Text: ISBN Codes. Every book has an International Standard Book Number (ISBN) code. This is a 10-digit code indicating the book's publisher and title. The tenth digit is a check digit satisfying (d1, d2, ..., d10) · (10, 9, ..., 1) ≡ 0 (mod 11). One problem is that d10 might have to be a 10 to make the inner product zero; in this case, 11 digits would be needed to make this scheme work. Therefore, the character X is used for the eleventh digit. So ISBN 3-540-96035-X is a valid ISBN code. (a)

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