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?

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?

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. . . .

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

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?

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

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

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

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?

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?

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?

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

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

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

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. . . .

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?

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

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?

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

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

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

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.

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

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

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.

This challenge combines addition, multiplication, perseverance and even proof.

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?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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?

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

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.