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

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

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.

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?

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

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

What's the largest volume of box you can make from a square of paper?

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?

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

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

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

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

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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

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

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".

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

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

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?

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

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

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

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

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

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

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?

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?

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?

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 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?

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

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

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

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

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

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

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?

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

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

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

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

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

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

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

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

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

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