Mathematics

Jarrett Wolfe

6 October, 10:24

You are in a room with 100 light bulbs. Each light bulb is numbered from 1 to 100 and each has its own switch. All lights begin in the off position. Your job is to switch the lights on or off according to the following procedure:

Pass 1 You go through and switch lights 1, 2, 3, 4, ect. (They are all now on)

Pass 2 You go through and switch lights 2,4,6,8 ect. (These lights are now off again)

Pass 3: You go through and switch lights 3,6,9,12, ect.

Pass 4 You go through and switch lights 4,8,12,16 ect

You continue this process for 100 passes until you have switched light #100 on pass #100.

Questions: After you have completed every pass, which lights are left on? What is special about these numbers?