Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
An investigation that gives you the opportunity to make and justify predictions.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Find the sum of all three-digit numbers each of whose digits is odd.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
Find out what a "fault-free" rectangle is and try to make some of your own.
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
How many centimetres of rope will I need to make another mat just like the one I have here?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
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 interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
This challenge asks you to imagine a snake coiling on itself.
It starts quite simple but great opportunities for number discoveries and patterns!
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.