### 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?

### Times Right

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

# Rachel's Problem

##### Stage: 4 Challenge Level:

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

(This problem was inspired by Rachel Galley's work on the problem called Giants in the June 1999 Six.)