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?

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.

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

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

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 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.

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

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

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

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.

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?

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

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

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

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 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.

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

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

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.

The clues for this Sudoku are the product of the numbers in adjacent squares.

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

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

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

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

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

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

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.

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

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

A Sudoku with clues given as sums of entries.

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

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?

What is the smallest perfect square that ends with the four digits 9009?

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

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

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.

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

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

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