Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
An investigation that gives you the opportunity to make and justify
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Got It game for an adult and child. How can you play so that you know you will always win?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
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.
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?
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?
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?
This activity focuses on rounding to the nearest 10.
Find the sum of all three-digit numbers each of whose digits is
This activity involves rounding four-digit numbers to the nearest thousand.
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you round these three-digit numbers to the nearest 100?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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.
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 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?
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.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
This challenge is about finding the difference between numbers which have the same tens digit.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
What happens when you round these numbers to the nearest whole number?
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.
This challenge asks you to imagine a snake coiling on itself.
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?
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?
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
Find out what a "fault-free" rectangle is and try to make some of
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?
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.