### 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.

### Overarch 2

Bricks are 20cm long and 10cm high. How high could an arch be built without mortar on a flat horizontal surface, to overhang by 1 metre? How big an overhang is it possible to make like this?

### An Introduction to Complex Numbers

A short introduction to complex numbers written primarily for students aged 14 to 19.

# 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:  A B C D E 3% 6% 9% 12% 15%$12,000 $14,000$16,000 $18,000$20,000

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