In this article, the NRICH team describe the process of selecting solutions for publication on the site.
A Sudoku with clues given as sums of entries.
A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
This article for primary teachers suggests ways in which to help children become better at working systematically.
Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.
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.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?
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.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Number problems at primary level that require careful consideration.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Find out what a "fault-free" rectangle is and try to make some of your own.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
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?
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.
How many different triangles can you make on a circular pegboard that has nine pegs?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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?
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?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
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 fill in the empty boxes in the grid with the right shape and colour?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
An investigation that gives you the opportunity to make and justify predictions.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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.