In yesterday’s post I posed a problem that has been the subject of much debate and argued amongst greater minds than even my Mensa brain.

One thing I should have added was that Chris Tarrant is the one who places the cheque in the box and therefore knows which one it is in.

The question was simply would you swop or keep with your original box?

Well, though the great minds may debate the puzzle, what isn’t in doubt is that you should ALWAYS SWOP from your original choice and the mathematics go something like…

When you first make your choice you have a 1 in 3 chance of getting it right. More importantly this would mean that you have a 2 in 3 chance of getting it wrong.

So when Tarrant dismisses one of the remaining two boxes your chosen box still gives you a 1 in 3 chance of winning while the other remains a 2 in 3 chance. This is because Tarrant has knowingly taken away an empty box.

By not switching you will only win once every 3 times you play and lose the other two.

By switching though you can expect to lose 1 time in 3 and therefore win 2 times out of 3.

If you’re still not sure you can try a working mock-up of the game (using cars and goats) at The New York Times website….

http://www.nytimes.com/2008/04/08/science/08monty.html?_r=1#

….Still baffled? Try the same problem with the lottery. If you picked your 6 numbers for the draw they would be approx 14 million - 1 to be the winning numbers. Not very good odds and there is a very high probability that you don’t have the correct entry.

Now imagine that Camelot ring you up to say that they will eliminate all but 2 of the possible number combinations and one of the lines will definitely win.  They give you the choice of your 6 numbers or one other set of 6 on the condition that you can only place 1 line.

I think you’d have to agree that given the poor odds you were of winning the Lottery before the phone call you’d be a fool not to use the other 6 numbers.

And if you still ended up losing then I’m afraid to say that you are the unluckiest man/woman on the planet!

Good luck,

Gavin.

P.S. With all this talk of the lottery going on I’ve got Dylan to use his Bingo machine again to pick me 3 lots of 6 numbers for tomorrow nights main draw. Much more fun than getting 24 strangers together and adding up columns of numbers. I’ll be placing the lines for the £100 to A Grand challenge and unlike Derren Brown I will put the numbers up on the page before the draw is made!

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