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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?


Stage: 3 Short Challenge Level: Challenge Level:1


The shaded area in Y is clearly half the area of the hexagon and the diagram below demonstrates why the shaded areas in X and Z are also both equal to half the area of the hexagon

This problem is taken from the UKMT Mathematical Challenges.