Children and light switches

1,161.8K Views
Answered

A room has 100 light switches, numbered by the positive integers 1 through 100.  There are also 100 children, numbered by the positive integers 1 through 100.  Initially, the switches are all off.  Each child k enters the room and changes the position of every light switch n such that n is a multiple of k.  That is, child 1 changes all the switches, child 2 changes switches 2, 4, 6, 8, …, child 3 changes switches 3, 6, 9, 12, …, etc., and child 100 changes only light switch 100.  When all the children have gone through the room, how many of the light switches are on?

Share
Add Comment

  • 1 Answer(s)
    Best answer

    All the perfect squares

    Yodha Expert Answered on 8th February 2016.

    How?

    on 22nd February 2016.
    Add Comment
  • Your Answer

    By posting your answer, you agree to the privacy policy and terms of service.
  • More puzzles to try-