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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.

How Long Is the Cantor Set?

Age 11 to 14 Challenge Level:

In the problem The Cantor Set, we met the Cantor set, which is the limit of $C_n$ as $n$ tends to infinity.
C_1, C_2, C_3

We can talk about the length of one of our sets $C_n$.
The set $C_1$ has length 1.
The set $C_2$ has length $\frac{2}{3}$, as this is the total length of the line segments in $C_2$.

What are the lengths of $C_3$, $C_4$ and $C_5$?

Can you find a general expression for the length of $C_n$?

By considering what happens as $n$ tends to infinity, can you find the length of the Cantor set?