Mathemagic: Shopping Spree

There are many mathematical effects but the majority of them fail to be of broad interest because they are presented as puzzles. I'm not against puzzles per se but for many young people they are annoying and symbolise the bad things about school - confusing things that have no relevance to my life.

This effect is an old one that is describes in many early 20th century magic books. The presentation here is what is important. Its based on an emotional hook that everyone can get into and is adapted from a version shown to me by Jeff McBride which he calls The Object of Desire.

You place a wallet, purse, or envelope (I use a back pocket cut off some jeans) on the table before beginning, ask everyone to close their eyes (optional but fun), then read the following aloud.

Shopping Spree

Imagine that you are shopping, looking at all the new things in the windows of the shops.

Something catches your eye. Something you really, really, really, want. You'd like to buy it so you look in your pocket, You have only pound coins and one or a few notes. You add them up.

Now remember how much you have.

Unfortunately the thing you want to buy is too expensive so you head for home to see if you have any more money there.

On the way you meet a friend and tell them about the thing you want to buy. They lend you the same amount of money that you have in your pocket.

Add them together and remember how much you now have.

You go back to the shop but the thing you wanted has been sold.

You go home feeling a little bit fed up. At home you find a letter saying that you have won a competition and with the letter there is a £10 note.

Add this to the money in your pocket and remember how much you now have.

Your friend calls and tells you that they have seen the thing you are looking for in a different shop so you dash out to get it. It costs half the amount of money you have in your pocket.

Remember how much you now have left.

Your friend meets you at the shop to admire your new purchase. You give them back the money you borrowed.

Remember how much you now have left.


This is all imagination but here is reality. Open your eyes. Here is the pocket. How much money do you have left in your imaginary wallet?

£5?

Look in the pocket and you will find a £5 note

maths: x + x + 10/2 - x = 5

What is fun is how the emotional focus of thinking about something you really want to buy stops you thinking about the calculations. We all understand that your ability to think logically can vanish when you want to buy something and this provides an good story to wrap the maths in.

Lets be clear however, that I don't see this just a way sugar coating some maths in order to sneak it in. This is an exercise in imagination and memory as much as in mathematics.