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 your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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?
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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.
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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.
Can you replace the letters with numbers? Is there only one
solution in each case?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
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
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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!
Ben has five coins in his pocket. How much money might he have?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
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!
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.
This dice train has been made using specific rules. How many different trains can you make?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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?
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.
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
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?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.