Avery: 1 minute. Blake: 2 minutes. Casey: 5 minutes. Drew: 10 minutes.
Rules:
• At most two people can be on the bridge at once.
• Anyone crossing must carry the single flashlight, so it has to be brought back each time.
• A pair walks at the speed of the slower person.
Can all four reach the other side within 17 minutes? If so, how?
💡 Hint
Time the obvious plan first, then ask which two travelers are most costly. Look for a way for them to pay that cost only once, with quick walkers handling the returns.
Reveal answer
Yes, in exactly 17 minutes: the two fastest cross first, and the two slowest cross together in the middle.
Step-by-step solution
- Avery and Blake cross together: 2 minutes (total 2).
- Avery brings the flashlight back: 1 minute (total 3).
- Casey and Drew cross together: 10 minutes (total 13). Their slow times overlap instead of adding.
- Blake, who has been waiting on the far side, brings the flashlight back: 2 minutes (total 15).
- Avery and Blake cross together again: 2 minutes (total 17).
- A computer search of every possible sequence of crossings confirms that 17 minutes is the fastest possible. The escort plan (Avery walks each person over) takes 10 + 1 + 5 + 1 + 2 = 19 minutes.
Why it fools people
Each step of the escort plan is locally smart: always use the fastest person to return the flashlight. But “smart at each step” is not the same as “smart overall.” The real cost is that Casey and Drew each make a separate slow trip. Pairing them wastes Casey’s time but saves 5 minutes overall, and parking Blake on the far side pays for the extra return. Greedy choices often miss the best plan.
Did you get it?
About This Puzzle
Four friends on a late hike in the Smoky Mountains reach a narrow rope bridge just as the light fades. The ranger station on the far side closes its gate in 17 minutes. The bridge is sturdy enough for two people at a time, the path is rough, and they have exactly one flashlight. Nobody will step onto the bridge without it. The four walk at very different speeds, and a pair has to move at the pace of the slower walker. The obvious plan comes in a couple of minutes too slow. The fast plan exists, but it asks you to do something that feels backward.
How to Think About It
Write down the obvious plan first and time it, so you know what you’re trying to beat. Then look at where the minutes go. Every trip across must be followed by a return trip with the flashlight, except the last one. Ask two questions: who should carry the flashlight back, and who should be paired with whom on the way over? The two slowest hikers are expensive. Every time either of them walks, the clock takes a big hit. See whether you can arrange things so their slow times overlap instead of adding up.
Common Traps
The natural plan is to let the fastest hiker escort everyone, since that person is the quickest to bring the flashlight back. It sounds efficient, and it totals 19 minutes, two over the limit. That plan is the main trap, because each step looks optimal on its own. The other trap is deciding the puzzle is impossible after trying a few variations of the escort idea. The winning plan sends the two slowest hikers across together, which feels wrong because neither of them can then make a quick return.
Where This Puzzle Comes From
The bridge-and-torch puzzle has been popular for decades and became famous as an interview question at technology companies. It belongs to the family of crossing puzzles, alongside the older river-crossing problems, and it is often used to show why greedy step-by-step choices can miss the overall best plan. This retelling uses an original hiking setting, with numbers chosen so the best plan is not the obvious one.
Try This Variation
Same bridge, same rules, but a different group: Avery takes 1 minute, Blake 4 minutes, Casey 5 minutes and Drew 6 minutes. What is the fastest time for all four to cross, and does the same trick still help?
Show the answer to the variation
The fastest is 17 minutes, and this time the escort plan wins: 4 + 1 + 5 + 1 + 6 = 17. The pairing trick gives 4 + 1 + 6 + 4 + 4 = 19. Pairing the slow hikers only pays when Blake’s two extra trips cost less than Avery’s escort trip plus Casey’s walk.