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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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How many zeros are there at the end of the number which is the product of first hundred positive integers?

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Rachel's Problem

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!


Age 14 to 16 Challenge Level:

In order to maximise the reciprocals we want to make $p$, $q$ and $r$ as small as possible. What happens when $p\geq 3$? Investigate values for $p=2$.