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?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
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
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.
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
My coat has three buttons. How many ways can you find to do up all
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
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?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
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 eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
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?
In this matching game, you have to decide how long different events take.
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenge is about finding the difference between numbers which have the same tens digit.
The pages of my calendar have got mixed up. Can you sort them out?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Can you find the chosen number from the grid using the clues?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Investigate the different ways you could split up these rooms so
that you have double the number.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?