Logic Puzzles

i like this thread, but this needs some damn order! One puzzle to be solved at a time. Then perhaps the champ gets to post the next?

And ignoring my own suggestion, in reference to this:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

I know it's in your advantage to switch, but i don't know the logic why. It's something i've been meaning to look up - so although i'm a geek, I'm not enough of a geek to have actually bothered to do that yet.

The odds of your first choice are 1/3. When one of the three is removed, the odds change to 1/2 - but only for the door you haven't chosen. That is, the door you're on remains 1/3 as it was so when you chose it, and it was not taken into consideration when the other door was removed.

So you can move from a 1/3 chance to a 1/2 chance by switching.

(It's called the Monty Hall Problem if you do want to read up on it).