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?
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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!
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.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
What happens when you add the digits of a number then multiply the
result by 2 and you keep doing this? You could try for different
numbers and different rules.
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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!
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Explore Alex's number plumber. What questions would you like to
ask? Don't forget to keep visiting NRICH projects site for the
latest developments and questions.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
Number problems at primary level that may require determination.
Number problems at primary level that require careful consideration.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
There were 22 legs creeping across the web. How many flies? How many spiders?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
This group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
What is happening at each box in these machines?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
This number has 903 digits. What is the sum of all 903 digits?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?