Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Find out about Magic Squares in this article written for students. Why are they magic?!
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Can you substitute numbers for the letters in these sums?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What two-digit numbers can you make with these two dice? What can't you make?
An investigation that gives you the opportunity to make and justify
What happens when you round these three-digit numbers to the nearest 100?
This activity focuses on rounding to the nearest 10.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Can you find the chosen number from the grid using the clues?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
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 task follows on from Build it Up and takes the ideas into three dimensions!
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
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.
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
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?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
My coat has three buttons. How many ways can you find to do up all
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?