In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
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
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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).
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
This is an adding game for two players.
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?
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?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
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?
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?
A lady has a steel rod and a wooden pole and she knows the length
of each. How can she measure out an 8 unit piece of pole?
Susie took cherries out of a bowl by following a certain pattern.
How many cherries had there been in the bowl to start with if she
was left with 14 single ones?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
What is happening at each box in these machines?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Find the sum of all three-digit numbers each of whose digits is
Investigate the different distances of these car journeys and find
out how long they take.
Use the information to work out how many gifts there are in each
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
In sheep talk the only letters used are B and A. A sequence of
words is formed by following certain rules. What do you notice when
you count the letters in each word?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
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
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
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?
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!
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?
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!
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
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.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Investigate what happens when you add house numbers along a street
in different ways.
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Max and Mandy put their number lines together to make a graph. How
far had each of them moved along and up from 0 to get the counter
to the place marked?
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?
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.
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Arrange three 1s, three 2s and three 3s in this square so that
every row, column and diagonal adds to the same total.
What is the sum of all the three digit whole numbers?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.