Mathematical Modelling - November 2007, Stage 3&4

Problems

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Twisting and Turning

Stage: 3 Challenge Level: Challenge Level:1

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

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More Twisting and Turning

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Turning Tangles

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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All Tangled Up

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you tangle yourself up and reach any fraction?

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Under the Ribbon

Stage: 4 Challenge Level: Challenge Level:1

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

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The Legacy

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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The Fire-fighter's Car Keys

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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 ?.

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The Invertible Trefoil

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

When is a knot invertible ?

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Funnel

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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 ?

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Cola Can

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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