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There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

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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?

Peaches Today, Peaches Tomorrow....

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2
The monkey will always keep a whole number of peaches.

For Part (ii), why not try a starting value and see what happens? Then decide whether you need to start with a bigger or smaller starting value next time.

For part (iii), you could use a tree diagram: at each stage, branch off the fractions it would be possible to try next so that all possibilities are checked.