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?

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

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?

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?

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.

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.

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?

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?

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

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

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.

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 based on clues that give the differences between adjacent cells.

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.

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

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?

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

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

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?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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.

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

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.

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?

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.

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?

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?

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.

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?

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

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

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

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.

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?

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

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

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.

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?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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