Question

Can the accidental transposition of two consecutive digits in an airline ticket identification number be detected using the check digit?

Short answer

$\text{If the two digits do not differ by}\mathbf{7}$

Step-by-step solution

Step 1

For a $\mathbf{\text{Itextbf{identificationnumbera}}{\mathit{a}}_{\mathbf{1}}\mathbf{\dots }{\mathit{a}}_{\mathbf{15}}\mathbf{\text{ofairlinetickets}}$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

The accidental transposition of two consecutive digits can be detected as long as the the two digits do not differ by $\mathbf{7}$(for example, switching a 0 and 7,1 and 8 or 2 and 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$\mathbf{7}$ .