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Broad Topics > Calculations and Numerical Methods > Addition & subtraction

Largest Number

Age 11 to 14 Challenge Level:

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.

Digit Sum

Age 11 to 14 Challenge Level:

What is the sum of all the digits in all the integers from one to one million?

Hot Pursuit

Age 11 to 14 Challenge Level:

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?

Subtraction Surprise

Age 7 to 14 Challenge Level:

Try out some calculations. Are you surprised by the results?

The Patent Solution

Age 11 to 14 Challenge Level:

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?

Like Powers

Age 11 to 14 Challenge Level:

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.

As Easy as 1,2,3

Age 11 to 14 Challenge Level:

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. . . .

Arrange the Digits

Age 11 to 14 Challenge Level:

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?

Eleven

Age 11 to 14 Challenge Level:

Replace each letter with a digit to make this addition correct.

Chameleons

Age 11 to 14 Challenge Level:

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. . . .

Alphabet Soup

Age 11 to 14 Challenge Level:

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.

3388

Age 11 to 14 Challenge Level:

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

Adding and Subtracting Positive and Negative Numbers

Age 11 to 14

How can we help students make sense of addition and subtraction of negative numbers?

Magic Squares for Special Occasions

Age 11 to 16

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.

Making Sense of Positives and Negatives

Age 11 to 14

This article suggests some ways of making sense of calculations involving positive and negative numbers.

And So on and So On

Age 11 to 14 Challenge Level:

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?

Jugs of Wine

Age 11 to 14 Challenge Level:

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?

Multiply the Addition Square

Age 11 to 14 Challenge Level:

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?

Kids

Age 11 to 14 Challenge Level:

Find the numbers in this sum

Got it Article

Age 7 to 14

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Cayley

Age 11 to 14 Challenge Level:

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Countdown

Age 7 to 14 Challenge Level:

Here is a chance to play a version of the classic Countdown Game.

Tis Unique

Age 11 to 14 Challenge Level:

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 possibility.

Have You Got It?

Age 11 to 14 Challenge Level:

Can you explain the strategy for winning this game with any target?

Football Sum

Age 11 to 14 Challenge Level:

Find the values of the nine letters in the sum: FOOT + BALL = GAME

Score

Age 11 to 14 Challenge Level:

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. . . .

Pairs

Age 11 to 14 Challenge Level:

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. . . .

Always the Same

Age 11 to 14 Challenge Level:

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?

Card Trick 2

Age 11 to 14 Challenge Level:

Can you explain how this card trick works?

Pyramids

Age 11 to 14 Challenge Level:

What are the missing numbers in the pyramids?

Playing Connect Three

Age 11 to 14 Challenge Level:

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

2010: A Year of Investigations

Age 5 to 14

This article for teachers suggests ideas for activities built around 10 and 2010.

Crossed Ends

Age 11 to 14 Challenge Level:

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Clocked

Age 11 to 14 Challenge Level:

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?

Cunning Card Trick

Age 11 to 14 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works?

Two and Two

Age 11 to 14 Challenge Level:

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Calendar Capers

Age 11 to 14 Challenge Level:

Choose any three by three square of dates on a calendar page...

Number Daisy

Age 11 to 14 Challenge Level:

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Aba

Age 11 to 14 Challenge Level:

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.

Weights

Age 11 to 14 Challenge Level:

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Consecutive Negative Numbers

Age 11 to 14 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Making Maths: Double-sided Magic Square

Age 7 to 14 Challenge Level:

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

More Children and Plants

Age 7 to 14 Challenge Level:

This challenge extends the Plants investigation so now four or more children are involved.

First Connect Three for Two

Age 7 to 14 Challenge Level:

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Top-heavy Pyramids

Age 11 to 14 Challenge Level:

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

More Plant Spaces

Age 7 to 14 Challenge Level:

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

Nice or Nasty

Age 7 to 14 Challenge Level:

There are nasty versions of this dice game but we'll start with the nice ones...

Pair Sums

Age 11 to 14 Challenge Level:

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Pole Star Sudoku 2

Age 11 to 16 Challenge Level:

This Sudoku, based on differences. Using the one clue number can you find the solution?

Constellation Sudoku

Age 14 to 18 Challenge Level:

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.