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Euler's Squares

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

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Odd Differences

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

How much peel does an apple have?

Dating Made Easier

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

Graph showing gain and loss

If a sum invested gains $10\%$ each year how long will it be before it has doubled its value?

If an object depreciates in value by $10\%$ each year how long will it take until only half of the original value remains?

Why aren't these two answers the same?

Is there a rate, used for both gain and depreciation, for which those two answers would actually be the same?


If this problem caught your interest and you know some Stage 5 mathematics this Plus article on Carbon Dating could be a good next step for you.