You will need a calculator with a square root button.

Enter your age (or any positive integer you want).

Take the square of it.

Add one to the result.

Now subtract twice your age.

Now hand me your calculator, and I will press one button and find your age.

(I press the square root button and mentally add one to the answer.)

Let’s try an example.

Suppose my age is 28.

I enter it into the calculator     28

I square it                                28*28 = 784

I add one to the result             784 + 1 = 785

I subtract twice my age           785 – 28 – 28 = 729

Now I hand the calculator to the person trying to guess my age.

The person takes the square root and mentally adds one to the answer

                    √729 = 27

                    27 + 1 = 28

The person says my age is 28. Correct!

Why does this give a correct answer?

Solution

Let A be your age.

Take the square of it: A*A.

Add one to the result: A*A + 1

Now subtract twice your age: (A*A + 1) – 2*A = A² - 2*A + 1 = (A – 1)²

You give me your calculator. I press the square root key and add 1 to the answer.

Now √((A-1)² )= A – 1

So, I add 1 to the result to get A.

No mystery!