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 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?

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?

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.

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

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 NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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.

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?

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

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

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.

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

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.

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?

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?

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

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 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?

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?

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

Use the differences to find the solution to this Sudoku.

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

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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. . . .

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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

A Sudoku with clues given as sums of entries.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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

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

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

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

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.

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?

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?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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

How many different symmetrical shapes can you make by shading triangles or squares?

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?