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?

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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.

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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?

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?

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

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

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.

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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?

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.

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.

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

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

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

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

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

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

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. . . .

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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 Sudoku that uses transformations as supporting clues.

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

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.

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

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

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

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?

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?

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.

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?

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

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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

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.

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