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 about a fiendishly difficult jigsaw and how to solve it using a computer program.

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?

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.

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.

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

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

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

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

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.

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.

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.

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?

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 problem consists of a pair of linked standard Suduko puzzles each with some starting digits

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

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

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

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?

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?

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. . . .

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

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

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

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

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

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

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

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?

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

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.

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

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

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.

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

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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.

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

A Sudoku based on clues that give the differences between adjacent cells.

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

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?