### 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.

### Factorial

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

### Rachel's Problem

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

# Fracmax

##### Stage: 4 Challenge Level:

Find the maximum of

$${1\over p} + {1\over q} + {1\over r}$$

where $p$, $q$ and $r$ are positive integers and

$${1\over p} + {1\over q} + {1\over r} < 1.$$

Prove that it is indeed a maximum.