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### Magic Squares for Special Occasions

##### Stage: 3 and 4

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.

### Eleven

##### Stage: 3 Challenge Level:

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

### Always the Same

##### Stage: 3 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?

### I'm Eight

##### Stage: 1, 2, 3 and 4 Challenge Level:

Find a great variety of ways of asking questions which make 8.

### Digit Sum

##### Stage: 3 Challenge Level:

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

### Tis Unique

##### Stage: 3 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.

### Crossed Ends

##### Stage: 3 Challenge Level:

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

### Make 37

##### Stage: 2 and 3 Challenge Level:

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.

### GOT IT Now

##### Stage: 2 and 3 Challenge Level:

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

##### Stage: 1 and 2 Challenge Level:

Who said that adding couldn't be fun?

### Card Trick 2

##### Stage: 3 Challenge Level:

Can you explain how this card trick works?

### Cunning Card Trick

##### Stage: 3 Challenge Level:

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

### Like Powers

##### Stage: 3 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.

### Arrange the Digits

##### Stage: 3 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?

##### Stage: 2, 3 and 4 Challenge Level:

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. . . .

### Numbered Cars

##### Stage: 2 Challenge Level:

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?

### Score

##### Stage: 3 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. . . .

### Dividing a Cake

##### Stage: 2 Challenge Level:

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?

### The Patent Solution

##### Stage: 3 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?

### Adding and Subtracting Positive and Negative Numbers

##### Stage: 2, 3 and 4

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

### Aba

##### Stage: 3 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.

### Spell by Numbers

##### Stage: 2 Challenge Level:

Can you substitute numbers for the letters in these sums?

### Super Value Shapes

##### Stage: 2 Challenge Level:

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 given totals?

### Pyramids

##### Stage: 3 Challenge Level:

What are the missing numbers in the pyramids?

### Top-heavy Pyramids

##### Stage: 3 Challenge Level:

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

### Calendar Capers

##### Stage: 3 Challenge Level:

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

### Oddly

##### Stage: 2 Challenge Level:

Find the sum of all three-digit numbers each of whose digits is odd.

### Diagonal Sums

##### Stage: 2 Challenge Level:

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?

### One Wasn't Square

##### Stage: 2 Challenge Level:

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

### Always, Sometimes or Never? Number

##### Stage: 2 Challenge Level:

Are these statements always true, sometimes true or never true?

### Cows and Sheep

##### Stage: 2 Challenge Level:

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

### Clocked

##### Stage: 3 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?

### 4 Dom

##### Stage: 1, 2, 3 and 4 Challenge Level:

Use these four dominoes to make a square that has the same number of dots on each side.

### Largest Number

##### Stage: 3 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.

### Domino Square

##### Stage: 2, 3 and 4 Challenge Level:

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

### Kids

##### Stage: 3 Challenge Level:

Find the numbers in this sum

### Cycling Squares

##### Stage: 2 Challenge Level:

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?

### Two Primes Make One Square

##### Stage: 2 Challenge Level:

Can you make square numbers by adding two prime numbers together?

### Cubes Within Cubes

##### Stage: 2 and 3 Challenge Level:

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?

### Four Goodness Sake

##### Stage: 2 Challenge Level:

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

### Amy's Dominoes

##### Stage: 2 Challenge Level:

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

### Rocco's Race

##### Stage: 2 Short Challenge Level:

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

### Number Pyramids

##### Stage: 3 Challenge Level:

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

### Calendar Calculations

##### Stage: 2 Challenge Level:

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

### Being Thoughtful - Primary Number

##### Stage: 1 and 2 Challenge Level:

Number problems at primary level that require careful consideration.

### Oranges and Lemons

##### Stage: 2 Challenge Level:

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

### Being Collaborative - Primary Number

##### Stage: 1 and 2 Challenge Level:

Number problems at primary level to work on with others.

### The Deca Tree

##### Stage: 2 Challenge Level:

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

### 1, 2, 3 Magic Square

##### Stage: 2 Challenge Level:

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.