A calculator with a display and nine buttons.

Think of a number. Take a paper and a pen to do the following operations:

  • Calculate its double
  • Add 10 units to the result
  • Calculate its half
  • Subtract the number that you thought.

The number that you get after these five operations was 5, was not it? Can you explain the trick?

Explanation

Let xx be the number that you thought.

Then, the four steps are:

2x2x
2x+102x+10
2x+102=x+5\frac{2x+10}{2}=x+5
x+5x=5x+5-x=5

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