Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Use these four dominoes to make a square that has the same number of dots on each side.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
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.
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. . . .
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. . . .
Find the sum of all three-digit numbers each of whose digits is
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. . . .
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
How can we help students make sense of addition and subtraction of negative numbers?
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?
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
In the following sum the letters A, B, C, D, E and F stand for six
distinct digits. Find all the ways of replacing the letters with
digits so that the arithmetic is correct.
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
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?
Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .
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?
Replace each letter with a digit to make this addition correct.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
What are the missing numbers in the pyramids?
This addition sum uses all ten digits 0, 1, 2...9 exactly once.
Find the sum and show that the one you give is the only
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Who said that adding couldn't be fun?
This Sudoku, based on differences. Using the one clue number can you find the solution?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Here is a chance to play a fractions version of the classic
Choose any three by three square of dates on a calendar page...
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Find a great variety of ways of asking questions which make 8.
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
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
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.
Are these statements always true, sometimes true or never true?
Delight your friends with this cunning trick! Can you explain how
Can you explain how this card trick works?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Investigate the different distances of these car journeys and find
out how long they take.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?