Bridge and Torch Puzzle Answer: Cross in 17 Minutes [Solved]

The bridge and torch puzzle answer is 17 minutes. Four investment bankers cross in this exact order: the Analyst and the Associate cross together (2 minutes), the Analyst returns with the torch (1 minute), the VP and the MD cross together (10 minutes), the Associate returns with the torch (2 minutes), and finally the Analyst and the Associate cross together (2 minutes). Total time: 2 + 1 + 10 + 2 + 2 = 17 minutes.

Four investment bankers need to cross a rickety bridge at night. The bridge holds at most two people at a time, there is a single torch, and anyone crossing must carry it. The Analyst crosses in 1 minute, the Associate in 2, the VP in 5, and the MD in 10. For example, two people crossing together move at the slower person’s pace, and someone has to carry the torch back after every crossing except the last. The answer is 17 minutes, and this post shows exactly how it is done.

The Bridge and Torch Puzzle Answer: Cross in 17 Minutes

The bridge and torch puzzle: four bankers cross a bridge at night with one torch. Crossing times: Analyst 1, Associate 2, VP 5, MD 10. At most two cross at the slower person’s pace, and the torch comes back each time. The answer: all four cross in 17 minutes.

Here is the sequence that achieves it, timed from the moment the first pair steps onto the bridge.

0:00: The Analyst and the Associate cross together. They move at the Associate’s pace, so this takes 2 minutes.

2:00: The Analyst takes the torch and hurries back alone. 1 minute.

3:00: The VP and the MD cross together. This is the big one: 10 minutes at the MD’s pace.

13:00: The Associate takes the torch and returns. 2 minutes.

15:00: The Analyst and the Associate cross together one last time. 2 minutes.

17:00: All four bankers are across the bridge.

Elapsed time	Who moves	Time added
0:00	Analyst + Associate cross	2 minutes
2:00	Analyst returns with the torch	1 minute
3:00	VP + MD cross	10 minutes
13:00	Associate returns with the torch	2 minutes
15:00	Analyst + Associate cross	2 minutes
17:00	Everyone is across	Total: 17 minutes

Why does this work when most people get stuck at 19? The key insight is pairing the two slowest together. The VP and the MD cross as a pair, so the brutal 10-minute crossing happens exactly once instead of twice. Every crossing needs a torch return except the final one, and returns are pure overhead, so the two fastest people make those trips: 1 minute and 2 minutes. The trade is simple: accept a slightly expensive final crossing (the fast pair crosses twice, 2 + 2) to collapse the two slow crossings into a single 10-minute trip. That one decision saves 2 minutes.

Why the Bridge and Torch Puzzle Answer Is Not 19 Minutes

Most candidates produce 19 minutes. In fact, interviewers hear this answer constantly. The instinct is to use the fastest person as a shuttle: the Analyst escorts each banker across and always brings the torch back.

0:00: The Analyst and the MD cross together. 10 minutes.

10:00: The Analyst returns with the torch. 1 minute.

11:00: The Analyst and the VP cross together. 5 minutes.

16:00: The Analyst returns with the torch. 1 minute.

17:00: The Analyst and the Associate cross together. 2 minutes.

19:00: Everyone is across. Total: 10 + 1 + 5 + 1 + 2 = 19 minutes.

Elapsed time	Who moves	Time added
0:00	Analyst + MD cross	10 minutes
10:00	Analyst returns with the torch	1 minute
11:00	Analyst + VP cross	5 minutes
16:00	Analyst returns with the torch	1 minute
17:00	Analyst + Associate cross	2 minutes
19:00	Everyone is across	Total: 19 minutes

This plan feels right because the Analyst is doing all the work and the torch keeps moving, but it pays the 10-minute and 5-minute crossings separately and still burns 2 minutes on return trips. However, nobody questions whether the Analyst should be the one making every return. That is the trap: the escort plan minimizes crossing time and forgets that return trips cost torch time too.

What the Interviewer Is Actually Testing

This puzzle is not a math test. It screens for four things, and the interviewer is listening for all of them in how you talk through the problem.

First, costly-move discipline. Every move in the puzzle has a price, including the returns. Candidates who only price the forward trips are doing half the accounting. Similarly, in real work, the same blindness shows up when someone optimizes the visible steps of a process and ignores the handoffs in between.

Second, the pairing insight. The natural reflex is to send the fastest person back and forth. The winning move is batching the two slowest so the expensive crossing happens once. Likewise, it is the instinct that matters on a live deal: you do not have your fastest analyst run every errand; instead, you batch the slow, expensive steps and protect the bottleneck.

Third, comfort with a counter-intuitive answer. Seventeen beats nineteen even though it involves a 2-minute return trip by the Associate, which looks wasteful. Candidates who cling to the escort plan under time pressure tell the interviewer how they handle being wrong. It is the same skill we walk through in our Monty Hall problem answer: the gut answer feels efficient, but the correct one only appears once you price every move.

Fourth, articulating the trade-off out loud. The candidate who gets the offer says something like: I will accept a 2-minute return to save a 10-minute crossing. The interviewer is grading the narration as much as the number, because that sentence is what a client hears when you recommend the cheaper structure.

Try Another One Tonight

If the bridge and torch puzzle clicked for you, try the Two Doors Riddle next: two guards, two doors, one question, and a solution that hinges on asking the right question instead of the obvious one. It is another interview favorite where stating the answer upfront and then proving it wins the room.

Bridge and Torch Puzzle FAQs

Can this be done faster than 17 minutes?

No. 17 minutes is the provable floor, and the proof comes down to the two slowest walkers, the VP and the MD. There are only two ways to get them across.

Plan 1: they cross together. One 10-minute crossing. The fast pair still needs two more forward crossings (2 + 2), and the two mandatory torch returns cost at least 3 minutes: after the Analyst’s 1-minute return, the second return must come from someone already across, and the cheapest of those is the Associate at 2 minutes. Total: 10 + 2 + 2 + 3 = 17.

Plan 2: they cross separately. A 10-minute crossing plus a 5-minute crossing, a 2-minute crossing for the fast pair, and two returns costing at least 2 minutes. Total: at least 10 + 5 + 2 + 2 = 19.

No plan beats 17, and the sequence above reaches it exactly.

What if the torch lasts only 15 minutes?

Then it cannot be done with these times. Interviewers sometimes set the torch limit below the optimum to see whether you spot that the task is impossible instead of forcing a wrong answer. Another well-known version of this puzzle uses crossing times of 1, 2, 7 and 10 minutes, and its fastest possible crossing is also 17 minutes. As a result, a 15-minute torch means failure there too.

Is there more than one correct sequence?

Yes. For example, the two return trips can swap between the two fastest people. In the solution above, the Analyst makes the first return and the Associate makes the second. Flip them and the total is still 17 minutes. The essential move is always the same: the VP and the MD cross together, and the two fastest handle the returns.

Where does this puzzle come from?

In fact, this exact setup, four investment bankers with crossing times of 1, 2, 5 and 10 minutes and a 17-minute answer, is documented by IBankingFAQ as an investment-banking brain teaser, and the general bridge and torch problem is documented on Wikipedia.

Follow-up variations interviewers use

The most common variation changes the times to 1, 2, 7 and 10. Some interviewers add a fifth person, or set the torch limit just below the optimum to test whether you recognize an impossible setup. The method is always the same. First pair the slowest, then price the return trips, and finally check whether the target time is even reachable.

Know someone prepping for consulting or IB interviews? Share this with them.