In this article, the NRICH team describe the process of selecting solutions for publication on the site.

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

This article for primary teachers suggests ways in which to help children become better at working systematically.

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

Given the products of diagonally opposite cells - can you complete this Sudoku?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Solve the equations to identify the clue numbers in this Sudoku problem.

A Sudoku with clues given as sums of entries.

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

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

A Sudoku that uses transformations as supporting clues.

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

Two sudokus in one. Challenge yourself to make the necessary connections.

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

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.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Each clue number in this sudoku is the product of the two numbers in adjacent cells.

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

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

Two sudokus in one. Challenge yourself to make the necessary connections.

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

You need to find the values of the stars before you can apply normal Sudoku rules.

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

Can you find all the different triangles on these peg boards, and find their angles?

Use the differences to find the solution to this Sudoku.