Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

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

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

If everyone in your class picked a number from 1 to 225, do you think any two people would pick the same number?

Can you work out the probability of winning the Mathsland National Lottery? Try our simulator to test out your ideas.

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

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

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

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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

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

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

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

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

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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

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

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

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?

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?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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 set of numbers that add to 10 have the largest product?

Can you find any two-digit numbers that satisfy all of these statements?

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?

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".

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

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Which countries have the most naturally athletic populations?

How well can you estimate 10 seconds? Investigate with our timing tool.

If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?

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

You'll need to know your number properties to win a game of Statement Snap...

Use your skill and judgement to match the sets of random data.

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

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

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

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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?

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

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?

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

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

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

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