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“Think of a Number” Trick – how do you do it?

31st October, 2020

You will have heard of that party trick where someone says,

“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?

"Think of a Number" Trick – how do you do it? 2
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.

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

“Think of a number, double it.

Add four. Halve your answer.

Take away your original number.

The number you now have is 2.”

"Think of a Number" Trick – how do you do it? 3
Try it yourself. Try it again with another starting number – the answer is ALWAYS 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 "Think of a Number" Trick – how do you do it? 4, and specific numbers added as "Think of a Number" Trick – how do you do it? 5 tokens.

Words

=

Pictures

“Think of a number”

"Think of a Number" Trick – how do you do it? 4

“Double it”

"Think of a Number" Trick – how do you do it? 4

"Think of a Number" Trick – how do you do it? 4

“Add four”

"Think of a Number" Trick – how do you do it? 4"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

"Think of a Number" Trick – how do you do it? 4"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

“Halve your answer”

"Think of a Number" Trick – how do you do it? 4"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

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

"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

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…

“Think of a number, double it.

Add ten. Halve your answer.

Take away your original number.

The number you now have is 5.”

"Think of a Number" Trick – how do you do it? 20
Demonstrated again with algebra:

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”

"Think of a Number" Trick – how do you do it? 4

“Add two”

"Think of a Number" Trick – how do you do it? 4"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

“Times it by three”

"Think of a Number" Trick – how do you do it? 4"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

"Think of a Number" Trick – how do you do it? 4"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

"Think of a Number" Trick – how do you do it? 4"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

“Take away your original number”

"Think of a Number" Trick – how do you do it? 4"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

"Think of a Number" Trick – how do you do it? 4"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

“Halve your answer”

"Think of a Number" Trick – how do you do it? 4"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

"Think of a Number" Trick – how do you do it? 5

“Take away your original number.

Your answer is 3!”

"Think of a Number" Trick – how do you do it? 5"Think of a Number" Trick – how do you do it? 5

"Think of a Number" Trick – how do you do it? 5

Now it’s your turn!

Nicola Bhalerao - Warwick Tutor

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+ to various computing skills, including website training.

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.

I am a WordPress expert at my other business, Smiling Panda Web Design, where I create quality websites with communication and trust.

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