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# Bull's Eye

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### Chocolate

### Tweedle Dum and Tweedle Dee

### Sum Equals Product

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Age 11 to 14

Challenge Level

- Problem
- Student Solutions

The diagram below shows circles with radii 3, 4, 5, 6 and 7 cm.

What fractions of the largest circle are each of the two shaded regions?

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?

Two brothers were left some money, amounting to an exact number of pounds, to divide between them. DEE undertook the division. "But your heap is larger than mine!" cried DUM...

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 ï¿½ 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?