Mind read any number

There are many algebraic number-guessing tricks. An example could be:

1) Pick any number from 0 to 10
2) Times it by 9
3) Add the digits together
4) Subtract 4
5) Divide it by 5
6) Mind read.
7) Your final number is 1.

These tricks are easy to understand with simple algebra. Using the fact that the base 10 number system allows us to represent the 10s digit as “10m” or the hundreds digit as “100n”, you can create your own number-guessing magic trick. The proof of the trick above is here:

Let the number chosen by the participant be “y”.
In step 1 : y * 9 = y * (10-1)
Then: y * (10-1) = 10y - y = 10(y-1) + (10-y)
so therefore : y * 9 = 10(y-1) + (10-y)
Allow the 2 digit number resulting from y * 9 to be represented by 10m + n (with “m” representing the digit in the 10s place and “n” representing the digit in the units place).
In this case, m=(y-1) and n=(10-y)

So adding the digits together is m+n=(y-1)+(10-y)= 9
Therefore the participant will always attain the number 9 at this stage.

In the next stage: 9 - 4 = 5 and then 5/5=1

So no matter which number the participant started with, they end with 1.

Admittedly, these tricks are only entertaining for those who have not yet learned algebra. It is often the case that proving the trick works is more interesting. If you come up with a better trick then the example above, send it to us via the “contact us” page.