Fun and games

With ISBN-13 a book can have a valid checksum and have a simple transcription error, if digits with a difference of five are transposed.

Using The Statistical Mechanics of Financial Markets as an example, we can see that 9783540009788 is the given ISBN, and is valid. However, 9738540009788 with the third and fourth characters transposed is also valid, yet is incorrect [1].

I’ll leave it as an exercise for the reader to figure out how often books with transposable ISBN-13 occur in a given library of n books.

[1]This example was chosen to show that sometimes it is still possible to catch during data entry as 973 isn’t a valid prefix