Question

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The first nine digits of the ISBN-10 of the European version of the fifth edition of this book are 0-07-119881.

What is the check digit for that book?

Answer 1

Check digits for ISBN10 satisfy: Sum of products of digits times position (taken from right) is 0 modulo 11

So if the check digit is x then we must have

$0\times 10+0\times 9+7\times 8+1\times 7+1\times 6+9\times 5+8\times 4+8\times 3+1\times 2+1\times x\equiv 0\pmod{11}$

So that $x+172\equiv 0\pmod{11}\Rightarrow x\equiv -172\pmod{11}\equiv 4$

Required check-digit is ${\color{Red} 4}$

$\blacksquare$

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