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

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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

Given the products of adjacent cells, can you complete this Sudoku?

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

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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

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?

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Can you use this information to work out Charlie's house number?

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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

Given the products of diagonally opposite cells - can you complete this Sudoku?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Find out about Magic Squares in this article written for students. Why are they magic?!

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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

An investigation that gives you the opportunity to make and justify predictions.

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square 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?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Investigate the different ways you could split up these rooms so that you have double the number.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.