Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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.
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?
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
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.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Can you use the information to find out which cards I have used?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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 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?
Follow the clues to find the mystery number.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
A Sudoku with clues given as sums of entries.
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?
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. . . .
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
This challenge extends the Plants investigation so now four or more children are involved.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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.
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.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Use these head, body and leg pieces to make Robot Monsters which are different heights.
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you cover the camel with these pieces?
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?