process continues with all students with odd numbers going through and "flipping" every th locker. How many lockers are open after this process?