The Torch and the Bridge
Four travellers reach an old rope bridge at night. It will hold at most two people at a time, and it is far too dangerous to cross without light. Between them they have one torch, and it cannot be thrown across — somebody has to carry it back.
They do not walk at the same speed. Crossing takes them 1, 2, 5 and 10 minutes. When two cross together they move at the pace of the slower one.
One torch. Two at a time. Somebody always walks it back.
Answer to type: the shortest possible total time, in minutes.
💡 I want a nudge
The two slow walkers cost you 5 + 10 if they cross separately. What if they crossed together?
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Answer: 17
- 1 and 2 cross together — 2 minutes. Total: 2.
- 1 walks the torch back — 1 minute. Total: 3.
- 5 and 10 cross together — 10 minutes. Total: 13. This is the whole idea: the two slow walkers are spent at the same time, so the 5 costs nothing at all.
- 2 walks the torch back — 2 minutes. Total: 15.
- 1 and 2 cross again — 2 minutes. Total: 17.
The trick: stop thinking about getting people across and start thinking about the slow ones. Every minute the 10 spends on the bridge is unavoidable — so make sure the 5 is spending those same minutes. Pairing your two worst cases together, instead of dragging each one separately, is a move that wins a surprising number of puzzles.