Overview
The bridge and torch problem is a scheduling classic: four people of different speeds must cross a dark bridge at night with a single shared torch, and the bridge can only bear two at once.
The naive instinct — always let the fastest person shuttle the torch back — is not optimal. The clever move is to make the two slowest people cross together, so their times overlap instead of adding up.
How to solve Bridge & Torch
- Send the two fastest (1 and 2) across first: 2 minutes.
- Send the fastest (1) back with the torch: 1 minute (total 3).
- Send the two slowest (5 and 10) across together, so you 'pay' 10 only once: 10 minutes (total 13).
- Send the second-fastest (2) back with the torch: 2 minutes (total 15).
- Send the two fastest (1 and 2) across again: 2 minutes (total 17).
The key insight
Group the two slowest people into a single crossing. Pairing 5 with 10 means their 5-minute cost is completely hidden inside the 10, instead of each slow trip being charged separately.
Variations & echoes
- For different times the optimum switches between two strategies; you compare '2 fastest shuttle' versus 'ferry the slowest as a pair'.
- It's a favourite technical-interview question about greedy versus optimal reasoning.
- The same overlap idea appears in job scheduling and parallel task batching.
Frequently asked questions
Why not always send the fastest back?
That 'greedy' plan costs 19 minutes here. Letting the two slowest cross together saves time by overlapping the 5 inside the 10.
Is 17 provably the minimum?
Yes, for the times 1, 2, 5, 10 there is no plan faster than 17 minutes.