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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Choose a symbol to put into the number sentence.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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!
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
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?
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?
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.
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?
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?
Can you hang weights in the right place to make the equaliser
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
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
This dice train has been made using specific rules. How many different trains can you make?
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?
This challenge is about finding the difference between numbers which have the same tens digit.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
Ben has five coins in his pocket. How much money might he have?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
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.
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?
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?
Find all the numbers that can be made by adding the dots on two dice.
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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!
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
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.