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?
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. . . .
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?
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. . . .
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.
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. . . .
What is the sum of all the digits in all the integers from one to
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. . . .
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.
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?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Replace each letter with a digit to make this addition correct.
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.
Find the numbers in this sum
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. . . .
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.
Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat. . . .
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
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 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 are the missing numbers in the pyramids?
How can we help students make sense of addition and subtraction of negative numbers?
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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Using the 8 dominoes make a square where each of the columns and rows adds up to 8
This Sudoku, based on differences. Using the one clue number can you find the solution?
Can you explain how this card trick works?
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
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?
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 be the first to complete a row of three?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Here is a chance to play a version of the classic Countdown Game.
Here is a chance to play a fractions version of the classic
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
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.
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?
An account of some magic squares and their properties and and how to construct them for yourself.
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
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.
Use these four dominoes to make a square that has the same number of dots on each side.
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?
Delight your friends with this cunning trick! Can you explain how
Find out about Magic Squares in this article written for students. Why are they magic?!
This article suggests some ways of making sense of calculations involving positive and negative numbers.
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?
In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?