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.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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!
In this investigation, you are challenged to make mobile phone
numbers which are easy to remember. What happens if you make a
sequence adding 2 each time?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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
There were 22 legs creeping across the web. How many flies? How many spiders?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
This is an adding game for two players.
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
This challenge is about finding the difference between numbers which have the same tens digit.
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.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Tell your friends that you have a strange calculator that turns
numbers backwards. What secret number do you have to enter to make
141 414 turn around?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
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
Well now, what would happen if we lost all the nines in our number
system? Have a go at writing the numbers out in this way and have a
look at the multiplications table.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
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?