Collaborative Choice

The effect is that the class all contribute to the free selection of a number which the teacher had predicted in advance.

To set up this trick you need to firstly choose the target number and write this down as your "prediction"! This should be done before the class have arrived for their lesson. Your prediction can be sealed in an envelope or, for more of a showy reveal, written on the back of a picture hanging in the room.

For the purposes of this explanation the target number is 36.9. Easy for you to remember as it is normal human body temperature (you knew that didn't you)?

So the trick begins with you asking a student at random to choose a number between 1 and 100 which you have written on the board like this:


If the student offers a number which is larger than the target number you replace the bottom number with the student's number, otherwise you replace the top number.

Let's imagine the student offers the number 40. Your board should now look like this:


The next number you ask for has to be between 1 and 40 (the new top and bottom numbers).

Let's imagine the next five students you pick at random offer the numbers 20, 30, 35, 37.5 and 36.5. Your board should now look like this:


Can you see how by deciding to put the students' numbers in either the top or bottom rows you are zooming in on the target number? Eventually one of the students will offer the target number. You then white it in large digits spanning both rows. You say something like "I think that's enough to ensure many of you have contributed to selecting the class' chosen number". You then reveal your prediction and all are amazed!


iPhone Calculation

This trick works best on the standard iPhone calculator though other calculators may have the same way of working and could also be used.

The effect is that pupils come up with random two and three digit numbers which you multiply together. Irrespective of what numbers they come up with the product will be the same as the number you had previously predicted.

To set up the trick you need to have previously chosen the large number as your prediction. This should be done before the class have arrived for their lesson. Your prediction can be sealed in an envelope or, for more of a showy reveal, written on the back of a picture hanging in the room.

The other essential part of the setup is to type your predicted number into the calculator then press the plus button, the zero button and the multiplication button … nothing else.

When the students call out their random two and three digit numbers you type them into the calculator pressing the multiplication button between each one. This should be done in full view of the students so that can see that you are not doing anything sneaky! After five or six numbers you press the equals sign and, as if by magic, the predicted number appears on the calculator screen. You then reveal your prediction and all are amazed!


How does it work? Well it involves the principle of the Order of Operations or BIDMAS. Let's imagine the students' numbers were 19, 345, 21, 999 and 456 and your prediction was 1,601,863.

The numbers entered into the calculator were:

1601863 + 0 x 19 x 345 x 21 x 999 x 456

The students didn't see the first two numbers entered as you did this before they arrived. The calculator performs the multiplications before the addition so the product of zero is added to your prediction. Magic!

Fibbing about Adding!

The effect is that you can add up ten numbers in your head faster than anyone in the class can do it with a calculator.

A volunteer from the class is chosen to be the calculator operator. Another student, with good handwriting, is chosen as the Scribe, to write on the board.

You, the teacher, and the calculator operator stand with your backs to the board so you can't see the numbers being written.

The scribe is told to write down a one digit number then, underneath that, to write a second one digit number.

A third number, the sum of the first and second numbers, should now be written down.

A fourth number, the sum of the second and third numbers, should also be written down.

The scribe continues to write down numbers, each one being the sum of the previous two, until there are ten numbers in the list altogether.

At this point you and the calculator operator turn to face the board in a race to find the total.

The trick is that rather than attempt to add all of the numbers together you simply multiply the seventh number by 11. It will give you the total that will take the calculator operator more time to work out. The class will be amazed at your numeracy skills!

How does it work? There are two tricks involved. The first is the quick way of multiplying by eleven and the other is related to the fact that this is a Fibonacci type sequence.

Let the first and second numbers selected be x and y respectively. The ten terms of the sequence will be x, y, x+y, x+2y, 2x+3y, 3x+5y, 5x+8y, 8x+13y, 13x+21y and 21x+34y.

The sum of this sequence is 55x + 88y which is 11 times 5x+8y.

Two Squares

This trick appears to be mathematical but perhaps it is not!





Coming Together


Playing Cards




Think of a number







Trick Tree

Update November 2014: The 96% and 85% on the tree diagram above were made-up figures for illustrative purposes only. We have now conducted our own survey to see what those figures should be. You can see the results on the Predictive Survey Results page.]

Amazing Adding








Letters In A Number







"Why does it always happen?"

"What about other languages?"


Mental Tricks


A list of such tricks can be found here.

Here are a couple of examples:

Quick Square


Q. What is 35 squared?
A. 3x4=12 stick on the 25

Do you know why it works?

Times Eleven


Q. What is 324 x 11 ?
A. Write down the first digit ... 3

The answer is 3564.

Try it yourself ... multiply 543 by 11

Do you know why it works?

Does it work for all three digit numbers?










"How does the trick work?"




The process continues. Sherlock uses the principles that:

Odd + odd = even

Even + even = even

Even + odd = odd

Odd + even = odd





Memory Tricks

A number of items can be memorised in order by associating each item with a place on a familiar journey.




One is bun
Two is shoe
Three is tree
Four is door
Five is hive
Six is sticks
Seven is heaven
Eight is gate
Nine is line
Ten is pen etc.




Mind Reading


Nine objects are arranged in a 3 by 3 grid formation

Magic 3 by 3



Students are encouraged to invent similar (more complex) illusions.



Numbered Cards


Magic Card



Here's a more detailed Interactive version
The Online Psychic

Real Magic Square



14 1 12 7
11 8 13 2
5 10 3 16
4 15 6 9





See also the Magic Square Puzzle.

Three Consecutive Primes (7,11,13)

The effect is that a pupil comes up with a three digit number and you challenge them to perform a calculation on that number using a calculator. You are always able to find the answer faster than thay can work it out.

The calculation involves multiplying the three digit number by 7, then the product is multiplied by 11 and then 13.

While the pupil is busy pressing buttons on the calculator you write down the three digit number twice to produce a six digit number which is the correct answer.

Example: 619

619 x 7 x 11 x 13

= 619619

It works because 7x11x13 is 1001.

Algebra Magic


Odds and Evens

Ask a friend to hold an odd number of coins in one hand and an even number of coins in the other but not to let you see. You will be able to work out in which hand the odd number of coins is hidden.

Ask the friend to multiply the number of coins in their left hand by three and the number of coins in their right hand by four then add the two totals together.

If the sum of their totals is odd then the odd number of coins is in their left hand otherwise the odd number of coins is in their right hand.

For a clue to realising why this trick works see Mix and Math.

Mathematical Mind Reader

Finally, a trick that is guaranteed to impress everyone you show it to. A trick people will beg you to show them how it works. This trick is truly mathemagical.

Student Activity

As this is the last trick in our collection we will let you ponder over it and discover the method for yourself. It is simple mathematics and if you try it enough times, keeping a record of your results, the secret will become clear. Good luck!

Mystic Mathematical Mind Reader

Your Magical Comments

D. Boyce, Rohwell

Monday, August 26, 2013


Sadhana Bhat,

Saturday, October 19, 2013

"Thank you and blessings."

Lisa Chalmers, Twitter

Sunday, September 6, 2015

"I did the collaborative choice 'trick' with yr7 last lesson Friday. Answer in an envelope. They whooped!"


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