The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Here is a chance to play a version of the classic Countdown Game.
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.
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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!
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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!
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
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
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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?
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?
Choose a symbol to put into the number sentence.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Use the information to work out how many gifts there are in each
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
If the answer's 2010, what could the question be?
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Number problems at primary level that may require determination.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Number problems at primary level that require careful consideration.
This number has 903 digits. What is the sum of all 903 digits?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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?
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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 complete this jigsaw of the multiplication square?