Before you start this trick, write the names of nine classes that students might be taking in a circular fashion as follows. Be certain to position MATH as shown, although the other eight positions can be anything that you want.
Tell students that they are going to pick their favorite subject with an experiment:
1. Choose a whole number with at least two digits (preferably three or more).
2. Write that number down.
3. Now mix up the digits any way that you wish to form a different number.
4. Subtract the smaller from the larger.
5. Find the sum of the digits of this answer and you have the magic number x.
6. Now begin counting at the top (BIOLOGY),
count around the circle in a clockwise direction
until you get to x, and that will be your favorite subject.
For example, if x = 6, then your favorite class would be Latin;
if x = 12, then your favorite class would be Spanish.
7. What is your favorite subject?
How does this work?
Everyone's favorite subject is math!
This works because the magic number x will always be a multiple of 9.
Therefore, you will always land on MATH.
In the two-digit case, for example, the original number can be expressed as 10x + y,
where x and y are the digits.
Its reversed form is 10y + x, and the subtraction yields 9x - 9y = 9(x - y)