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?
An environment for exploring the properties of small groups.
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?
Which of these games would you play to give yourself the best possible chance of winning a prize?
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.
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.
Seventh challenge cipher
In how many ways can the number 1 000 000 be expressed as the
product of three positive integers?
Discover a handy way to describe reorderings and solve our anagram
in the process.
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.