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One Hundred Lockers

I found this riddle online. It’s a bit math oriented, but still relatively easy for non-math geeks to solve 😛

Lockers in a row are numbered 1 , 2 , 3 , . . . , 100. At first, all the lockers are opened. A person goes and closes every locker. Next, another person walks by and opens every other locker, starting with locker #2. Thus lockers 2 , 4 , 6 , . . . , 98 , 100 are open. Another person walks by and “toggles” every third locker (ie closes a locker if it is open, opens a locker if it is closed), starting with locker #3. Then another person toggles every fourth locker, starting with #4, etc… This process continues until no more lockers can be altered.

Question: At the end of all the toggling, which lockers will be closed?

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Categories: Riddles
  1. June 12, 2013 at 12:55 pm

    I got the answer using programming in Python, but it took a long time. Then I read the solution online and I was sad

    • June 26, 2013 at 10:48 pm

      AHAHAHA yes the solution is surprisingly simple. You weren’t supposed to use a program to find the answer though -_-

  2. June 12, 2013 at 2:47 pm

    Every perfect square?

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