Five Desks, Five Operators, One Internally Inconsistent Log
Five AWO/TPO operators - A, B, C, D and E - were on the night shift, each at exactly one of five numbered desks: desk 1 Control, desk 2 Traffic, desk 3 PCR dispatch, desk 4 Repeater monitoring, desk 5 Teleprinter. The supervisor's note records only these facts: E was at desk 2; A sat at the desk immediately before D's, that is, A's desk number is one less than D's; D was not at desk 5; B sat at an odd-numbered desk; and C was not on a desk adjacent to E's. The morning log needs the full desk-to-operator mapping. Later, a constable states that he took a message from C at the PCR dispatch desk, and the relief clerk insists he is certain that B was on an even-numbered desk. Neither statement can be squared with the supervisor's note as it stands, and the shift supervisor wants to know which record to trust.
1. Derive the complete desk-to-operator mapping from the supervisor's note, showing each deduction step.
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Step 1. E = desk 2 (Traffic).
Step 2. A is immediately before D, so (A, D) can only be (1,2), (2,3), (3,4) or (4,5).
- (1,2) impossible - desk 2 is E's.
- (2,3) impossible - desk 2 is E's.
- (4,5) impossible - the note says D was not at desk 5.
- Therefore A = desk 3 (PCR dispatch), D = desk 4 (Repeater monitoring).
Step 3. Desks 1 and 5 remain for B and C. B is on an odd-numbered desk, which both 1 and 5 are, so this clue alone does not settle it.
Step 4. C is not adjacent to E at desk 2, so C ≠ 1 and C ≠ 3. Desk 3 is already A's, so C = desk 5 (Teleprinter) and therefore B = desk 1 (Control).
Answer
- Desk 1 Control - B
- Desk 2 Traffic - E
- Desk 3 PCR dispatch - A
- Desk 4 Repeater - D
- Desk 5 Teleprinter - C
Check every clue: E at 2 ✔; A immediately before D ✔; D not at 5 ✔; B at an odd desk ✔; C (desk 5) not adjacent to E (desk 2) ✔. Exactly one assignment survives, so the note is internally consistent.
2. The constable says he took a message from C at the PCR dispatch desk. Test that claim against the deduction and state what should be verified first.
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Test PCR dispatch is desk 3, which the deduction fixes as A's. If C were at desk 3, then E is at 2, so A and D must take consecutive desks from 1, 4 and 5. The only consecutive pair left is (4,5), but D cannot be at 5, and (A,D) = (1,2) or (2,3) is blocked by E anyway. No arrangement exists.
So the claim contradicts the note on three independent counts: the position of E, the adjacency rule and the rule that D is not at desk 5. A statement that breaks one clue is a probable error; one that breaks three is almost certainly a misremembering or a misattribution.
What to verify first Verify the cheapest, most independently recorded fact first - not the claim itself:
- E's desk. Traffic desk attendance is visible on the call-taking sheet and on the traffic channel's own log, so it is checkable without asking anyone's memory.
- D's desk. The repeater desk keeps an equipment log with entries timed to the minute; if D signed it during the night, D was at desk 4 and the whole chain holds.
- Only then ask the constable whether the message came from desk 3 or desk 5 - a tired constable at 03:00 may simply have confused the extension number with the operator's identity.
Conclusion to record The supervisor's note is consistent and uniquely solvable; the constable's recollection is not merely unverified but arithmetically impossible unless at least one recorded fact is wrong. Record the discrepancy, the verification done, and the corrected attribution - do not silently overwrite the log.
3. The relief clerk insists B was on an even-numbered desk. What does that do to the record, and what is the minimum set of facts you would re-verify?
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Effect on the record An even-numbered desk for B would have to be 2 or 4, but desk 2 is fixed to E and desk 4 to D. There is no even desk left, so the clerk's statement makes the whole note unsatisfiable - not merely different. That is a stronger result than a competing solution: it proves that at least one of the recorded facts is wrong, not that the answer is uncertain.
Minimum re-verification set Work backwards from what is hardest to get wrong:
- D at the repeater desk (desk 4). The repeater desk produces its own timed equipment log - an independent, contemporaneous record. If D's entries run through the night, D is fixed at 4, and any even desk for B is impossible.
- E at desk 2. The traffic desk's call sheet is the second independent record.
- The clerk's own duty roster, to see whether he was even present at the changeover when B's desk was recorded - a witness who was not there is not evidence.
Judgement Do not amend the note to accommodate the clerk. Amend it only when an independent record contradicts it, and then record both the original entry and the correction with the reason. Two human recollections against two machine-generated logs is not a close contest; the AWO should say so plainly in the log rather than leaving a contradiction for someone else to discover in an inquiry.