A square is divided by six line segments. What fraction is brown?

Scroll down for a solution to this problem.

## Solution

The brown fraction is 1/2.

Notice that the centre of the square coincides with a shared vertex of the smaller squares. Now rotating 90° around this centre, it is easy to see that the brown polygons map exactly onto the lighter ones and vice versa. Their total areas therefore are the same.

## Poem

Two colours

A black and white square

A game born in India

And called chaturanga

Chess a game of strategy

With much incertainty

Made of marble, wood or ivory

Gamers are like warriors

A mathematical battle

Queen and King and castle

They all join the fight

Who wins in the end ?