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?

If you move the tiles around, can you make squares with different coloured edges?

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

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

Can you find the values at the vertices when you know the values on the edges?

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

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

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. . . .

Where should you start, if you want to finish back where you started?

A game that tests your understanding of remainders.

Can you do a little mathematical detective work to figure out which number has been wiped out?

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

There are nasty versions of this dice game but we'll start with the nice ones...

What happens when you add a three digit number to its reverse?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

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?

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

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Can you work out which spinners were used to generate the frequency charts?

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

Engage in a little mathematical detective work to see if you can spot the fakes.

Play around with sets of five numbers and see what you can discover about different types of average...

Why not challenge a friend to play this transformation game?

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

What is the smallest number of answers you need to reveal in order to work out the missing headers?

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

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

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

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

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?

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

How many moves does it take to swap over some red and blue frogs? Do you have a method?

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Can you find a way to identify times tables after they have been shifted up?

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Can you find the hidden factors which multiply together to produce each quadratic expression?