Oct 9: lamp lit 5:58 p.m., high water 7:10 p.m.
Oct 10: lamp lit 5:56 p.m., high water 8:00 p.m.
Oct 11: lamp lit 5:54 p.m., high water 8:50 p.m.
Oct 12: lamp lit 5:52 p.m., high water 9:15 p.m.
Oct 13: lamp lit 5:50 p.m., high water 10:30 p.m.
Oct 14: lamp lit 5:48 p.m., high water 11:20 p.m.
The facts:
1. Here, sunset comes exactly 2 minutes earlier each night, and the evening high water comes exactly 50 minutes later each night. Both rules held all week.
2. Exactly one entry is forged. Every honest entry follows both rules.
3. The island dock can be used only within 60 minutes before or after high water, inclusive. The supply boat can leave only at those times.
4. On the forged night all three keepers were on the island at sunset. Each later said he or she left on the boat: Hank says he left at 8:25 p.m., Ruth says 10:30 p.m. and Eli says 9:20 p.m.
5. Exactly one of them did not leave. That keeper is the one who forged the entry. The other two told the truth.
Which entry is forged, and which keeper wrote it?
💡 Hint
Compare the gaps between consecutive evening tides with the stated rule, and find the night that breaks it. Recompute that night’s correct time before testing any keeper’s claim.
Reveal answer
The Oct 12 entry is forged, and Hank wrote it. The true high water that night was 9:40 p.m., so the dock was usable from 8:40 to 10:40 p.m.
Step-by-step solution
- Check the high water gaps: 7:10 to 8:00 is 50 minutes, 8:00 to 8:50 is 50, 8:50 to 9:15 is only 25, 9:15 to 10:30 is 75, 10:30 to 11:20 is 50. The Oct 12 entry is the odd one: Oct 11 to Oct 13 is 100 minutes, which is two nights of 50.
- Check sunset: 5:58, 5:56, 5:54, 5:52, 5:50, 5:48. All follow the 2 minute rule, so only the Oct 12 high water is wrong. The forged entry is Oct 12.
- The correct high water on Oct 12 is 8:50 plus 50 minutes, 9:40 p.m. The dock window runs from 8:40 to 10:40 p.m.
- Test the claims. Hank’s 8:25 p.m. is before 8:40, so that boat could not have docked. Ruth’s 10:30 p.m. is inside the window. Eli’s 9:20 p.m. is inside the window.
- Only Hank’s story is impossible, so Hank stayed on the island and forged the entry. (A code check confirmed that only Oct 12 can be forged, and only Hank fits.)
Why it fools people
The forger did the hardest thing right: the lamp time on the forged night is exactly correct. The invented number was the tide, which cannot be copied from the day before because it moves a lot. The trap inside the trap is that the false 9:15 would make Ruth look guilty and Hank look innocent, so a solver who skips the forgery check gets the wrong keeper with a clean-looking argument. Verify your data first, then use it.
Did you get it?
About This Puzzle
Cutler’s Ledge Light stands on a rocky island off the coast of Maine, reached only by the supply boat and only at the right moment of the tide. Three keepers share the work of tending the lamp. Every night the keeper on watch writes down when the lamp was lit and when high water reached the landing. One October night a fishing boat struck the ledge in the dark, and the inspector found the lamp cold. The logbook says otherwise, and one of its entries was written by someone who was not honest. You will not need real tide tables: every number you need is printed below.
How to Think About It
Treat the logbook as a pattern with a rule, then look for the one row that breaks it. Write down the differences between neighboring nights for sunset and for high water, and compare them with the rule. When one entry sits wrong, check whether the other five agree with each other across the gap. Then use the real, corrected high water for that night, not the written one, to build the window when the boat could use the dock. Test each keeper’s claimed time against that window. Be careful about which time you trust.
Common Traps
The first trap is to hunt for a keeper who looks guilty. The second is to trust the high water time on the forged night, because the forger chose it to look plausible. If you use the written time, the dock window slides 25 minutes earlier, and a different keeper then looks like the liar. A third trap is to assume the sunset time is the clue: here the lamp time on the forged night is perfectly correct, and only one number is wrong. Always check every entry against the rule before you use any of them.
Where This Puzzle Comes From
This is an original case in the tradition of Golden Age detective fiction, where timetables, tides and train schedules often hide the key clue. Logbook puzzles belong to the family of consistency puzzles: a set of records follows a simple rule, one record breaks it, and the break tells the story. The tide pattern used here is simplified for the puzzle and is not real tide data.
Try This Variation
A different logbook, same two rules (sunset 2 minutes earlier, high water 50 minutes later each night): Oct 1, 5:40 and 6:05 p.m. Oct 2, 5:38 and 6:55. Oct 3, 5:36 and 7:45. Oct 4, 5:34 and 8:25. Oct 5, 5:32 and 9:25. Which night is forged?
Show the answer to the variation
Oct 4. The high water times run 6:05, 6:55, 7:45, so Oct 4 should read 8:35 p.m., and Oct 5 should read 9:25, which it does. Only the 8:25 entry is off, and all the sunsets follow the 2 minute rule. A code check confirmed it.