Part 1: ISBN-10 ISBN is an acronym for International Standard Book Number. This book identifier originated in 1970. It is now known as an ISBN-10 since it is 10 digits long. An ISBN-10 is arranged in 4 groups. The first digit corresponds to the language of the book, the next 2 to 7 digits give the publisher, the next 1 to 6 digits are for the title, and the final digit is a check digit for detecting errors (this scheme catches all single digit errors and most double digit transposition errors). The check digit is assigned so that the sum-product of the ISBN with the vector is 0 (mod 11). Since 10 takes 2 digits to write instead of 1, the letter X is used for 10 (X is the Roman numeral for 10). In other words, if we write the ISBN of a book as dddd dddd d do where d is a single digit for 0 i 10, then it must follow that 10d1 +9d2 +8d3 +7d4 + 6d5 +5d6 + 4d7 + 3d8 +2dg+1d10 (mod 11) = 0 Questions 1. Find any ISBN-10 book online of your choosing. Show that it adheres to the rule above. 2. We often refer to modular arithmetic as "clock arithmetic". Like a clock resets back to 1 after 12, so, too, does a quantity that is being modded by a particular divisor. This is why the check digit is particularly important. Why is dividing (mod 11) essential to ensure that the check digit is correct? (Think about what would happen if we used something smaller, say, (mod 5) or something larger, say (mod 15).)