Lee WFour people, one torch and a rickety bridge that only takes two at a time.
Four people have to cross a rickety bridge at night. They have one torch, the bridge holds two at a time, and nobody can cross without the torch. They take 1, 2, 5 and 10 minutes to cross, and a pair walks at the slower one’s pace. What is the shortest time it takes to get all four over?
Sending the fastest person back every time is not the quickest plan.
The 1 and the 2 cross, two minutes, and the 1 brings the torch back, one. The 5 and the 10 cross together, ten, and the 2 brings it back, two. The 1 and the 2 cross again, two more: seventeen.
Most people say nineteen, because they send the fastest back every time and make the two slowest cross separately.
Source: Saul X. Levmore and Elizabeth Early Cook, Super Strategies for Puzzles and Games, 1981