### Farey Sequences

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

### 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 $1 200. What were the assets of the players at the beginning of the evening? ### Plutarch's Boxes According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes? # Rod Fractions ##### Age 11 to 14 Challenge Level: Terry from Warren Comprehensive School sent us his solution to this problem: The Red rod is$\frac{1}{4}$of the Brown rod. The Green rod is$\frac{2}{3}$of the Blue rod. The Pink rod is$\frac{2}{5}$of the Orange rod. The Green rod is$\frac{3}{10}\$ of the Orange rod.

The method for working out the short rod as a fraction of the long rod is:

When you complete the rows of rods so that they match, the number of long rods is the numerator for the fraction and the number of short rods is the denominator for the fraction.

It is easy to see why this works when you use only one long rod - you can return to the interactivity to see why this works in general.

Well done Terry.