Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Choose a symbol to put into the number sentence.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Who said that adding couldn't be fun?
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?
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
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 substitute numbers for the letters in these sums?
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?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
This is an adding game for two players.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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!
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?
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.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
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 arrange 5 different digits (from 0 - 9) in the cross in the
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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?
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.
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 draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
Ben has five coins in his pocket. How much money might he have?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
This dice train has been made using specific rules. How many different trains can you make?
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?
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.
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?
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.
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
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.