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The chess board

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 ?

Bella

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