### 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?

### One Basket or Group Photo

Libby Jared helped to set up NRICH and this is one of her favourite problems. It's a problem suitable for a wide age range and best tackled practically.

# Below 400

##### Stage: 4 Short Challenge Level:

440

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.

This problem is taken from the UKMT Mathematical Challenges.