Four People, One Torch
Everyone has to cross, the bridge holds two, and there is only one torch.
Four people need to cross a bridge at night. It is dark enough that nobody crosses without the torch, and there is only one torch between them.
- The bridge holds at most two people at a time.
- Two people crossing together move at the pace of the slower one.
- The torch cannot be thrown back — somebody has to carry it, which means crossing again.
They take 1, 2, 5 and 10 minutes to cross.
Get all four across in seventeen minutes.
Almost everybody finds nineteen first, and nineteen is a perfectly sensible answer to a slightly different question. Getting to seventeen means giving up something that feels obviously right.
- nobody
Everyone starts on this side, with the torch. Somebody has to carry it back.
If you are stuck
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The instinct is to have the fastest person carry the torch back every time, since they waste the least on the return trip. That is the nineteen-minute answer, and it is worth working out exactly why it costs so much: the ten still has to cross, and whoever escorts them is spending ten minutes too.
So the question becomes: is there a way for the ten to cost ten minutes once, rather than dragging somebody else along with it?