### How Big?

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

### 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? ### Oh for the Mathematics of Yesteryear A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45 days against the siege of the enemy? # Mixing Paints ##### Stage: 3 Challenge Level: Experiment with different combinations of paints A and B (and paints C and D). The ratio$1:4 = 2:8 = 3:12 = 4:16$... The ratio$1:5 = 2:10 = 3:15 = 4:20\$ ...

B is whiter than A (and D is whiter than C), so what will be special about the combinations that achieve the paler shades of pink?

What is the relationship between the ratios of the original paints and the ratio of the mix?