### 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!

### 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?

# Odd Differences

##### Age 14 to 16 Challenge Level:

 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. Note that 15 = 8² - 7² as well as 4² - 1². Write the number 105 as the difference of two squares in as many different ways as you can? The number 1155 can be written as the difference of two squares in eight different ways, can you find them?