The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

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?

A Sudoku that uses transformations as supporting clues.

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

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.

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.

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.

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?

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

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

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

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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.

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?

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?

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

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

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

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

Use the differences to find the solution to this Sudoku.

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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

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. . . .

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

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

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.

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.

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

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

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 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.

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

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 challenge extends the Plants investigation so now four or more children are involved.

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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.

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