If: A + C = A; F x D = F; B - G = G; A + H = E; B / H = G; E - G = F and A-H represent the numbers from 0 to 7 Find the values of A, B, C, D, E, F and H.

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

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?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

There are lots of different methods to find out what the shapes are worth - how many can you find?

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

How many winning lines can you make in a three-dimensional version of noughts and crosses?

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .

Is there an efficient way to work out how many factors a large number has?

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

Can you find the area of a parallelogram defined by two vectors?

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

How many different symmetrical shapes can you make by shading triangles or squares?

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

Water freezes at 0°Celsius (32°Fahrenheit) and boils at 100°C (212°Fahrenheit). Is there a temperature at which Celsius and Fahrenheit readings are the same?

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

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

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Explore the effect of combining enlargements.

Explore the effect of reflecting in two parallel mirror lines.

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

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?

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

Can you describe this route to infinity? Where will the arrows take you next?

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?