“Think of a number” then they get you to add on something, double it, take away something, add 5, halve it, etc, etc, and then they tell you the number you now have?

Is it magic? Kind of. It’s mathematical magic!

Let me try to explain how it’s done, using the power of maths.

## Here’s an example of a think of a number trick you can use on your friends and family

Add four. Halve your answer.

Take away your original number.

The number you now have is 2.”

Maybe when you use it on your friends you want to don’t repeat it, else you’ll spoil the trick. But, if you read on some more about how it’s done, then you can create your own and many more to impress your friends with.

## “Think of a number” with pictures

So how does this work? Why does that “trick” always end up with 2?

To show this visually, in the table below I am representing the number you think of as a , and specific numbers added as tokens.

### Words

#### =

### Pictures

“Think of a number”

“Double it”

“Add four”

“Halve your answer”

“Take away your original number. Your answer is 2!”

## Think of a number explained with algebra

The above example, using the letter “x” for the number thought of, becomes this:

½ (2x + 4) – x

And if we simplify it (multiply out the brackets, then collect like terms and the x cancels out):

x + 2 – x

2

The answer is 2.

### Try with another number – how does this work?

As you can see from above, whenever we double x (our original number) we end up halving it and then taking away the x – hence it disappears.

But how did we get the final answer of 2? It came from halving the 4.

We can try this now with another number instead of 4, but always make it even as we need to halve it.

Let’s try 10…

Add ten. Halve your answer.

Take away your original number.

The number you now have is 5.”

½ (2x + 10) – x

x + 5 – x

5

Try it for yourself with any even number, you will always end up with half that!

## How can I make my own “think of a number” trick?

Yes, you can use the first number trick, maybe just the once, or maybe vary it slightly by adding a different even number each time, but how do you create your own?

The answer is that you can use the picture method above, trying different arithmetic until you “see” a final answer.

The only rules are, you can’t cut the original number up, or split the tokens apart!

### Words

#### =

### Pictures

“Think of a number”

“Add two”

“Times it by three”

“Take away your original number”

“Halve your answer”

“Take away your original number.

Your answer is 3!”