The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.

Some relationships are transitive, such as `if A>B and B>C then it follows that A>C', but some are not. In a voting system, if A beats B and B beats C should we expect A to beat C?

To draw lots each player chooses a different upright, the paper is then unrolled, the paths charted and the results declared. Prove that no two paths ever end up at the foot of the same upright?

This article for students and teachers tries to think about how long would it take someone to create every possible shuffle of a pack of cards, with surprising results.

Discover a handy way to describe reorderings and solve our anagram in the process.

A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .

Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .

The four digits 5, 6, 7 and 8 are put at random in the spaces of the number : 3 _ 1 _ 4 _ 0 _ 9 2 Calculate the probability that the answer will be a multiple of 396.

Which of these games would you play to give yourself the best possible chance of winning a prize?

In how many ways can the number 1 000 000 be expressed as the product of three positive integers?