What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Can you substitute numbers for the letters in these sums?
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?
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 digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Use the information to work out how many gifts there are in each
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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
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?
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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?
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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 task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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!
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!
Number problems at primary level that require careful consideration.
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?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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 do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you find all the ways to get 15 at the top of this triangle of numbers?
This dice train has been made using specific rules. How many different trains can you make?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This task combines spatial awareness with addition and multiplication.