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.
Replace each letter with a digit to make this addition 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
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Find a great variety of ways of asking questions which make 8.
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?
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. . . .
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. . . .
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?
How can we help students make sense of addition and subtraction of negative numbers?
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?
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
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?
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.
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 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.
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?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
Can you substitute numbers for the letters in these sums?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Who said that adding couldn't be fun?
What are the missing numbers in the pyramids?
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?
Find the numbers in this sum
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.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Choose any three by three square of dates on a calendar page...
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.
Are these statements always true, sometimes true or never true?
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Can you explain how this card trick works?
Delight your friends with this cunning trick! Can you explain how
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Vera is shopping at a market with these coins in her purse. Which
things could she give exactly the right amount for?
Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Can you follow the rule to decode the messages?
Can you score 100 by throwing rings on this board? Is there more
than way to do it?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
An environment which simulates working with Cuisenaire rods.
This task combines spatial awareness with addition and multiplication.
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?