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What fractions can you find between the square roots of 65 and 67?

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Canny Fraction

Weekly Problem 4 - 2012
What fraction of the volume of this can is filled with lemonade?

Circuit Training

Age 14 to 16 Challenge Level:

Running Clockwise

Why do runners always run around the track in an anticlockwise direction?

Do they develop a clinical lean?

Mike and Monisha meet at the race track, which is $400 \; \text{m}$ round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise, normally Mike can complete a circuit of the track in two thirds of the time Monisha takes.

They agree to stop when they both meet at the start again. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?