Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Find the sum of all three-digit numbers each of whose digits is
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. . . .
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?
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.
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.
Find the numbers in this sum
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.
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
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?!
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. . . .
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. . . .
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
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.
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?
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?
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?
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. . . .
What are the missing numbers in the pyramids?
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?
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?
Who said that adding couldn't be fun?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
This Sudoku, based on differences. Using the one clue number can you find the solution?
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.
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?
Here is a chance to play a fractions version of the classic
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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.
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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
Choose any three by three square of dates on a calendar page...
What is the sum of all the digits in all the integers from one to
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Delight your friends with this cunning trick! Can you explain how
Find a great variety of ways of asking questions which make 8.
Can you explain how this card trick works?
Are these statements always true, sometimes true or never true?
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?
Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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.