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.

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

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

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 ?

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. . . .

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?

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

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

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

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

If a sum invested gains 10% each year how long before it has doubled its value?

Use the differences to find the solution to this Sudoku.

Can all unit fractions be written as the sum of two unit fractions?

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

Explore the effect of reflecting in two parallel mirror lines.

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

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

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

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

Explore the effect of combining enlargements.

The sums of the squares of three related numbers is also a perfect square - can you explain why?

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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?

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

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

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

What is the largest number which, when divided into 1905, 2587, 3951, 7020 and 8725 in turn, leaves the same remainder each time?

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

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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?

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

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

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

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. . . .

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?

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

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

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

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?

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

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. . . .

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?

An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?