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.

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?"

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

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?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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?

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?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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

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?

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?

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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

Have a go at balancing this equation. Can you find different ways of doing it?

Can you work out some different ways to balance this equation?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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...

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

A Sudoku that uses transformations as supporting clues.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

In this matching game, you have to decide how long different events take.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

The pages of my calendar have got mixed up. Can you sort them out?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.