## … and one and a half brainteaser

By David Shaw, 7 December 2020

**Difficulty: Extreme**

I’m thinking of a number. When you add one and a half to it, you get the same result as if you multiplied it by one and a half.

What’s the number I’m thinking of?

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

It might be easier if the puzzle is written as an equation:

_ + 1.5 = _ x 1.5

## Brainteaser answer

One way to solve this is to look at each operation as an increase.

• When you add one and a half to the number, you increase it by 1.5.

• When you multiply the number by one and a half, you increase it by half the number.

These increases must be the same. That means half the number is 1.5, so the number is 3.

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