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Weekly Problem 11 - 2007

Stage: 3 and 4 Challenge Level: Challenge Level:1

$4/\pi$

The circumference of the circle is $2\pi$. This is the distance its centre moves each time the circle rolls for one revolution. When the circle moves from one corner to an adjacent corner, its centre moves a distance 2, so the circle makes $1/\pi$ revolutions. As it needs to do this four times before the circle returns to its original position, the number of revolutions is $4/\pi$.

This problem is taken from the UKMT Mathematical Challenges.

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