Five Serials, One Check Digit, Ninety Seconds
You are checking a batch of five money order serials before they are entered into the log. Each serial is 11 digits: ten digits of serial number followed by a check digit. The station rule is that the check digit equals the last digit of the sum of the first ten digits - for example, 1-2-3-4-5-6-7-8-9-0 sums to 45, so the check digit is 5. The batch was read aloud over the phone and typed by one employee, so a single-position error is likely. Your trainer expects the batch to take about 90 seconds. A serial that fails the rule must be flagged, not corrected from memory; the source document is locked in the supervisor's office until 8:00 a.m.
1. Which serial fails the rule? Show your work for each one. 44281073650 92630581723 17394260585 60419372811 83150927464
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| Serial | Sum of first ten digits | Required check digit | Printed | Result |
|---|---|---|---|---|
| 4428107365-0 | 4+4+2+8+1+0+7+3+6+5 = 40 | 0 | 0 | pass |
| 9263058172-3 | 9+2+6+3+0+5+8+1+7+2 = 43 | 3 | 3 | pass |
| 1739426058-5 | 1+7+3+9+4+2+6+0+5+8 = 45 | 5 | 5 | pass |
| 6041937281-1 | 6+0+4+1+9+3+7+2+8+1 = 41 | 1 | 1 | pass |
| 8315092746-4 | 8+3+1+5+0+9+2+7+4+6 = 45 | 5 | 4 | fail |
The failing serial is 83150927464. Flag it and hold it; do not rewrite the last digit as 5 from memory, because the error might be in the tenth digit instead, and a note claiming the record was verified when it was reconstructed is worse than an open flag.
2. What kinds of error does this check digit fail to catch, and what would you add?
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What it catches: every single-digit substitution. Changing one digit changes the sum by at most 9, so the last digit of the sum must change too.
What it misses:
- Transpositions. Swapping two digits leaves the sum unchanged, so 16504 and 16540 both pass, as do Apt 12 and Apt 21 typed as digits. This is the most common keyboard error and the rule is blind to it.
- Compensating errors. Two changes that offset each other, such as 4 becoming 5 while 6 becomes 5, leave the sum identical.
- Self-consistent wrong data. The check digit proves the digits are internally consistent, not that you read the right serial off the right document.
What to add: a position-weighted check - multiply digits by alternating weights of, say, 1 and 3, then reduce mod 10 - which changes under adjacent transposition. Failing a system change, add an independent read-back against the source, and make the check-digit pass a second gate rather than the only one.
3. You are at 70 seconds with two serials left. What do you do?
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Speed up the method, not the standard.
- Keep a running total reduced mod 10 as you go: add each digit, subtract 10 the moment the total reaches 10 or more, so the running value never leaves 0 through 9. At the end the running value is the expected check digit, and you never do a large addition or a division at the end.
- Work in digit groups of three or four, glancing at the printed check digit only after finishing the sum, so you are not anchored by the number you are trying to verify.
- Do not re-verify serials that already passed. Log results in a column as you finish each one.
If you run out of time, submit the batch marked incomplete with the final two serials explicitly unverified - or ask for the extra 30 seconds - rather than passing them through unexamined. Marking something checked that you did not check is the one error in this task that no later control can catch.