You are lost in an ancient, mountain top castle and cannot find your way out. The castle is deserted and there's no-one around to help you. Every door that looks like it might be a way out is locked. Eventually you meet a wise old man who offers to help and he leads you down some stone steps and into a long tunnel that runs beneath the castle.

The tunnel is carved deep into the rock and is lit by candles along its length. At the end of the tunnel are three doors and behind one of them, the man tells you, he has placed a golden key that will unlock any door in the castle, as well as a map that will guide you on your way. All you have to do is guess which door they are behind.

The doors are numbered, 1, 2 and 3. When you pick a door, the old man, who knows which door the key and the map are behind, will open one of the empty doors. He then gives you the choice to either stick with your chosen door or pick the other one. Would changing your mind improve your chances of picking the right door, or wouldn't it make any difference?

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This is a variation of an old classic and many of you may already know it, but did you know that it can also be turned into an impressive party trick? Read on to find out how. For those of you who have never come across this puzzle before here's the solution.

First of all remember that the old man knows which door the key and the map are behind. When you pick a door there is approximately a 66% chance that you are wrong, meaning there is a 66% chance that the key and the map are behind one of the other two doors.

Assuming that you are wrong and the items are behind one of the other doors, the old man will then show you the other empty door -- remember, if you are wrong then you've already picked one of the empty doors. That leaves the remaining door with the key and the map behind it, so when the man shows you an empty door, you'd be statistically better off changing your mind!

Party trick

To turn this into a party trick you need a participant, let's call him Jim, three upturned cups and something to place under one of them, like a coin. Without Jim looking you place the coin under one of the cups and ask him to touch the cup he thinks the coin is under. Let's say that Jim guesses incorrectly and you then show him the other empty cup.

Ask Jim if he'd like to stick with his original choice or change his mind. Unless he's a mathematician, the chances are he'll stick with his original choice, and the chances are he'll be wrong. Now you tell the audience that using your amazing powers, or whatever, you're going to challenge Jim 10 times to find the coin, and then you're going to get a member of the audience, or an assistant, to do it to you. You guarantee that you will correctly find the coin more often than Jim, and, with statistics on your side you probably will.

All you have to do is change your mind each time you are shown one of the empty cups. The more often you do this the greater are your chances of winning. It was once done on TV with 100 rows of three cups per person. They chose to do it so many times because the more you do it the more impressive the results are, in the sense that you will choose correctly a greater number of times. Nearly 70 out of 100 is more impressive than 6 or 7 out of 10!