Bridge

Problem: this one is a classic that many of you have probably already heard, but all the more reason why it should definitely be included here. four people are on this side of the bridge. the bridge will be destroyed by a bomb in 17 minutes. everyone has to get across before that. problem is that it’s dark and so you can’t cross the bridge without a flashlight, and they only have one flashlight. plus the bridge is only big enough for two people to cross at once. the four people walk at different speeds: one fella is so fast it only takes him 1 minute to cross the bridge, another 2 minutes, a third 5 minutes, the last it takes 10 minutes to cross the bridge. when two people cross the bridge together (sharing the flashlight), they both walk at the slower person’s pace. can they all get across before the bridge blows up?

person A: 1 minute
person B: 2 minutes
person C: 5 minutes
person D:10 minutes

Solution

Of course its possible, otherwise it wouldn’t be a very interesting question. the only trick is in realizing that you want to get the two slowest people across together, because otherwise you are wasting too much time. but then once you get them across, how do you not make one of them walk back with the flashlight? well, you just have one of the fast people already there waiting to sprint the flashlight back across.

1. A & B cross. total time: 2 minutes.

C |==========================| A D | | B |==========================| flashlight   2. B comes back. total time: 4 minutes.   C |==========================| A D | | B |==========================| flashlight   3. C & D cross. total time: 14 minutes.   B |==========================| A | | C |==========================| D flashlight   4. A comes back. total time: 15 minutes.   A |==========================| C B | | D |==========================| flashlight   5. A & B cross. total time: 17 minutes.   |========= =============| A | KABOOM! | B |========= =============| C D flashlight  

another solution which is valid is to have A bring the flashlight back in step 2. it only changes the solution slightly. this is supposed to be a “classic” microsoft interview question but it seems absurdly easy to be a good interview question (especially coupled with the fact that everyone has probably heard it already).

2026 Update: Scheduling and Resource Optimization

Bridge crossing puzzles — variants of the Torch/Bridge problem with different group sizes, speeds, and constraints — are optimization problems that test greedy algorithm thinking. The key insight is a provably optimal strategy that minimizes total crossing time.

The general algorithm for N people and one torch:

def min_bridge_crossing(times):
    """
    Minimum time for all people to cross a bridge with one torch.
    Only 2 can cross at once; torch must be carried back.
    Greedy: always use the two-fast-escort strategy when beneficial.
    Time: O(n log n) for sorting.
    """
    times = sorted(times)
    n = len(times)

    if n == 1: return times[0]
    if n == 2: return times[1]
    if n == 3: return times[0] + times[1] + times[2]

    total = 0
    while len(times) > 3:
        # Option A: Fastest escorts slowest two separately
        opt_a = times[0] + times[-1] + times[0] + times[-2]
        # Option B: Top two cross together; fastest goes back; then slowest two cross
        opt_b = times[1] + times[0] + times[-1] + times[1]
        total += min(opt_a, opt_b)
        times = times[:-2]  # Two slowest crossed

    total += times[0] + times[1] + times[2]
    return total

# Classic example from Microsoft interviews
print(min_bridge_crossing([1, 2, 5, 10]))  # 17
print(min_bridge_crossing([1, 2, 3]))      # 6
print(min_bridge_crossing([1, 2, 4, 8, 16]))  # 35

2026 engineering parallel: This exact problem appears in database migration scheduling (minimize total downtime when migrating services one at a time with limited maintenance windows) and Kubernetes rolling update planning (minimize time to update all pods with a limited surge capacity). The greedy two-option analysis is the same.

Still asked at (2026): Microsoft (classic from their interview canon), Amazon (operations research), and any company where infrastructure scheduling comes up in system design rounds.