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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.

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!

Really Mr. Bond

Age 14 to 16 Challenge Level:

115 2 = (110 x 120) + 25
that is 13225

895 2 = (890 x 900) + 25
that is 801025

Can you explain what is happening and generalise?