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?
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
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 numbers in this sum
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?
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.
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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?
What is the sum of all the digits in all the integers from one to
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?
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?
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. . . .
What is the sum of all the three digit whole numbers?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Find the sum of all three-digit numbers each of whose digits is
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.
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
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
How would you count the number of fingers in these pictures?
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. . . .
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 do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Find a great variety of ways of asking questions which make 8.
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?
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.
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
This challenge is to make up YOUR OWN alphanumeric. Each letter
represents a digit and where the same letter appears more than once
it must represent the same digit each time.
Can you follow the rule to decode the messages?
Can you use the information to find out which cards I have used?
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?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?
Can you substitute numbers for the letters in these sums?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Dotty Six is a simple dice game that you can adapt in many ways.
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?
How can we help students make sense of addition and subtraction of negative numbers?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.