## Peter’s staircase

By David Shaw, 5 September 2018

Peter’s just finished building a new staircase up to the attic. It just fits along the four-metre-long wall of his lounge room, and it’s three metres tall. It has exactly 15 steps.

Peter wants to have a carpet running along the staircase. How long does it need to be?

Scroll down for the answer!

## Brainteaser answer

You might be tempted to work out how big one step is, but you don’t need to! Here’s the quick way to solve the puzzle.

The carpet needs to cover both the front and the top of each step. The total height of all the fronts is three metres – the total height of the staircase. The total length of all the steps is four metres – the length of the staircase. Add them together and you’ll find the carpet needs to be at least seven metres long.

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