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?

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 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.

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

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 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 the equations to identify the clue numbers in this Sudoku 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?

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?

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.

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

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?

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

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

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.

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.

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?

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?

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?

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.

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

A Sudoku with clues given as sums of entries.

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 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?

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

A Sudoku that uses transformations as supporting clues.

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

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

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

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

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

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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

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?

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?

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

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

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

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

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?