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?

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

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?

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.

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.

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?

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?

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.

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

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

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

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?

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

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.

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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.

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

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

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

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.

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

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

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.

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

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

A Sudoku that uses transformations as supporting clues.

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

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

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

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?

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.

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?

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

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

A Sudoku with clues given as sums of entries.

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

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

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

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

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. . . .

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

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