### 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? # Punky Fish ##### Stage: 3 Short Challenge Level: If there are f females and m males then$86=8f+9m=8(f+m)+m$. Now$86=8\times 10+6=8 \times 9+14...$Only the first of these is feasible so m=6 and f=4. Therefore the ratio of male to female fish is$3:2$. Alternatively, dividing the stripes into groups of$8$, there are$6$left over. One left over is produced by each male, so there are$6$or$14$or... males. However, as$14 \times 9 = 126 > 86$, there must be six males. Then, this leaves$32$stripes remaining, so there are$4$females. Therefore the ratio of male to female fish is$3:2\$.

This problem is taken from the UKMT Mathematical Challenges.