Working systematically

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

How would you design the tiering of seats in a stadium so that all spectators have a good view?

How can you quickly sort a suit of cards in order from Ace to King?

Can you work out where these 5 riders came in a not-quite-so-famous bike race?

In 1% of cases, an HIV test gives a positive result for someone who is HIV negative. How likely is it that someone who tests positive has HIV?

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

DNA profiling is an invaluable tool for the police. However, when it comes to probability, things aren't always as straightforward as they seem.

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

A player has probability 0.4 of winning a single game. What is his probability of winning a 'best of 15 games' tournament?

This Sudoku problem consists of a pair of linked standard Sudoku puzzles each with some starting digits.