Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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.
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.
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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 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?
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!
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
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?
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?
Number problems at primary level that require careful consideration.
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?
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?
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
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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
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?
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
If the answer's 2010, what could the question be?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Use the information to work out how many gifts there are in each
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.
How would you count the number of fingers in these pictures?
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
What is happening at each box in these machines?
Number problems at primary level that may require determination.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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.
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?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
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?
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?
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.