Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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?
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
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!
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 Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Choose a symbol to put into the number sentence.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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!
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
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 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 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?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
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?
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 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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
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?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Ben has five coins in his pocket. How much money might he have?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
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?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
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
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
This is an adding game for two players.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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.