A Sudoku with clues given as sums of entries.

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

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

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.

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.

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

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.

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.

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

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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.

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you find all the different ways of lining up these Cuisenaire rods?

Find out what a "fault-free" rectangle is and try to make some of your own.

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

Can you find all the different triangles on these peg boards, and find their angles?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

How many different triangles can you make on a circular pegboard that has nine pegs?

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.

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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?

What happens when you try and fit the triomino pieces into these two grids?

How many different rhythms can you make by putting two drums on the wheel?

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.