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 differences to find the solution to this Sudoku.

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

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?

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

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.

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?

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

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

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

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?

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

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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?

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

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

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

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

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

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

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

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

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

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

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.

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

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

This challenge extends the Plants investigation so now four or more children are involved.

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

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

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

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.

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.

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?

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

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

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

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?

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.

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.

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

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

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. . . .

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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?