A room has 100 light switches, numbered by ................?

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, 鈥? child 3 changes switches 3, 6, 9, 12, 鈥? 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?
A room has 100 light switches, numbered by ................?
10.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100
A room has 100 light switches, numbered by ................?
99.

Basically if Child 1 enters, changes all even numbers, 50 switches are on.

Child 3 enters, switches all odd numbers, 100 switches are on ( ODD + EVEN )

Child 100 turns out one switch ( 鈩?100 ) so that 99 Switches are now on.

control panel buttons

hair lyrics