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At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.

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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?

The Greedy Algorithm

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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...

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

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

so

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



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