The Torn Register
The single-door registry room of a district office is fitted with a logbook in which every entrant writes an in-time and an out-time, read from a wall clock inside the room. On Tuesday the entries were: Mehta 09:10–12:40; Nair 10:05–11:30; Oberoi 11:45–13:20; Pillai 12:10–14:00. On Wednesday morning the sealed register kept in the room's steel cupboard was found with two pages torn out. The cupboard key is held by the supervisor, who was away from the office from 12:00 to 13:00 on Tuesday and carried the key with her. The standing instruction is that tampering with the register requires the person to be alone in the room for at least 15 continuous minutes. A service door for the air-conditioning duct, not covered by the logbook, is opened only when maintenance is called; the technician's register shows a visit on Tuesday, but the time column was left blank. The wall clock is known to run seven minutes fast.
1. Construct the occupancy timeline for Tuesday and identify every official who had a solo window of at least 15 continuous minutes.
Read the worked answer
Merge the four intervals and note where the count of persons inside equals one:
| Window | Inside | Duration |
|---|---|---|
| 09:10–10:05 | Mehta | 55 min |
| 10:05–11:30 | Mehta, Nair | 85 min |
| 11:30–11:45 | Mehta | 15 min |
| 11:45–12:10 | Mehta, Oberoi | 25 min |
| 12:10–12:40 | Mehta, Oberoi, Pillai | 30 min |
| 12:40–13:20 | Oberoi, Pillai | 40 min |
| 13:20–14:00 | Pillai | 40 min |
Solo windows of 15 minutes or more: Mehta (55 min, and again exactly 15 min) and Pillai (40 min). Nair and Oberoi were never alone: Nair always shared with Mehta, and Oberoi was with Mehta until 12:40 and with Pillai thereafter.
Note the boundary convention: the second Mehta window is exactly 15 minutes, so it satisfies 'at least 15' only if the log times are exact. That is worth flagging rather than assuming.
2. Using the key constraint, state who could have tampered with the register and draft the finding you would place on file.
Read the worked answer
Cross-check against the key. The cupboard could only be opened while the supervisor was away, i.e. after 12:00 and carrying the key, or after her return at 13:00.
- Mehta's solo windows end at 10:05 and 11:45 - both before 12:00. Mehta had solitude but no key. Excluded.
- Nair and Oberoi never had solitude at all. Excluded on the first test.
- Pillai was alone from 13:20 to 14:00, 40 minutes, entirely after the key returned. Pillai is the only official who possessed both solitude and access.
Finding to place on file: 'On the evidence of the logbook and the key custody record, Pillai is the only official who cannot be excluded; no other official can be included.' That wording matters. It is not a finding of guilt, because the logbook records declared presence, not actual presence - a person may write an out-time and stay, or write an in-time and never come. The unlogged technician's visit is also unresolved, and the 12:10–12:40 three-person window is not automatically safe: one person can open the cupboard while another provides apparent cover.
Further steps: seal and photograph the logbook, preserve the torn edges for a paper examination, take the technician's timing from the AMC vendor's job card rather than memory, and record statements from all four separately before any of them compares notes.
3. The wall clock is seven minutes fast. Does that change any conclusion, and does it matter at all?
Read the worked answer
No conclusion changes. Every entry in the log, and the supervisor's 12:00–13:00 absence as written in the same room's record, is read from the same fast clock. The offset is a constant, so it cancels: durations are unchanged (11:30–11:45 is still 15 minutes of solitude; 13:20–14:00 is still 40), and the relative ordering of entries is unchanged. A uniform shift cannot create or destroy an overlap.
But it matters for one specific operation. The moment you compare a logbook time with a time from any other source - the gate CCTV server, a mobile call record, a lift log, the technician's job card - the seven minutes becomes a live error. A person who appears to have left at 12:40 (logbook) actually left at 12:33 (true time). If CCTV shows someone at the corridor door at 12:37, an uncorrected comparison would place them outside the room; a corrected one places them inside. The correction must be applied once, explicitly, in the working note, and applied in the same direction to every external comparison.
Practical instruction: add a one-line calibration note to the file - 'room clock +7 min; all external timings converted to true time' - and have the clock itself corrected the same day, so that Wednesday's entries are not silently mixed with Tuesday's.