### 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 $1 200. What were the assets of the players at the beginning of the evening? ### Oh for the Mathematics of Yesteryear A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45 days against the siege of the enemy? # Cereal Mix ##### Age 11 to 14 Challenge Level: A farmer is supplying a mix of seeds, nuts and dried apricots to a manufacturer of crunchy cereal bars. The ingredients cost: • dried apricots$£7$per kg • nuts$£6$per kg • seeds$£4$per kg He has been asked to supply a mix which costs$£5\$ per kg.

What combination of ingredients could he supply?

Is there a relationship between the amounts of each ingredient that he could supply?