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.