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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?
Stage: 3 Challenge Level: 
An elephant, a hippopotamus and a rhinoceros are entered for a
race. The odds for the rhinoceros and the hippopotamus are:
2 to 1 against the rhinoceros winning and
3 to 2 against the hippopotamus winning.
What are the odds against the elephant winning if the race?
Editor's note: The hint explains 2 to 1 against in fractional form
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.