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The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

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Peeling the Apple or the Cone That Lost Its Head

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

A plastic funnel is used to pour liquids through narrow apertures.

Have you ever tried pouring a drink from a glass back into a bottle ?

If we imagine a funnel as a complete cone (why isn't it?), what shape cone would use the least amount of plastic to manufacture a funnel containing a set volume?

You don't need a specified volume, but it may help to ask what proportion cone would hold a litre of liquid using the least amount of plastic.

See the Hint for more help.