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
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?