### Chocolate

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?

### F'arc'tion

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.

### 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 $1 200. What were the assets of the players at the beginning of the evening? # The Cantor Set ##### Stage: 3 Challenge Level: Liam from Wilbarston School sent us this well-explained solution: Only the middle thirds of line segments are removed, so endpoints of line segments will not be removed. Therefore, all I need to do is determine which are endpoints and which are not.$\frac{1}{3}$is an endpoint of C2, so it is in the Cantor set.$\frac{3}{81}$=$\frac{1}{27}\frac{1}{27}$is an endpoint of C4, and therefore$\frac{3}{81}$is in the Cantor set.$\frac{4}{9}$is between$\frac{1}{3}$and$\frac{2}{3}$, thus it is in the middle third of C1 and is removed from C2 and as such isn't in the Cantor set.$\frac{4}{81}$is between$\frac{1}{27}$and$\frac{2}{27}\$ and therefore is in the middle third of C3.
It is removed from C4 and therefore does not belong.