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?
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?
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
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?
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
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?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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?
Find all the numbers that can be made by adding the dots on two dice.
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.
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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 you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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.
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!
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
My coat has three buttons. How many ways can you find to do up all
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?
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?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
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 find out in which order the children are standing in this
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
How many different shapes can you make by putting four right-
angled isosceles triangles together?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
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!
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
This dice train has been made using specific rules. How many different trains can you make?