EXAMPLE 5 ISBN-10 Transposition-Error Detection

Let's trace through an example to see how the ISBN-10 method detects adjacent transposition errors. Say 1-4292-0900-3 is mistaken as 1-2492-0900-3 (digits in positions 2 and 3 are transposed). Because the second and third digits in the weighted sum of the correct number contribute to the total of 176 and the second and third digits of the incorrect number contribute to the weighted sum, we know that the weighted sum of the incorrect number is , which is not evenly divisible by 11.