# Mathematical Modelling - November 2007, Stage 4&5

## Problems

### Under the Ribbon

##### Stage: 4 Challenge Level:

A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ?

### The Legacy

##### Stage: 4 Challenge Level:

Your school has been left a million pounds in the will of an ex- pupil. What model of investment and spending would you use in order to ensure the best return on the money?

### The Fire-fighter's Car Keys

##### Stage: 4 Challenge Level:

A fire-fighter needs to fill a bucket of water from the river and take it to a fire. What is the best point on the river bank for the fire-fighter to fill the bucket ?.

### The Invertible Trefoil

##### Stage: 4 Challenge Level:

When is a knot invertible ?

### Funnel

##### Stage: 4 Challenge Level:

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

### Bridge Builder

##### Stage: 5 Challenge Level:

In this short problem we investigate the tensions and compressions in a framework made from springs and ropes.

### Overarch 1

##### Stage: 5 Short Challenge Level:

This short question asks if you can work out the most precarious way to balance four tiles.

### Odd One Out

##### Stage: 5 Short Challenge Level:

In this short problem, can you deduce the likely location of the odd ones out in six sets of random numbers?

### Making More Tracks

##### Stage: 5 Challenge Level:

Given the equation for the path followed by the back wheel of a bike, can you solve to find the equation followed by the front wheel?

### More Bridge Building

##### Stage: 5 Challenge Level:

Which parts of these framework bridges are in tension and which parts are in compression?