Three hundred and thirty-three.

Think of a number with three equal digits. Do the following operations:

  • Sum the three digits
  • Divide the number that you thought by the sum found in the first step.

The number that you get after these operations was 37, was not it? Can you explain the trick?

Explanation

Let xxx be the three equal digits number that you thought.

Then,

xxx=100x+10x+x

x+x+x=3x

\frac{xxx}{x+x+x}=\frac{100x+10x+x}{3x}

\frac{xxx}{x+x+x}=\frac{x\left(100+10+1\right)}{3x}

\frac{xxx}{x+x+x}=\frac{100+10+1}{3}

\frac{xxx}{x+x+x}=\frac{111}{3}=37

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