A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

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

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

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?

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.

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.

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

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?

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

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

Explore the effect of reflecting in two parallel mirror lines.

Explore the effect of combining enlargements.

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

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

Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

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

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?

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

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

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

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?

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.

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

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

Can you see how to build a harmonic triangle? Can you work out the next two rows?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...

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.

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?

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

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.

A jigsaw where pieces only go together if the fractions are equivalent.

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?

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?

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

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

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

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

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?