# Mathematical Modelling - November 2007, Stage 3&4

## Problems

### Twisting and Turning

##### Age 11 to 14 Challenge Level:

Take a look at the video and try to find a sequence of moves that will take you back to zero.

### More Twisting and Turning

##### Age 11 to 14 Challenge Level:

It would be nice to have a strategy for disentangling any tangled ropes...

### Turning Tangles

##### Age 11 to 14 Challenge Level:

Look carefully at the video of a tangle and explain what's happening.

### All Tangled Up

##### Age 11 to 14 Challenge Level:

Can you tangle yourself up and reach any fraction?

### Cola Can

##### Age 11 to 14 Challenge Level:

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

### Under the Ribbon

##### Age 14 to 16 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

##### Age 14 to 16 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

##### Age 14 to 16 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

##### Age 14 to 16 Challenge Level:

When is a knot invertible ?

### Funnel

##### Age 14 to 16 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 ?