### 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?

### Cushion Ball

The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

# Epidemic Modelling

##### Stage: 4 and 5 Challenge Level:
There are many variables in this model. You will need to choose your variables and carry out the trial a sufficient number of times to suggest a theory about the likely outcome when the disease has 'run its course'. Then change only one variable and repeat the experiment and see whether the outcome changes and if so how it changes.