Case 46 · timetable deduction · Medium · About 5-10 minutes
The island archive closes its parcel hatch at 08:30. You are waiting at Quay at 07:58 with a small box that must reach Island as early as possible. The harbor clerk offers a timetable. One tempting connection is too tight.
Every time below is exact. There are no delays, shortcuts, or other services. Your task is to find the earliest possible arrival, rather than merely an arrival before closing.
The harbor rules
You may wait at any stop. Changing boats requires at least two full minutes between arrival and departure. This also applies at Quay before your first departure. A boat departs on time; arriving one minute before departure is too late to board.
| From | To | Departs | Arrives |
|---|---|---|---|
| Quay | Lock | 08:00 | 08:12 |
| Quay | Glass | 08:00 | 08:08 |
| Glass | Island | 08:09 | 08:20 |
| Glass | Reed | 08:12 | 08:18 |
| Lock | Reed | 08:14 | 08:19 |
| Lock | Island | 08:15 | 08:26 |
| Reed | Island | 08:20 | 08:29 |
What route gives the earliest legal arrival at Island? Give the arrival time and explain why the apparently faster alternative fails.
A useful way to work is to write the earliest time you are ready to board at each stop. That time is two minutes after arrival. Do not confuse reaching a pier with being ready to leave it.
Hint 1 - reveal when you want a nudge
There are only three listed arrivals at Island. Test the earliest one first.
Hint 2 - reveal when you want a nudge
Arriving at Glass at 08:08 makes you ready to board at 08:10.
Reveal the solution and explanation
Take Quay to Lock at 08:00, then Lock to Island at 08:15. You arrive at 08:26.
The first boat reaches Lock at 08:12. Your two-minute change is complete at 08:14, so the 08:15 departure is legal. You started at Quay at 07:58, which also satisfies the first boarding requirement.
The timetable's 08:20 Island arrival looks better. It belongs to the boat leaving Glass at 08:09. Your only way to Glass arrives at 08:08. You would need to be there by 08:07 to catch that boat, so this connection cannot be made.
The remaining Island arrival is 08:29 from Reed. You can reach it by Quay-Glass-Reed: 08:18 plus two minutes permits boarding at 08:20. Quay-Lock-Reed fails because 08:19 plus two minutes is 08:21. Either way, no Reed route beats 08:26. These are all listed Island arrivals, so the earliest legal choice is unique.
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