### 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?

# Racing Odds

##### Stage: 3 Challenge Level:

This is a nice solution from Andrei of School 205 Bucharest. Thank you Andrei.

Looking at the first race.

If the odds are 2 to 1 against the rhinoceros, then the probability that the rhinoceros will win is 1/(1 + 2) = 1/3. For the hippopotamus, the probability that he will win is 2/(2 + 3) = 2/5.

The total probability (that there is a winner) is 1. So, the probability that the elephant will win is:

1 -1/3 -2/5 = 4/15

So, the odds for him are 11 to 4 against the elephant.