“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?

WOW! How do they do that?

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

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

(See below for free “think of a number” worksheets)

Table of Contents

## 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

### 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!”

### Now it’s your turn!

## FREE Worksheet to practise “Think of a Number” Questions

Want to practise “Think of a number” questions? Here’s a free resource to download.

## Recommended maths puzzle books

And if you like problem solving, delving into the maths, here is a selection of recommended maths books for all ages!

## Like this? Read more below…

## About Me

My name is Nicola Bhalerao and I am a private tutor based in Warwick. Since 2013, I have provided one-to-one tuition for children and adults. I specialise in maths tutoring, but cater for different requests, ranging from 11+ / entrance exams to various uses of maths, e.g. : interviews, job promotions, GCSE retakes, Functional Skills, nursing, teaching – any situation where **confidence** in maths is required.

My background is in computing, with a Computer Science degree from Warwick University. I have worked many years as a programmer, latterly in the games industry. Both my sons were tutored by me for the 11+ (they went to a local grammar school). I received training for teaching secondary school maths and I am fully CRB checked.

Read here for more information on **tuition for your child** or **tuition for yourself or another adult**.

"Nicola has been very supportive by helping me to fill in the blanks left over from my high school education. This has been crucial to improving my confidence in mathematics"

"I was lacking confidence in maths. Nicola was a fantastic teacher and really helped to improve my technique and approach to maths problems. She is patient, understanding and friendly"

"She was very friendly and professional. After a few sessions I felt much more confident in my ability and passed the numerical reasoning tests. She explains things very clearly"

"Nicola was a patient tutor, always helpful in answering any questions I had. I’d always found maths quite a scary subject, but through Nicola's tutoring I found I built confidence with the subject"

"Nicola has been very supportive by helping me to fill in the blanks left over from my high school education. This has been crucial to improving my confidence in mathematics"

"I was lacking confidence in maths. Nicola was a fantastic teacher and really helped to improve my technique and approach to maths problems. She is patient, understanding and friendly"

"She was very friendly and professional. After a few sessions I felt much more confident in my ability and passed the numerical reasoning tests. She explains things very clearly"

"Nicola was a patient tutor, always helpful in answering any questions I had. I’d always found maths quite a scary subject, but through Nicola's tutoring I found I built confidence with the subject"