Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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?
Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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!
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
An activity making various patterns with 2 x 1 rectangular tiles.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Find out what a "fault-free" rectangle is and try to make some of
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 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?
Number problems at primary level that require careful consideration.
Can you find all the different ways of lining up these Cuisenaire
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
How many different triangles can you make on a circular pegboard that has nine pegs?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
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?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.