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.

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

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

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...

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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?

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?

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?

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

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

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.

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

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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.

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

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

Use the differences to find the solution to this Sudoku.

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

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. . . .

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 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?

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

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. . . .

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

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

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

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?

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?

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

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

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

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

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

Explore the effect of combining enlargements.

What does this number mean ? Which order of 1, 2, 3 and 4 makes the highest value ? Which makes the lowest ?

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?

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

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

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

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.

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

Explore the effect of reflecting in two parallel mirror lines.

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. . . .