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?
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?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
This challenge is about finding the difference between numbers which have the same tens digit.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Find all the numbers that can be made by adding the dots on two dice.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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?
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?
Can you make square numbers by adding two prime numbers together?
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?
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?
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?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
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!
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.
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.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Number problems at primary level that require careful consideration.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
If the answer's 2010, what could the question be?
Can you hang weights in the right place to make the equaliser
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?
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?
Can you substitute numbers for the letters in these sums?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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.
Leah and Tom each have a number line. Can you work out where their counters will land? What are the secret jumps they make with their counters?