Dear Sudoku fans: As you know, Sudoku is all about numbers 1 through 9. Did you know that almost all books published in the last 50 years have a 10- or 13-digit unique number assigned to them that is made up of digits 0 through 9? It’s called the International Standard Book Number, or ISBN. The numbers in an ISBN can reveal all kinds of information about the book—language, country where published, publisher, etc. But it’s the last digit, the check digit, that we think some of you puzzle solvers may find especially interesting.
The check digit is a form of redundancy check that is used for error detection: it confirms the other numbers that make up the ISBN. In 13-digit ISBNs, if you multiply the first digit by 1, the second digit by 3, the third by 1, the fourth by 3, and so on through the 12th digit, then add all those values together, the check digit will be whatever number needs to be added in order to make the grand total a multiple of 10!
Let’s do this with the first hardcover edition of Kristin Hannah’s The Women. You can usually find the ISBN on the back cover and nearly always on the back of the book’s title page, what’s known in the trade as the verso. The ISBN is 978-1-250-17863-3. That last digit, 3, is our check digit. Let’s run the numbers to see if they add up!
| digit | multiplier | product |
| 9 | x1 | 9 |
| 7 | x3 | 21 |
| 8 | x1 | 8 |
| 1 | x3 | 3 |
| 2 | x1 | 2 |
| 5 | x3 | 15 |
| 0 | x1 | 0 |
| 1 | x3 | 3 |
| 7 | x1 | 7 |
| 8 | x3 | 24 |
| 6 | x1 | 6 |
| 3 | x3 | 9 |
Now, if we add all the numbers in the product column, we get 107. In order to raise that number to a multiple of 10—in this case, 110—we need to add 3…which turns out to be our check digit!
Use this knowledge to impress your friends! Tell them to give you the first 12 digits of any book’s ISBN, and you will tell them what the 13th digit is. It just takes a little arithmetic. And very patient friends.
We hope you enjoy this month’s sudoku!