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?

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

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?

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

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.

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.

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.

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.

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.

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

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

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?

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

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?

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

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.

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

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

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

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

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. . . .

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

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 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?

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

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

A Sudoku based on clues that give the differences between adjacent cells.

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

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

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

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

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

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

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

Can you swap the black knights with the white knights in the minimum number of moves?

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

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?

What is the smallest perfect square that ends with the four digits 9009?