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There are **73** NRICH Mathematical resources connected to **Odd and even numbers**, you may find related items under Properties of numbers.

Problem
Primary curriculum
Secondary curriculum
### Eightness of Eight

What do you see as you watch this video? Can you create a similar video for the number 12?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Carroll Diagrams

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Always, Sometimes or Never? Number

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Always, Sometimes or Never?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What Could It Be?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Play to 37

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square Subtraction

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Take Three Numbers

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Odd Times Even

This problem looks at how one example of your choice can show something about the general structure of multiplication.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Two Numbers Under the Microscope

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Magic Letters

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Odds, Evens and More Evens

Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Largest Even

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Pairs of Numbers

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Curious Number

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Odd

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Light the Lights

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Our Numbers

These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### I Like ...

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Even and Odd

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Magic Vs

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What Do You Need?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Domino Sorting

Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Differences

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Numbers in the Ring

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ring a Ring of Numbers

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Share Bears

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Break it Up!

In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Odd Squares

Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Picturing Square Numbers

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Mixed-up Clock

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Make 37

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

Age 7 to 11

Challenge Level

Problem
Live Primary curriculum
Secondary curriculum
### Grouping Goodies

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Number Round Up

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

Age 5 to 7

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Odds and Threes

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.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sets of Numbers

How many different sets of numbers with at least four members can you find in the numbers in this box?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What Number?

I am less than 25. My ones digit is twice my tens digit. My digits add up to an even number.

Age 5 to 7

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Diagonal Trace

You can trace over all of the diagonals of a pentagon without lifting your pencil and without going over any more than once. Can the same thing be done with a hexagon or with a heptagon?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Prime Magic

Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Great Granddad

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Comparing Continued Fractions

Which of these continued fractions is bigger and why?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Score

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 a total of 15 with 6 odd numbers?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Summats Clear

Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.

Age 16 to 18

Challenge Level