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?

Plutarch's Boxes

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?

3388

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

Racing Odds

Age 11 to 14 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

Visualising. Calculating with ratio & proportion. Ratio. 2D shapes and their properties. Probability. Experimental probability. Similarity and congruence. Calculating with fractions. Tree diagrams. Theoretical probability. Fractions.