Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Choose a symbol to put into the number sentence.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Can you hang weights in the right place to make the equaliser
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 put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
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.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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!
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Here is a chance to play a version of the classic Countdown Game.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
If you have only four weights, where could you place them in order
to balance this equaliser?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Can you use the information to find out which cards I have used?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Can you substitute numbers for the letters in these sums?
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
An environment which simulates working with Cuisenaire rods.
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?