Question

Which errors in a single digit of a 15 -digit airline ticket identification number can be detected?

Short answer

If the absolute difference between the error digit and the correct digit is not7

Step-by-step solution

Step 1

For a $\mathbf{\text{Itextbf{identificationnumbera}}{\mathbf{a}}_{\mathbf{2}}\mathbf{\dots }{\mathbf{a}}_{\mathbf{15}}\mathbf{\text{ofairlinetickets}}$the check digit is calculated using the following expression

${\mathit{a}}_{\mathbf{15}}\mathbf{=}{\mathit{a}}_{\mathbf{1}}{\mathit{a}}_{\mathbf{2}}\mathbf{\dots }{\mathit{a}}_{\mathbf{14}}\mathbf{mod}\mathbf{7}$

Step2

A single error in a single digit of a 15-digit airline ticket identification number can be detected as long as the absolute difference between the error digit and the correct digit is not 7 (for example, replacing a 0 by 7,1 by 8 or 2 by 9 will not be detected), because the two numbers will then result in the same value for ${\mathit{a}}_{\mathbf{15}}$due to the modulo 7 .