Magic in Mathematics

Magic in Mathematics

When you want to have fun with your schoolmates, if you have some curiosity, learn some "tricks" that involve mathematical operations. Apparently magic works when it says:

• Think a number.

• Multiply it by two

• Add 12

• Divide the sum between two

• Subtract the number you thought at the beginning

• The number that remains is 6.

In the same style are these games, where the residuals are 3, 5 and 15 respectively.

What is the secret? Actually, there is an algorithm with which you can create all the tricks of this group and any residue number. Note that the four basic mathematical operations are involved.

Think a number: a

Multiply it by n: n * a

Add a number m (this is the key to the trick): n * a + m (m must be a multiple of n)

Divide it between n: 1 / n * (n * a + m)

Since m is a multiple of n, say m = k * n, when dividing it remains: 1 / n * (n * a + n * k) = a + k

Finally, subtract the thought number: a + k - a = k

Result: M / n = k (always)

If you have understood the structure, you can instantly create any structure. Let's see:

Think a number: 4

Multiply it by 5, add 20, divide it by 5, subtract the number you thought. The result is the number of sides of the square? Do you think you can create another magic game with more mathematical operations?