What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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!
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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 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!
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
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?
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?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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?
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
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?
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. . . .
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.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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
Number problems at primary level that require careful consideration.
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
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.
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
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?
Here is a chance to play a version of the classic Countdown Game.
There are four equal weights on one side of the scale and an apple
on the other side. What can you say that is true about the apple
and the weights from the picture?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.