Re: CarTalk Puzzler

[tbone1]

The Hall of 20,000 Ceiling Lights

There are 20,000 lights on. A person comes through and pulls the cord on every second light. A third person comes along and pulls the cord on every third light, etc. When someone comes who pulls every 20,000th chain, which lights are on?

Um, only the first light is on; all the others have had their plugs pulled. Obvious, isn't it, or am I missing something?

I mean, I'm all for trying to solve things programmatically, but do we need a program for this?

[chas]

Well, consider that light number 4 is originally on, then gets turned off since it is a multiple of 2, then gets turned on since it is a multiple of 4, and then that's it for number 4.

[Aristotle]

That confused me too. After reading the responses, I figured out that the puzzle refers to the cord – not plug – that switches a light on and off. So if a light has its cord pulled once, it’s off, twice, it’s on again, thrice, off again, etc. So the guy who pulls every 3rd cord will switch the 6th light back on, as well as the 12th, the 18th, etc. (In fact, he turns one light back on for each light that he turns off.)

Hope that clears the confusion.

(And that you weren’t jesting.)