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. . . .
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
There were 22 legs creeping across the web. How many flies? How many spiders?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
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?
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!
This challenge combines addition, multiplication, perseverance and even proof.
This task combines spatial awareness with addition and multiplication.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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.
An old game but lots of arithmetic!
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!
Use the information about Sally and her brother to find out how many children there are in the Brown family.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Number problems at primary level that may require determination.
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?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
This number has 903 digits. What is the sum of all 903 digits?
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Number problems at primary level that require careful consideration.
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?