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?

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

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

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

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?"

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

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

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.

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

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

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?

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?

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

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

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

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

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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?

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

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?

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

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.

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

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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

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

Number problems at primary level that require careful consideration.

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

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.

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.

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?

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?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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...

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Can you replace the letters with numbers? Is there only one solution in each case?

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?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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?

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.

This task follows on from Build it Up and takes the ideas into three dimensions!

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?

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?

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