The Rescue Window
At an orbital rescue dock, the entrance opens on every shared flash of two beacons, and never otherwise.
Beacon A flashes every 4 minutes, starting at 21:00.
Beacon B flashes every 6 minutes, starting at 21:02.
You arrive at 21:10. Both schedules continue unchanged.
When does the dock next open?
All times use the same clock. “Shared flash” means both beacons flash at the same instant. Find the first opening after your arrival. The illustration is decorative and contains no additional clues.
Need a Hint?
List each beacon’s flash times after 21:10. Starting times matter: the two schedules did not begin together.
Reveal Answer & Explanation
The dock next opens at 21:20 (9:20 p.m.).
Continue A’s schedule. Beginning at 21:00 and adding four minutes gives 21:00, 21:04, 21:08, 21:12, 21:16, 21:20.
Continue B’s schedule. Beginning at 21:02 and adding six minutes gives 21:02, 21:08, 21:14, 21:20.
Take the first shared time after arrival. Both flashed at 21:08, but you arrive at 21:10. The next shared flash is 21:20, so you wait ten minutes.
| Time | Beacon A | Beacon B | Dock opens? |
|---|---|---|---|
| 21:12 | Flashes | Does not flash | No |
| 21:14 | Does not flash | Flashes | No |
| 21:16 | Flashes | Does not flash | No |
| 21:20 | Flashes | Flashes | Yes |
After their shared flash at 21:08, they coincide every 12 minutes, the least common multiple of 4 and 6. Their shared times are 21:08, 21:20, 21:32, and so on. Therefore 21:20 is the unique next opening after 21:10.
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