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:

Substitute some numerical values in a systematic way and make a conjecture about the maximum. Then prove your conjecture.