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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.

Bull's Eye

Age 11 to 14 Challenge Level:
We have had correct responses to this problem from a number of students: Andrei Lazanu (aged 12) from No. 205 School in Bucharest (Romania), Chua Zhi Yu (aged 13) from River Valley High School in Singapore, Michael Brooker (aged 10) educated at home, Belinda Guo (aged 14) from Riccarton High School in Christchurch (New Zealand), Prateek Mehrotra, Sim Jingwei (aged 12) from Raffles Girls' Primary School in Singapore, and Fiona Watson from Stamford High School. Well done to you all.

Everyone reasoned in a similar way:

Area of circle $=\pi r^2$

Area of the largest circle $= \pi \times 7^2 = 49 \pi cm^2$

Area of the red ring $= \pi \times 4^2 - \pi \times 3 ^ 2 = 7 \pi cm^2$

$\frac{7}{49}= \frac{1}{7}$

The red ring is $\frac{1}{7}$ of the whole circle.

Area of the green ring $= \pi \times 6^2 - \pi \times 5^2 = 11 \pi cm^2$

The green ring is $\frac{11}{49}$ of the whole circle.