How Quickly Can You Cross This Bridge?

Before you is a rickety bridge, at your back a raging wildfire. With you are three people, some of them slower than others. Can you all cross to safety in time?

Photo Credit: zerega | CC BY-NC-ND 2.0

This week’s puzzle was suggested by Anirudh, a reader from Chicago. He says he first heard this classic riddle in middle school, back in India, and that it’s stuck with him ever since. We’ve reproduced it below, with some minor clarifying edits.

Sunday Puzzle #31: The Perilous Bridge-Crossing

Four people fleeing a fire come to a river in the night. Spanning the river is a narrow bridge, which they must cross to safety before they are consumed by the fire.

The bridge is narrow and ill-kept, and can therefore support just two people at any one time. The four people share but one dim torch, which they must use to traverse the dilapidated bridge safely. Anyone who attempts a crossing without the torch is as good as dead.

All four people are injured in different ways, and so it takes them different amounts of time to cross the bridge. Person A can cross the bridge in one minute, person B in two minutes, person C in five minutes, and person D in ten minutes. When two people cross together, they must do so at the slower person’s pace.

With the fire growing closer by the minute, time is of the essence. What is the fastest time in which all four people can cross the bridge to safety?

Hint

We’ll be back next week with the solution – and a new puzzle! Got a great brainteaser, original or otherwise, that you’d like to see featured? E-mail me with your recommendations. (Be sure to include “Sunday Puzzle” in the subject line.)

SOLUTION To Sunday Puzzle #30: Blowin’ in the Wind

Last week, I asked you to compare the flight times of a round-trip flight with and without a constant wind. The answer, I warned you, was not what you might expect.

My warning was a clue. It’s tempting, when solving this puzzle, to suppose that the forces of a headwind when flying from A to B and those of a tailwind when returning from B to A would balance one another out—but this is not the case! In fact, a roundtrip flight in zero wind will always be faster than one in a wind with constant velocity.

The easiest way to understand this conceptually is to note that the time during which the plane’s speed is decreased is longer than the time during which it is increased. Commenter e_is_real_i_isnt took this explanation to its extreme by imagining a scenario in which a headwind is equal to the plane’s airspeed:

If the wind speed is the same as the air speed then it takes an infinite amount of time to fly against it, which is not the same time as when there is no wind. Since the travel time doesn’t abruptly change from ‘same’ to ‘infinite’ one can guess that at any windspeed the time will be larger when the wind is blowing.

Commenter OutrageIsTheNewJoy later imagined another scenario involving an engine speed of 100mph and a windspeed of plus or minus 10 mph. Their approach allows us to calculate trip times that clearly show the wind scenario takes longer. A few minutes later, commenter mwhite66 broke the problem down with a handy chart:

Wind results in a longer round-trip flight time; beginning pilots are taught this. A simple example flying at 120 kts true airspeed over a 300 nm route (each way):

Wind Speed Outbound Inbound Total

0 kt 2:30 2:30 5:00

20 kt 3:00 2:09 5:09

40 kt 3:45 1:53 5:38