Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Use Farey sequences to obtain rational approximations to irrational numbers.

Investigate Farey sequences of ratios of Fibonacci numbers.

Can you find the maximum value of the curve defined by this expression?

How do you choose your planting levels to minimise the total loss at harvest time?

Small circles nestle under touching parent circles when they sit on the axis at neighbouring points in a Farey sequence.

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

In this article Jenny talks about Assessing Pupils' Progress and the use of NRICH problems.

This article sets some puzzles and describes how Euclid's algorithm and continued fractions are related.

The first of three articles on the History of Trigonometry. This takes us from the Egyptians to early work on trigonometry in China.