Working systematically

A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?

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

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

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

Can you find triangles on a 9-point circle? Can you work out their angles?

Discs are flipped in the air. You win if all the faces show the same colour. What is the probability of winning?

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the dot affects the distance it travels at each stage.

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

Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?