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Ball Bearings

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Air Routes

Find the distance of the shortest air route at an altitude of 6000 metres between London and Cape Town given the latitudes and longitudes. A simple application of scalar products of vectors.


The probability that a passenger books a flight and does not turn up is 0.05. For an aeroplane with 400 seats how many tickets can be sold so that only 1% of flights are over-booked?

Debt Race

Age 16 to 18
Challenge Level

On 1st June 2008 five people A, B, C, D and E each borrow $100,000.

Each year, starting 1st June 2009, each is charged interest on the amount owed at the start of the previous year, which is added to the balance. Each year, each will pay off a lump sum of their debt, which is taken from the balance.

The rates and amounts for each borrower is as follows:

3% 6% 9% 12% 15%
$12,000 $14,000 $16,000 $18,000

The question is this: Which borrower will be the first to pay off their debt?

Extension: You might like to consider the importance of the figure $100,000 in this calculation