Just For Fun

The Magic Number 10 – A mathematical trick

Here’s another maths magic trick that you can use to impress your friends.

This trick works for ANY number that you choose.

Follow these instructions and you will always end up with 10.

  1. Pick a number.
  2. Multiply it by 3.
  3. Then add 30.
  4. Then multiply by 2.
  5. Then divide by 6.
  6. Subtract your original number.

You will always end up with 10 (if you did everything correctly!).

Let’s try an example.

Say we chose 16.
16 × 3 = 48
48 + 30 – 78
78 × 2 = 156
156 ÷ 6 = 26
26 – 16 (our original number) = 10.

Let’s try it with a bigger number.

Say we chose 335.
335 × 3 = 1005
1005 + 30 = 1035
1035 × 2 = 2070
2070 ÷ 6 = 345
345 – 335 (our original number) = 10.

You could spend all day trying every number you can possibly think of, it will always end up with 10!

Now, I know what question you are probably going to ask – why is 10 so special? Well, it isn’t.

This trick can be changed to work for any number. Before explaining how, let me first explain how this trick works.

How GCSE Maths Algebra can make you a magician

We can prove this will always work with a bit of help from our old friend, algebra.

Say the number you chose is x.

We are now going to use GCSE algebra to work out what number we will end up with.

First, we multiply x by 3, which gives us 3x
Then we add 30, which gives us 3x + 30
Then we multiply by 2, which gives us 2(3x + 30)
Expanding that bracket, we get 6x + 60
Then we divide by 6, which gives us (6x + 60) ÷ 6
Which when simplified, gives us x + 10
Then, we subtract the original number, which was x: x + 10 – x
Which leaves us with…. 10.

So, this is why it does not matter what value of x you chose, because the x’s always cancel out.

What this also means is that you can edit this trick with infinite possibilities.

So let’s say I didn’t like the number 10 and I wanted the magic number to be 12 this time. All I would need to do is change the third step.

Here, I have edited the trick so that 12 is the magic number. Adding 36 instead of 30 will lead to 12 being the end product as 36 ÷ 6 = 12.

  1. Pick a number.
  2. Multiply it by 3.
  3. Then add 36.
  4. Then multiply by 2.
  5. Then divide by 6.
  6. Subtract your original number.

Let’s try it.

Say I chose 44.
44 × 3 = 132
132 + 36 = 168
168 × 2 = 336
336 ÷ 6 = 56
56 – 44 (our original number) = 12.

Try creating your own unique maths magic trick! The possibilities are endless! Thanks, algebra!

There are many benefits to playing mathematical games like this. 

Firstly, they are good fun and you can amaze and entertain your friends and family, but also they are a great way to strengthen your mental maths muscles. If you can do the sums above without using a calculator then you will be exercising your brain and developing cognitive pathways that will help you throughout life, not just when it comes to passing your GCSE maths exams. 

We have a series of other exercises detailed in our blog, from helping you master your multiplication tables to mind-bending games such as Kaprekar’s Constant.

If you are struggling with any aspect of your maths revision, get in touch with us today to book a free session with one of our Bristol maths tutors. We can help make learning maths fun.

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