5 Mathematical Bets That Will Win You Free Pints At The Pub

Squeeze coins through holes that should be too small, read people's minds, and work out their bank details – all using maths.

1. Bet someone that their pint glass has a bigger circumference than height.

Getty Images/iStockphoto JamieAW

Getty Images/iStockphoto JamieAW

A standard UK pint glass is actually around 1.8 times greater in circumference than in height, but you'd never guess from looking at it.

So when you are next in a pub, bet someone that their drinking vessel is further around than it is high. If there is a 'pot' beer glass (the ones with handles) in the pub, then you're sorted: they are typically three times as far around as they are tall, so you can dramatically stack two of them and claim it is still further around than up.

Producing a tape measure at this point may cause your victims to question the spontaneity of the whole exercise, so use a nearby straw as a makeshift ruler.

If you'd like to subtly check your drinking glass, try to wrap your hand all the way around it. Your fingers and thumb will not meet on the other side. But place your hand on the side of the glass and it'll probably reach all the way to the top.

2. Bet someone you can fit a two-pence coin through a hole the size of a five-pence coin.

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Draw a circle exactly the same size as a five-pence coin. Cut it out of the paper, leaving as perfectly circular a hole as possible. Your challenge now is to fit a two-pence coin through that hole without ripping the paper.

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A standard UK two-pence piece coin is 25.9mm across, making it substantially bigger than the 18mm-diameter five-pence hole you have cut out. It's entirely reasonable to expect that you cannot fit this larger coin through the smaller hole without ripping the piece of paper – but it can be done.

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Even though paper is a 2D surface, the key here is that it can be distorted in three dimensions. Instead of leaving the piece of paper flat, you can curve it into a 3D shape and the coin will easily pass through. Fold the paper in half so that the hole looks like a semicircle from the side. Then grasp each side and move them together so that the semicircular hole is stretched out. The two-pence piece will easily fit through the hole.

3. Bet someone that you can read their mind.

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Get your volunteer to take any number and multiply it by 9 (they can use their phone if they like). Then get them to tell you all the digits in the number except the last one.

All you need to do to work out the last digit is add up the ones they read out, and subtract that from 9.

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For example, say the volunteer starts with 27. They then multiply that by 9 to get 243. They'll read out the first two digits to you: "2, 4...". You'll add 2 to 4 to get 6. Then take 6 away from 9 to find 3 – which was the final number they didn't tell you earlier!

4. Bet someone you can find any card they choose from a deck.

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There is a whole class of magic tricks called self-working tricks which are really just magic by algorithm. As long as the magician follows the instructions step by step, the magic trick will always work.

This is one of them. Commonly called the Three Pile Trick, it's traditionally performed with 21 cards, for reasons I cannot fathom: exactly the same trick works with up to 27 cards.

The magician (that's you) boasts that she will find any card chosen randomly by a volunteer. Here's how to do it.

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1. Get your volunteer to pick a card from a deck of 27 cards, remember it, and replace it

2. Deals the cards out face up in three piles (consistently dealing one card on each pile at a time, in the same direction).

3. Get your volunteer to indicate which pile their card is in, but not what the card itself is.

4. Picks the piles up, putting the pile with their card in the middle of the pack.

5. Repeat steps 2, 3 and 4 twice.

Your volunteer's card is now exactly in the middle of the 27-card pack, i.e. it's the fourteenth card from the top. Then all you need to do is reveal the fourteenth card however you like.

BONUS ROUND: Instead of always placing the selected pile in the middle, a very carefully calculated combination of putting it top, middle and bottom can move their card to any position within the 27. Some extra working out required.

5. Bet your friend that if he reads all but one digit of his bankcard number to you, you can tell him the missing digit.

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There's a pattern built into all bankcard numbers so that it's easy to check if it is correct or not. It's how a website can instantly tell you if you made a mistake entering your number.

It is possible to use this knowledge in a magic trick so that if someone were to read all but one digit of a number to you, you can calculate the missing digit.

Extracted from Matt Parker's new book "Things to Make and Do in the Fourth Dimension"

Take out a bankcard and find the 16 digit number which appears on the front, then write out the digits on a piece of paper. Now cross out the first digit, then every alternate number.

Above each number you cross out, double the number and write the new digit above. If doubling a digit gives a two-digit answer, add those two digits together and write the total above. If you now add all the numbers together, I can guarantee that your total is a multiple of ten.

If someone gives you every digit from their bankcard except the last one, all you need to do is work out the difference between the total you find using this method, and the next multiple of ten. (In the example above, you'd get 73 and work out that the last digit was 80 - 73 = 7.)

If your friend is not impressed, you now have their bankcard details anyway. Go and treat yourself to something nice.

This is an edited extract from Matt Parker's new book, Things to Make and Do in the Fourth Dimension.