Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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.
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.
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.
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.
Find out about Magic Squares in this article written for students. Why are they magic?!
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 particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Can you find all the different ways of lining up these Cuisenaire rods?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
An investigation that gives you the opportunity to make and justify predictions.
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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.
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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 four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other 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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these two grids?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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 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. . . .
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
Can you find all the different triangles on these peg boards, and find their angles?