in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

Use the clues about the shaded areas to help solve this sudoku

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

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.

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.

A Sudoku that uses transformations as supporting clues.

This Sudoku requires you to do some working backwards before working forwards.

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.

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

Find out about Magic Squares in this article written for students. Why are they magic?!

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

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

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. . . .

A Sudoku with clues given as sums of entries.

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

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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

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

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

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

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

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.

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

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

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.

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

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

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

The challenge is to find the values of the variables if you are to solve this Sudoku.

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

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.

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

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.