Step back and reflect! This article reviews techniques such as substitution and change of coordinates which enable us to exploit underlying structures to crack problems.

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

A pair of Sudoku puzzles that together lead to a complete solution.

From the atomic masses recorded in a mass spectrometry analysis can you deduce the possible form of these compounds?

How many generations would link an evolutionist to a very distant ancestor?

Four small numbers give the clue to the contents of the four surrounding cells.

This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits

A random ramble for teachers through some resources that might add a little life to a statistics class.

All the words in the Snowman language consist of exactly seven letters formed from the letters {s, no, wm, an). How many words are there in the Snowman language?

A small circle in a square in a big circle in a trapezium. Using the measurements and clue given, find the area of the trapezium.

This Sudoku, based on differences. Using the one clue number can you find the solution?

Like all sports rankings, the cricket ratings involve some maths. In this case, they use a mathematical technique known as exponential weighting. For those who want to know more, read on.

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

By inscribing a circle in a square and then a square in a circle find an approximation to pi. By using a hexagon, can you improve on the approximation?

In how many different ways can I colour the five edges of a pentagon red, blue and green so that no two adjacent edges are the same colour?

Using the 8 dominoes make a square where each of the columns and rows adds up to 8