Yesterday “Raised by Penguins” got its ISBN, and I was surprised to see that it ends with an X. That’s right, nine digits, followed by the letter X.
Confused and bewildered, I Googled for some kind of explanation for this aberrant character. I found it here: Mathematics and Writing in Action: The International Standard Book Number Check Digit Scheme.
The ISBN Check Digit Scheme
For a1a2a3a4a5a6a7a8a9a10, the ten digit ISBN, the check digit a10 is appended to the nine digit identification number a1a2a3a4a5a6a7a8a9 such that a10 satisfies the equation
10a1 + 9a2 + 8a3 + 7a4 + 6a5 + 5a6 + 4a7 + 3a8 + 29 + a10 = 0 (mod 11)
If the check digit a10 is 10, the letter X is used instead.
The remainder when a number is divided by 11 could be any digit from 0 to 9 or the number 10. Since the ISBN scheme uses modulo 11 arithmetic and wants the check digit a10 to be a single character, it assigns a10 the value of X when 10 is to the check digit. The ISBN for the book Linear Algebra and its Applications, by David Lay, is 0-201-52032-X. The X indicates that the check digit is the number 10.
So X, as it turns out, is a legitimate character for an ISBN, and my book has one. Great, except that the catalog form at Cafe Press rejects any letters in the ISBN.