Are these statements always true, sometimes true or never true?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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
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 ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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?
Here are two kinds of spirals for you to explore. What do you notice?
This challenge is about finding the difference between numbers which have the same tens digit.
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?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Find the sum of all three-digit numbers each of whose digits is
This activity involves rounding four-digit numbers to the nearest thousand.
This challenge asks you to imagine a snake coiling on itself.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
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?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
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?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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.
Nim-7 game for an adult and child. Who will be the one to take the last counter?
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.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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 two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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.
What happens when you round these three-digit numbers to the nearest 100?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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