Given the products of diagonally opposite cells - can you complete this Sudoku?

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

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.

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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

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.

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.

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

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

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

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

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.

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.

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

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

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

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

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

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.

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.

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

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.

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. . . .

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

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.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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

A Sudoku that uses transformations as supporting clues.

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.

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?

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

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.

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

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

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

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?

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?

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?

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

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

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