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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:

Note that after the payments on the 1st June 2009 the debts will be

100,000 (1+R) - P

where R is the interest rate and P is the payment.

The interest charged in the second year will be (1+R) lots of this amount