The chess board

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

Scroll down for a solution to this problem.


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.


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 ?


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