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.
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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
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 were 22 legs creeping across the web. How many flies? How many spiders?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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 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?
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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?
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?
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
How would you count the number of fingers in these pictures?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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 same height?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
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 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?
Find the next number in this pattern: 3, 7, 19, 55 ...
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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
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.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
What is happening at each box in these machines?
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?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
Number problems at primary level that may require determination.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
This number has 903 digits. What is the sum of all 903 digits?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Number problems at primary level that require careful consideration.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?