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.

How Old Am I?

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

Note that the number at the end of the $n$th row is $n^2$, so 400 will lie at the end of the 20th row. The row below will end in 21$^2$, i.e., 441, so the number directly below 400 will be 440.