In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you replace the letters with numbers? Is there only one
solution in each case?
What two-digit numbers can you make with these two dice? What can't you make?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Can you find the chosen number from the grid using the clues?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Can you substitute numbers for the letters in these sums?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Follow the clues to find the mystery number.
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.
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Place the 16 different combinations of cup/saucer in this 4 by 4
arrangement so that no row or column contains more than one cup or
saucer of the same colour.
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
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?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
What could the half time scores have been in these Olympic hockey
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
Can you use the information to find out which cards I have used?
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?
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?
In how many ways can you stack these rods, following the rules?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?