100 Doors

Posted: June 9, 2009 in M@th puzzles
Tags: ,

100 closed lockers. You begin by opening all 100 lockers. Next, you close every second locker. Then you go to every third locker and close it if it is open or open it if it is closed (call this toggling the locker). After your 100th pass of the hallway, in which you toggle only locker number 100, how many lockers are open?

Solution

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Comments
  1. Aadya says:

    All those numbers from 1- 100, that have even number factors will be closed and those with odd number of factors will be open.
    And since only squares have odd number of factors,
    all the squares will be open i.e.1,4, 9, 16, 25,36,49,64,81,100

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