Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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

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?

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

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

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?

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

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. . . .

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

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

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

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?

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

Find the frequency distribution for ordinary English, and use it to help you crack the code.

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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?

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

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

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...

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.

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

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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

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

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?

Play this game and see if you can figure out the computer's chosen number.

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?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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

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

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

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

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

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?

Why not challenge a friend to play this transformation game?

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

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?

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

Use the differences to find the solution to this Sudoku.

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

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

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

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

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

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

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?

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