Four people are walking in the dark, and they have only one torch. They stumble upon a long and narrow bridge, which they need to cross. To cross the bridge they need the torch, and once it has been carried to the far side, someone needs to bring it back to the ones who are waiting. Only two can cross the bridge at the same time.
One of the group is quite slow and takes 10 minutes to cross the bridge. The others take 5, 2 and 1 minutes, respectively.
What is the fastest way for the group to cross the bridge?
Answer
The fastest way to cross the bridge requires 17 minutes.
The 1 and 2 minute persons cross the bridge first, and the 1 minute person carries the torch back to the starting position. This takes 2 minutes to the far side, 1 minute back. Next the 10 minute and 5 minute persons walk across, taking 10 minutes. The 2 minute person goes back and fetches the 1 minute person. Together they cross the bridge, and now the entire group is on the far side. This sums up to 17 minutes.