Feedback shouldn't be surprised that Euler's constant e appears in the number of ways of making a linear picture from 24 cards (8 March). This number is e times 24 factorial - which is 24 × 23 × 22... × 2 × 1 and written 24!, which to the nearest whole number works out as 1,686,553,615,927,922,354,187,745, not 1,686,553,615,927,922,354,187,744 as reported.
The number of pictures is the number of ways of choosing any set of cards, and arranging them in any order. Given n cards, there is one way of choosing all of them, and n! ways of putting them in order.
There are n ways of choosing n-1 cards and (n-1)! ways of ordering them, giving another n! pictures. There are n × (n-1)/2 ways of choosing n-2 cards and (n-2)! orderings of each set, giving another n!/2 pictures; and so on.
The eventual total works out as n! ...
To continue reading this article, subscribe to receive access to all of newscientist.com, including 20 years of archive content.