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

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?

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.

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

Use the differences to find the solution to this Sudoku.

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?

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

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.

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

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

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?

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.

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.

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?

A Sudoku that uses transformations as supporting clues.

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.

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

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Given the products of adjacent cells, can you complete 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?

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.

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

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.

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

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.

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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.

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

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.

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

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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?

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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

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. . . .