Brain Teasers · The Rope Bridge
Rope Bridge Puzzle 1 2 5 10 - The 17-Minute Answer
The torch-and-bridge puzzle as a story: speeds of 1, 2, 5 and 10, and a storm 17 minutes out.
What is the bridge and torch puzzle?
The bridge and torch puzzle (also called the bridge crossing puzzle) is a classic optimisation puzzle: a group of people, each with a different individual crossing time, must get across a bridge at night using a single torch that must be carried on every crossing and cannot be thrown or relayed. The bridge can hold at most two people at once, and a pair crossing together can only move as fast as the slower of the two. The task is to find the minimum total time for everyone to cross.
The most common version uses four people with crossing times of 1, 2, 5, and 10 minutes, and it's a fixture of technical interview puzzles because the obvious strategy is wrong in an instructive way. The intuitive plan - have the fastest person escort each of the others across one at a time - forces both the 5-minute and the 10-minute person to be paid for in full, since each of their crossings happens separately.
The optimal strategy instead sends the two slowest people across together, so that the larger crossing time absorbs the smaller one instead of paying for it twice, at the cost of one extra return trip by a fast walker to make that pairing possible. Finding this requires questioning the greedy assumption that the fastest person should always be the one escorting, and asking where two 'slow' costs can be overlapped into one.
As with other optimisation puzzles disguised as logic puzzles, the bridge and torch problem tests whether a candidate defaults to the first plan that works, or checks whether the expensive parts of the plan can be made to overlap - the same instinct that matters in scheduling, resource allocation, and any problem where a few large costs dominate the total and the naive plan pays for them separately when it doesn't have to.
How it works
Four friends reach a gorge at night with one torch. The bridge holds at most two people, whoever is on it must have the torch, a pair moves at the slower walker's pace, and the torch cannot be thrown back. Their crossing times are 1, 2, 5 and 10 minutes, and the storm hits in 17. The story asks for the minimum time to get all four across. You lock in a guess, then step through the answer and breakdown.
How scoring works
No grading - your guess is displayed back beside the answer. The story teasers share one lifetime unlock for free users.
The key insight
The instinctive plan - the fastest walker escorts everyone - costs 19 minutes because the 10 and the 5 are both paid in full. The winning move sends the two slowest across together so the 5 is absorbed inside the 10, at the price of an extra fast return trip: 1+2 across, 1 back, 5+10 across, 2 back, 1+2 across, for 17 exactly.
The full step-by-step solution lives at /brain-teasers/bridge-crossing/solution.
A worked example
Dee (1) and Cass (2) cross: 2. Dee returns the torch: 1. Amal (10) and Bo (5) cross together: 10. Cass returns: 2. Dee and Cass cross again: 2. Total 2 + 1 + 10 + 2 + 2 = 17, with the two fastest handling every return trip and the two slowest making one shared journey.
Common mistakes
• Answering 19 - the ferry-with-the-fastest plan feels efficient but pays both slow crossings separately.
• Pairing each slow walker with a fast one, which wastes the fast walker's speed entirely.
• Stopping at the first schedule that works instead of asking where the expensive minutes overlap.
Why interviews test this
Interviewers watch for the moment you question the greedy assumption: computing 19, noticing it misses 17, and hunting for overlapped cost is the optimisation instinct being tested. The written solution is at /brain-teasers/bridge-crossing/solution.
Play The Rope Bridge on Outcry
The Rope Bridge is free to play on Outcry, in the Brain Teasers section, and every run is timed and scored. Read the guide once, then play The Rope Bridge and check your score against the strategy above. The guide book has a written guide for every other game, and the practice hub and mock assessments put the same skills under a real screen's clock.