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
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Explore the different snakes that can be made using 5 cubes.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
How many different shapes can you make by putting four right-
angled isosceles triangles together?
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?
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?
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
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
My coat has three buttons. How many ways can you find to do up all
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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?
Can you find out in which order the children are standing in this
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 the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
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?
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?
The brown frog and green frog want to swap places without getting
wet. They can hop onto a lily pad next to them, or hop over each
other. How could they do it?
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.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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 help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
Investigate the different ways you could split up these rooms so
that you have double the number.
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.