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?

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

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?

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. . . .

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. . . .

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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.

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

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

How would you count the number of fingers in these pictures?

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

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. . . .

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?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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

Dotty Six game for an adult and child. Will you be the first to have three sixes in a straight line?

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

Dotty Six is a simple dice game that you can adapt in many ways.

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?

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?

Can you use the information to find out which cards I have used?

Investigate what happens when you add house numbers along a street in different ways.

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?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

These two group activities use mathematical reasoning - one is numerical, one geometric.

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Can you score 100 by throwing rings on this board? Is there more than way to do it?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?