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?

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

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

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.

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?

There are lots of different methods to find out what the shapes are worth - how many can you find?

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

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

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

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?

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

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

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

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

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

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

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?

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?

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

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?

Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

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?

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

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?

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

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?

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

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

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?

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.

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

Can you find rectangles where the value of the area is the same as the value of the perimeter?

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

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

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

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

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

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

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?

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?