Riddle of the Week

Riddle of the Week: Crossing a Sketchy Rope Bridge in the Middle of the Night

Difficulty level: Moderate

By Jay Bennett

Here is the second in a series of weekly riddles from your puzzle-loving nerds at Popular Mechanics. This week's riddle is a little trickier than last week's, The Farmer's Dilemma, but the two are similar in concept and the solutions have some things in common. So check out last week's riddle if you haven't already—especially if you are struggling with this one, because solving last week's will get you on the right track.

PROBLEM

You've taken a job as a researcher in a remote and mysterious laboratory high in the Swiss Alps. Late one night, while you're working in the lab, you hear a loud crash just before the lab assistant bursts through the door, fleeing from the outstretched arms of a reanimated corpse. You and the lab assistant manage to get out into the hallway and bar the door shut behind you. Rounding a corner, you bump into the janitor and the old professor who oversees the lab work. They tell you that you must escape through an emergency exit at the back of the building that hasn't been used in years, as the front entrance has been overrun with zombies.

You grab a flashlight and flee with your three companions out the rear emergency exit, into the darkness and down a hill before you arrive at a dilapidated rope bridge with fraying ropes and missing footboards. The bridge spans a wide gorge, and a fall means certain death, but it's your only method of escape. You hear the zombies crash through the emergency exit of the lab, and the professor quickly estimates that they will arrive at the foot of the bridge, where you are standing, in 17 minutes.

Because the bridge is so worn and weathered, only two people can cross at once. Because it is pitch dark out with no moon to light your way, one person must come back across the bridge with the flashlight after they have crossed to allow anyone else to cross. And because the bridge is so rickety, you need to get everyone all the way across before the zombies arrive. (They'll run out onto the bridge and collapse it, so even if you're most of the way across when they reach the foot of the bridge, you'll die.)

You are a spry young researcher, and it only takes you 1 minute to dash across the bridge. The lab assistant is a bit slower, and it takes her 2 minutes to cross the bridge. The janitor managed to twist his ankle coming down the hill, so it will take him 5 minutes to cross. And the professor is an hunched old man with arthritis—it takes him a full 10 minutes to cross the bridge.

How do you get everyone across the bridge to safety in 17 minutes or less?

The Short Version: Four people are trying to cross a sketchy rope bridge in the middle of the night. Only two can cross at a time. They only have one flashlight, and so one person must bring it back across the bridge to the starting side before anyone else can cross. One person takes 1 minute to cross, another takes 2 minutes to cross, another takes 5 minutes to cross, and the last person takes 10 minutes to cross. Hypothetically, if the 2-minute person and the 5-minute person crossed together, that would take a total of 5 minutes (but someone needs to bring the flashlight back, resulting in 7 minutes spent if the 2-minute person returns with the light). Everyone needs to get across in 17 minutes or less, otherwise they will be ripped apart and consumed by zombies.

HINT

Are you sure you want a hint? Here it is:

The first assumption that many people make when attempting to solve this riddle is that the 1-minute person shuttles everybody across, returning with the flashlight every time. This is incorrect. There is a faster way.