Maths Busking, maths through street performance since 2010

Twenty Quid Game

Two players take it in turns to take one, two or three post-it notes (/pegs) from a pile/volunteer. The £20 note must be left until last, and the winner is the person who takes the £20 note on their turn.

Strategy for winning

Always let them go first or you will have to hope for a bit of luck! Multiples of four are key to winning this trick.
Start with 11 post-sticks and a £20 note OR 15 post-sticks and a £20 note, as each of these gives a multiple of 4 things.
Once your opponent has chosen their post-sticks, then take a number to give a total of 4. If they take 3, you take 1. If they take 2, you take 2.
If you go first, try taking 1 and hope that they will not take 3! As if your opponent take 1 or 2 then you can then take enough to reach that multiple of 4 and be back in the game.

The great puzzle writer Henry Dudeney created a harder version of this game in the early part of the 20th Century called The Pebble Game, see his book Amusements in Mathematics for more information.

Here is a version you can play with coins:
Two players place fifteen coins in front of them. Each then takes one, two or three coins on their turn. The winner is the player with an odd number of coins at the end of the game. For example if you end up with seven and your opponent has eight, you win.
How many coins should the first player take on their first turn, to guarantee winning?

The game of Twenty Quid has a long history in mathematics, see The Game of Nim for more information.

Trick Explanations


If you like this trick
you may enjoy the book:
Martin Gardner,
magic show
Penguin Books, 1985