If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
If each of these three shapes has a value, can you find the totals
of the combinations? Perhaps you can use the shapes to make the
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?
Can you use the information to find out which cards I have used?
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
The picture shows a lighthouse and many underwater creatures. If
you know the markings on the lighthouse are 1m apart, can you work
out the distances between some of the different creatures?
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
Whenever two chameleons of different colours meet they change
colour to the third colour. Describe the shortest sequence of
meetings in which all the chameleons change to green if you start
with 12. . . .
How is it possible to predict the card?
Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.
There are exactly 3 ways to add 4 odd numbers to get 10. Find all
the ways of adding 8 odd numbers to get 20. To be sure of getting
all the solutions you will need to be systematic. What about. . . .
Find the sum of all three-digit numbers each of whose digits is
A combination mechanism for a safe comprises thirty-two tumblers
numbered from one to thirty-two in such a way that the numbers in
each wheel total 132... Could you open the safe?
Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .
What is the sum of all the digits in all the integers from one to
Number problems at primary level to work on with others.
You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre
jug is full of wine, the others are empty. Can you divide the wine
into three equal quantities?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit
numbers such that their total is close to 1500?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Using 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
Who said that adding couldn't be fun?
This Sudoku, based on differences. Using the one clue number can you find the solution?
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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?
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?
This is an adding game for two players.
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?
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
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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?
Is it possible to rearrange the numbers 1,2......12 around a clock
face in such a way that every two numbers in adjacent positions
differ by any of 3, 4 or 5 hours?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
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?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?