The Bridge Problem

Logic Level 3

You get hired by a science industry. In the middle of the night, you wake up to get some cookies. While you are downstairs in the laboratory kitchen, you see a button that says, "Do Not Press." Guessed it yet? That's right, you pressed it.

The button opens up a few capsules that were holding zombies, and now they are after you. Quickly, you put your coat on and wake up the others, (who I will introduce in a minute.) When you get outside, you all start heading away from the lab, with the zombies chasing you out. Eventually, you run to a bridge, which is the only way to safety.

The bridge is too rickety that if more that two people at a time even step on it, It will collapse under your feet and you will fall into a huge gorge. Plus, it's so dark outside that the lantern you happened to salvage when evacuating the lab can only illuminate a small area of the bridge. This means that you have to hold the lantern or be right next to the person who is holding it.

Each of you take your own time to run across the bridge:

You 1 Minute
Assistant 2 Minutes
Janitor 5 Minutes
Elderly Professor 10 Minutes

Here, you can see them showing how fast they run, in minutes:

The professor calculates it will take 17 minutes for the zombies to catch up to you.

How many rounds will it take to get everyone across the bridge safely?


The answer is 5.

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1 solution

Sameer Syed
Feb 12, 2017

It will take 5 rounds. First, you and your assistant take the lantern and pass the bridge. This takes 2 minutes. Then, you, being the quickest, take the lantern and run across the bridge to hand it to the janitor and professor. That is another minute, which totals up to 3 minutes. When the professor and the janitor take the lantern and run across it takes 10 minutes. Now you have used 13 of 17 minutes. But you are still on the wrong side of the bridge. Now remember, your assistant is on the right side of the bridge. She takes the lantern from the janitor and professor and runs to you. 15 minutes have gone past. Then, last, you and the assistant run across once again to total up to 17 minutes, and 5 rounds taken.

Idea from Ted-Ed and Alex Gandler

Fun question and nicely presented. One small typo to note: in the picture it shows the Elderly Professor taking 10 minutes to cross the bridge, but in the table it shows his time as 6 minutes, (which is clearly the correct time otherwise the minimum time would be 17 minutes, allowing the zombies to catch up). Can the picture be changed? If not, then a small note of correction would suffice.

The general bridge crossing puzzle is discussed here .

Brian Charlesworth - 4 years, 3 months ago

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Thank you. I got the picture from the youtube video I first saw and tried to solve it from. Yet I remember it as 6 minutes because for some reason my brain keeps thinking of 6 when the number I am trying to think of is 10. I will put a note in the problem.

Sameer Syed - 4 years, 3 months ago

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