## Thursday, April 28, 2005

### A quick, throw-away puzzle.

Rumour has it that the following puzzle is used by at least one company during job interviews to test an applicant's critical thinking skills. Through exhaustive search, it's pretty easy to find the solution, but it's a bit more challenging to analyze the puzzle to zero in on the solution based on pure logical deduction. So, we're not just after the solution, we're after how you got to it. (By the way, apparently job applicants are given only five minutes to solve it, which is why the logical deduction thing is not a bad idea.)

"U2" has a concert that starts in 17 minutes and the group members must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help them across to the other side. It is night. There is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either one or two people, must have the flashlight to see. The flashlight must be walked back and forth, it cannot be thrown, etc. Each band member walks at a different speed. A pair must walk together at the rate of the slower man's pace, based on this information:

* Bono: - 1 minute to cross

* Edge: - 2 minutes to cross

* Adam: - 5 minutes to cross

* Larry: - 10 minutes to cross

For example: if Bono and Larry walk across first, 10 minutes have elapsed when they get to the other side of the bridge. If Larry then returns with the flashlight, a total of 20 minutes will have passed and you will have failed.

And ... go. Tick, tick, tick ...

OPEN FOR SOLUTIONS, noon Eastern time, Friday, Apr 29, so don't post any answers yet.

Mehdi Afellat said...

First, Bono and the edge cross. That's 2 min. Then, Bono goes back and gives the flashlight to Adam and Larry. That makes 1 more min. Adam and Larry cross. That makes 10 more min. Then the edge goes back to get bono. That makes 2 min. Then Bono and the Edge cross, and that makes 2 more min. It all adds up to 17 min.
My way og getting the solution was kind of a try and see. After a couple of minutes I realised that Adam and Larry should cross together. After that, it took me another couple of minutes to try 2 or 3 combinations and get to the final solution

CC said...

"After a couple of minutes I realised that Adam and Larry should cross together."

That's the critical observation -- that the slowest two people have to cross together since, given that the slowest person is the bottleneck, you might as well send the second slowest person with him.

Next, it's easy to see that the general sequence of crossings will be:

--> 2 people -->
<-- 1 person <--
--> 2 people -->
<-- 1 person <--
--> 2 people -->

As soon as you accept that pattern of crossings, there's only one place where it makes sense to send Adam and Larry across -- that middle crossing.

Everything else is just detail.