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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.

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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?

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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?

Bird-brained

Stage: 5 Challenge Level: Challenge Level:1
If you are stuck on this, don't worry! It's not meant to be easy! If you're having problems with the graph, try calculating the value of p for some values of s and plotting points. This will help you to work out the general shape of the graph.
 
When working out what optimal egg size is, try defining the function that you are attempting to maximise - the payout. In this case this is the expected number of chicks that will hatch, which is equal to the number of eggs multiplied by the probability that each egg has of survival. What is the total number of eggs equal to? How might you go about working out what the maximum of a function is? Once you've defined your function it might help to sketch a graph of it.