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.

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

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?

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?

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.

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 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?

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?

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

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

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?

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

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

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

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?

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?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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.

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

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?

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

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

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

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?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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?

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?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

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?

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.

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

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.