Amazing Number Tricks
Want to amaze and astound your students? Here are seven classic number tricks which are guaranteed to surprise and delight. All these tricks have something in common – they are powered by maths, and the magic continues when pupils find out how maths makes them work.
It’s down to your judgement as a teacher to decide whether to ‘reveal’ the mathematical basis of the trick, or to let your pupils investigate it for themselves.
Think of a Number Trick
Think of a Whole Number
Double it
Add four
Then halve it
Then take away your original number
I can read your mind – is your number 2?
For anyone who is familiar with algebra it is easy to see what is going on here:
Original Number: x
Double it: 2x
Add four: 2x+4
Halve it: x+2
Take away your original number and you are left with the answer of 2.
While this is not the most complicated trick, it is nice to be able to show clearly why it works using algebra. Here is a worksheet where pupils can analyse lots of other similar Number Tricks using algebra. Pupils will also enjoy making up their own number tricks and trying them out on their friends.
Repeated Digit Trick (Calculator Trick)
Think of a number between 1 and 9. This is your ‘Magic Number’.
Multiply it by 3
Then multiply by 12345679 (Yes you are correct, the 8 is missing from this number.)
Multiply by 3 again
What do you notice?
For example, choose 5
5 x 3 = 15
15 x 12345679 = 185185185
185185185 x 3 = 555555555
This trick relies on the prime factorisation of 111111111
111111111= 3 x 3 x 37 x 333667
This trick also uses the quirky fact that 37 X 333667 = 12345679 which feels like a special number to use. There are other tricks using the idea of ‘repunits’ – numbers which only contain the digit one. Here are some of the prime factorisations of repunits. Which ones do you think you could use to create your own number trick?
111 = 3 x 37
1111 = 11 x 101
11111 = 41 x 271
111111= 3 x 7 x 11 x 13 x 37
For this trick we were inspired by a similar trick from the great Rob Eastaway, Broadcaster and Director of Maths Inspiration.
(Binary) Magic Card Trick
Top Tip: Don’t mention the word Binary unless you want to spoil your trick!
First, download and print these six cards.
Shuffle them up and give them to your volunteer. Ask them to look at the cards and choose a number which appears somewhere on the cards. This is their ‘Magic Number’.
Ask your volunteer to divide the cards into two piles. One pile contains the cards with their number on. The other pile contains the cards without their number on.
Option 1: Look at the pile of cards containing their number. Add up all the numbers on the top left space on each card (first row, first column). This is their Magic Number!
Option 2: Look at the pile of cards which don’t contain their number. Add up the numbers on the top left space on each card. Mentally subtract this total from 63. This is their Magic Number!
This trick relies on Binary. For example, if you choose the number 41, then it appears on the cards with 1,8 and 32 in the top left corners. This is because 41 is 101001 in Binary. 41 = 32+8+1. For a general introduction to Binary Numbers look at this BBC Bitesize page.
What's in a Name Trick
Think of a whole number 1-100.
Write down the name of your number as word.
Count the number of letters, giving you a new number.
Now write down the name of this new number as a word.
Carry on this process and stop when you have written down the same number as a word three times.
I can guess the number you have written. Is it Four??!!
This trick relies on the fact that Four is the only number in the English Language which is the same size as the length of its written name. Pupils might want to investigate different numbers. Which numbers reach ‘Four’ in the most/fewest steps?
1089 Trick
This famous trick was popularised by mathematician and author David Acheson who wrote the great little book 1089 and All That.
“Take any 3-digit number in which the first and last digits differ by 2 or more.
Reverse the number,
and subtract the smaller of the two numbers from the larger (e.g. 782-287=495).
Then reverse the result and add
(thus 495+594=1089).”
David Acheson writing in Plus Magazine.
The answer will always be 1089. To find out how the trick works, check out this video.
Two Dice Trick
Ask a volunteer to roll two standard six-sided dice. For simplicity try and use two different colours, such as a red and a yellow dice. Stand far enough away from your volunteer so that you can’t see the dice.
On a piece of paper ask your volunteer to write down four answers.
Multiply together the numbers which are on the top two faces of the dice.
Multiply together the numbers which are on the bottom two faces of the dice.
Multiply together the top number of the red dice with the bottom number of the yellow dice.
Multiply together the top number of the yellow dice with the bottom number of the red dice.
Add your four answers together. I can read your mind – it’s 49!
This trick uses the awesome fact that on a standard dice, opposite faces always add up to seven!
Using algebra, let the top face of the red dice be ‘a’ and the top face of the yellow dice be ‘b’.
Then your whole calculation is ab+(7-a)(7-b)+a(7-b)+b(7-a). If you simplify this, you will be left with 49.
Matrix Trick
Draw a 4 x 4 grid containing the numbers 1-16 in ascending order:
Ask a volunteer to choose a number. Cross out all the other numbers in that row and column.
Then choose another uncrossed out number. Cross out all the other numbers in that row and column.
Continue until your volunteer has selected four numbers and crossed out all the other numbers.
Add up the four numbers. I can read your mind – you have 34!
For an explanation of this problem check out the NRich website and the solutions which were submitted by students. To make it more interesting, challenge pupils to draw grids containing other sequences of ascending numbers (e.g. 2-17). To disguise their grids further, it is possible to swap columns and with other columns and then to swap rows with other rows.
Stage Craft & Performance
Image by OpenClipart-Vectors from Pixabay
To deliver a successful Number Trick it is also worth paying attention to your stage craft. Take some time to develop a convincing story around your trick. Think up some ingenious banter and make sure you practise before hand, so you are not caught having to peek at your notes. Before long you will be your school’s resident mathemagician!
------
Keep up-to-date with the latest Maths Scholarships news:
Find us on X (Twitter), Instagram, LinkedIn, YouTube, and Facebook.
Join our mailing list or get in touch Here.