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.

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

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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?

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.

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.

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

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 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. . . .

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

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

Can you use the information to find out which cards I have used?

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?

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.

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.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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

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?

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

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.

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

A Sudoku with clues given as sums of entries.

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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.

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.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

An investigation that gives you the opportunity to make and justify predictions.

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Number problems at primary level that require careful consideration.

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

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?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?