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?
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.
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.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
In this article, the NRICH team describe the process of selecting solutions for publication on the site.
A challenging activity focusing on finding all possible ways of stacking rods.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Follow the clues to find the mystery number.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Find out about Magic Squares in this article written for students. Why are they magic?!
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
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 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?
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.
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?
Can you use the information to find out which cards I have used?
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.
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?
A Sudoku with clues given as sums of entries.
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.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
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.
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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 a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
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?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
Can you fill in the empty boxes in the grid with the right shape and colour?