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Coloured Black

Age 14 to 16 Short Challenge Level:

A square ink stamp has sides of length 1 cm.

It is covered in black ink and carefully placed in the middle of a piece of white paper.

The stamp is then rotated $180^o$ about one of its corners so that all of the square remains in contact with the paper throughout the turn, leaving a black trail.

The stamp is then removed from the paper.

What area of paper, in cm$^2$, is coloured black?





This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.