Books are identified by an International Standard Book Number (ISBN), a 10-digit

Question

Books are identified by an International Standard Book Number (ISBN), a 10-digit code x1x2…x10, assigned by the publisher. These 10 digits consist of blocks identifying the language, the publisher, the number assigned to the book by its publishing company, and finally, a 1-digit check digit that is either a digit or the letter X (used to represent 10). This check digit is selected so that 10i=1ixi0 mod 11 and is used to detect errors in individual digits and transposition of digits.

(a) The ISBN for a book is 851532734Q where Q is the check digit. What is Q?

(b) The ISBN of another book is 570715M258. Find the digit M.

Explanation / Answer

Here by above given rule, we have

8 * 1 + 5 * 2 + 3 * 1 + 4 * 5 + 5* 3 + 6* 2 + 7 * 7 + 8 * 3 + 9 * 4 + 10 * Q = 0 mod 11

i.e. 177 + 10Q= 0 mod 11

on subtracting 177 each side,

10Q = 0 mod 11 - 230= 10mod 11     because 231 = 11 x 17

or 10Q = 10    (because by trial and error 10 mod 11 = 10)

or Q= 10/10=1

so the answer of part a) is 1.

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