Working systematically

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?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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?

On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?