Marcus Kazmierczak

The Hallway of 20,000 Lights [Brain Teaser]

Date: Nov 22, 2005

I haven't posted a new math brain teaser in a while. This one's a good one, not too difficult and an elegant solution, at least I think so.

Imagine there is a long hallway with 20,000 lights in a row each with a drawstring which when pulled will turn them on or off, opposite of their previous state.

If all the lights are initially off; the first person walks by and pulls every cord, turning on all the lights. The second person starting at light #2 walks by and pulls every 2nd cord, the 3rd person walks by starting at light #3 and pulls every 3rd cord.... and so on for 20,000 people.

What lights are on/off at the end? Why?