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

This Sudoku, based on differences. Using the one clue number can you find the solution?

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?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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?

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.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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.

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.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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

A few extra challenges set by some young NRICH members.

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

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 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.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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. . . .

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

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

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

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

A challenging activity focusing on finding all possible ways of stacking rods.

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

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

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

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?

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?

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?

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?