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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?

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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?

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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.

The Greedy Algorithm

Age 11 to 14 Challenge Level:

Is your fraction bigger than $\frac{1}{2}$?
If not, is it bigger than $\frac{1}{3}$?
If not, is it bigger than $\frac{1}{4}$?
Now subtract the largest unit fraction you can.

Here's another example of the Greedy Algorithm at work...

$\frac{4}{5} = \frac{1}{2} + \frac{3}{10}$

$\frac{3}{10} = \frac{1}{4} + \frac{1}{20}$


$\frac{4}{5} = \frac{1}{2} + \frac{1}{4} + \frac{1}{20}$

If you're not sure which is bigger, you could use a calculator and convert your fractions into decimals.