Question

Determine which transposition errors are detected by the USPS money order code.

Short answer

When the transposition error involves the check digit and if the digit with which it is interchanged is different from the true value.

Step-by-step solution

Step 1

For a USPS code ${\mathit{x}}_{\mathbf{1}}{\mathit{x}}_{\mathbf{2}\mathbf{\dots }}{\mathit{x}}_{\mathbf{1}}$the check digit is calculated using the following

Expression:

${{\mathit{x}}_{\mathbf{11}}}^{\mathbf{0}}{\mathit{x}}_{\mathbf{1}}\mathbf{+}{\mathit{x}}_{\mathbf{2}}\mathbf{+}\mathbf{\dots }\mathbf{+}{\mathit{x}}_{\mathbf{10}}\mathbf{mod}\mathbf{9}$

Step 2

A transposition error is an error due to digits being switched.

When the transposition errors do not include the check digit, then the error is not detected due to the commutative property of addition.

When the transposition error involves the check digit and if the digit with which it is interchanged is different from the true value, then it is possible to detect the error.