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.

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

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

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 numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

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?

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?

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

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

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?

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

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?

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

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.

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?

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.

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.

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?

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?

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.

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.

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

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.

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?

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.

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

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

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

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.

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

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.

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

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.

This Sudoku requires you to do some working backwards before working forwards.

A Sudoku with clues given as sums of entries.

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

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

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

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?