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Farey Sequences

There are lots of ideas to explore in these sequences of ordered fractions.

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Do Unto Caesar

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?

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Plutarch's Boxes

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?

Diminishing Returns

Age 11 to 14 Challenge Level:

Try making the pattern by folding and cutting up two squares of paper in contrasting colours.

How does this help you work out what proportion of the total area of the square is taken up by each colour?