Working systematically

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?

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

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

Can all unit fractions be written as the sum of two unit fractions?

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?