The ISBN of a book is a unique 13-digit code', also known as ISBN-13, that encodes information about the publisher, registrant, place of publication, and so on. If the ISBN-13 of a book is Y1Y2Y3 •· * · Y13, then it must satisfy the following congruence: y1 + 3y2 + y3 + 3y4 + y5 + 3y6 + y7 + 3ys + yo + 3y10 + y11 + 3y12 + Y13 = 0 (mod 10). (a) Find a book at home and take a picture of it showing the 13-digit ISBN. Then show that its ISBN satisfies this congruence. (b) Suppose vou have another book whose ISBN is partially erased so that vou can't read the fifth digit

Np Ms Office 365/Excel 2016 I Ntermed
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Chapter3: Performing Calculations With Formulas And Functions
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For c), is it possible? Using ISBN: 9780756649791 from a)

The ISBN of a book is a unique 13-digit code', also known as ISBN-13, that encodes information about
the publisher, registrant, place of publication, and so on. If the ISBN-13 of a book is
Y1Y2Y3 · *· Y13,
then it must satisfy the following congruence:
yı + 3y2 + y3 + 3y4 + y5 + 3y6 + y7 + 3ys + y9 + 3y10 + y11 + 3y12 + Y13 = 0 (mod 10).
(a) Find a book at home and take a picture of it showing the 13-digit ISBN. Then show that its ISBN
satisfies this congruence.
(b) Suppose you have another book whose ISBN is partially erased so that you can't read the fifth digit
Y5. Can you compute it using the above congruence? Explain why you can always do this.
978 - 1? 215 8 7 6 6 0
(c) What if two digits were removed from an ISBN-13? Would you be able to recover the ISBN? Demon-
strate using your book from (a) as an example.
Transcribed Image Text:The ISBN of a book is a unique 13-digit code', also known as ISBN-13, that encodes information about the publisher, registrant, place of publication, and so on. If the ISBN-13 of a book is Y1Y2Y3 · *· Y13, then it must satisfy the following congruence: yı + 3y2 + y3 + 3y4 + y5 + 3y6 + y7 + 3ys + y9 + 3y10 + y11 + 3y12 + Y13 = 0 (mod 10). (a) Find a book at home and take a picture of it showing the 13-digit ISBN. Then show that its ISBN satisfies this congruence. (b) Suppose you have another book whose ISBN is partially erased so that you can't read the fifth digit Y5. Can you compute it using the above congruence? Explain why you can always do this. 978 - 1? 215 8 7 6 6 0 (c) What if two digits were removed from an ISBN-13? Would you be able to recover the ISBN? Demon- strate using your book from (a) as an example.
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