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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...

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Lower Bound

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

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Sum Equals Product

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 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?

Weekly Problem 52 - 2008

Stage: 3 Short Challenge Level: Challenge Level:1
Of the $5$ tyres, $4$ are used at any one time, so each tyre is used for $\frac{4}{5}$ of the journey, or $$\frac{4}{5} \times 30000 \; \text{km} = 24000 \; \text{km}$$

This problem is taken from the UKMT Mathematical Challenges.

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