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.

Design your own scoring system and play Trumps with these Olympic Sport cards.

One day five small animals in my garden were going to have a sports day. They decided to have a swimming race, a running race, a high jump and a long jump.

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

Did you know that ancient traditional mazes often tell a story? Remembering the story helps you to draw the maze.

Can you spot circles, spirals and other types of curves in these photos?

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

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Can you lay out the pictures of the drinks in the way described by the clue cards?

Here's a very elementary code that requires young children to read a table, and look for similarities and differences.

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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

This problem is designed to help children to learn, and to use, the two and three times tables.

Some children have been doing different tasks. Can you see who was the winner?

Can you each work out what shape you have part of on your card? What will the rest of it look like?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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?

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

Looking at the 2012 Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place?

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Can you rank these quantities in order? You may need to find out extra information or perform some experiments to justify your rankings.

Can you place these quantities in order from smallest to largest?

How many legs do each of these creatures have? How many pairs is that?

You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need.

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

Written for teachers, this article discusses mathematical representations and takes, in the second part of the article, examples of reception children's own representations.

Can you draw the shape that is being described by these cards?

A random ramble for teachers through some resources that might add a little life to a statistics class.

Using the 8 dominoes make a square where each of the columns and rows adds up to 8