The one where you have 3 bulbs and 3 switches? You can turn any one on or off but can't change your mind after you have chosen?

Are they're in different rooms, so you can't see until you go look?

Yes, and one of them controls the release of a deadly gas into a box with a cat in it.

Whilst on a treadmill, trying to work out if it'll take off in an infinite resistor network...

Surrounded by lots of trees and no one around to hear anything.

When I read the first part of CW's original post, I thought it was Monty Hall, then I read the second part and went "Huh?"...

Going off-topic in my own thread, but the riddle is this:

You have a closet with a door in front of it. To one side of the door, there's three switches - all identical and unlabelled. There's a lightbulb inside the closet and one of the switches will control the lightbulb. The other two switches don't control the lightbulb. You have to guess which one. You can press the switches any number of times you wish, but once you have opened the door, you cannot press the switches and you must state which switch controls the lightbulb. There are no hints or tips such as light leaking around the door - the door is almost hermetically sealed.

HIGHLIGHT for answer

The answer is: Turn on switch A for a few minutes, turn it off. Then turn on Switch B and open the door and examine the lightbulb.

If the bulb is on, Switch B controls it.
If it is off, it is either Switch A or C.
Touch the light bulb. If it is warm, it must be A (as the bulb will still be warm from when it was lit).
If it is cold, if must be C.

Doesn't work so well for energy efficient bulbs, then...

That's basically the same as the three bulb puzzle.

Turn on A for a minute, then turn it off and and turn on B.

Go to the other room. The bulb that is lit is B, the warm bulb is A and the cold bulb is C.

Energy bulbs stay warm for quite a while, unless they're the very low wattage LED ones.

Back to the original topic and to clarify my original post.

The odds that the prize is behind the second door you open depends on when you decided which door to open second:-

If you decide, without opening any doors first, which sequence you will open the doors then the odds that the prize is behind the second door you open will still be 1 in 3. The odds that the prize is any door is 1 in 3. Whichever two doors you decide to open in whichever order, the odds that the prize is behind the second door always remain 1 in 3.

Now, the MH variant of this is essentially that you pick the two doors you want to open and then open the first one. If the prize is not behind the first door opened it it is prudent to change your choice of second door to open as the odds that the door you originally decided to open second has the prize behind it are 1 in 3 for but 2 in 3 against.

The final variant here is as follows. You only pick which door to open first and do so immediately. If there is nothing behind it you have reduced the odds that the second door you open will have the prize to 1 in 2. It doesn't matter which door you choose to open second as they now have equal odds of having the prize behind them.

It's only if you pre-determine which door you open second that the odds of the prize being behind the second door remain 1 in 3.

Does that make sense?

Here it is explained and demonstrated by Alan Davies and Marcus du Sautoy.

http://www.youtube.com/watch?v=axqT323GHVc

Can you guess who wins BEFORE you watch the experiment?

OK, here's another one.

3 women go to a restaurant for a meal.

At the end of the meal they get the bill for £15 (cheap I know). They give the waiter £5 each and he takes it to the manager to put into the till.

The manager realises that a mistake has been made and the bill should only be £10 so he gives the waiter £5 to give back to the women.

On the way back to the table he works out that he can't split the £5 into 3 so he deicdes to keep £2 for himself and give each lady £1 back.

Everything is done and the ladies leave.

So, the ladies paid £4 each (£5 minus the £1 they got back) and the waiter has £2 in his pocket.

That's a total of £14. What happened to the other £1?

Because there is 3 doors. Which makes your probability. 1/3

If you open one door out of the 3, and still the prize isn't there, your probability is 1/3 still, even though you've eliminated one door.

Just the same if you opened one door from the 3, and found the prize. The probability is still 1/3, with a hint of luck!

The ladies paid 5 pounds each. The bill was adjusted from 15 to 10.

15-10 = 5

The waiter pockets 2.

5-2 = 3

The waiter then distributes the remaining three to the ladies

3-3 = 0

There is nothing leftover.