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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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!
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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!
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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
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 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?
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?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
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?
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 happens?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
What is the sum of all the three digit whole numbers?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
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 each time?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Find the next number in this pattern: 3, 7, 19, 55 ...
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?
Use the information to work out how many gifts there are in each pile.
How many starfish could there be on the beach, and how many children, if I can see 28 arms?
Number problems at primary level that require careful consideration.
Here is a chance to play a version of the classic Countdown Game.
What is happening at each box in these machines?
This number has 903 digits. What is the sum of all 903 digits?
Number problems at primary level that may require resilience.
Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?
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?
If the answer's 2010, what could the question be?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
How will you work out which numbers have been used to create this multiplication square?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
How would you count the number of fingers in these pictures?
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?
This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
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?
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.