Re: statistical problem - cave teaser


"Phil Holman" <piholmanc@yourservice> wrote in message news:A4qdnYzJLsh1m-bbnZ2dnUVZ_j6dnZ2d@xxxxxxxxxxxxxx

"Johan" <johanditmar@xxxxxxxxx> wrote in message news:1182458626.938176.195030@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Hello,

I was at a job interview today and I was asked a brain teaser that I
can't let go. The problem is as follows:

Suppose you are in a magic cave system and you start in a cavern with
three exits:

exit 1 takes you out of the cave system in one hours time

exit 2 returns you to the starting cavern after an hour

exit 3 returns you to the starting cavern after an hour initially.

However, each time exit 3 is taken, travel time back to the cavern
through this exit doubles.

Due to the magic of the cave system, when you return to the starting
cavern, your knowledge of which exits you've previously attempted is
forgotten.

Now, what is the expected time for escaping the cave system?

The answer told to me after failing to answer this question at the
interview was that the expected time is infinite. However, changing
the properties of exit two to leave the cave after one hour apparently
makes the expected value converge. Is this actually true? I attempted
this problem via monte carlo simulation without conclusive results for
the problem as stated, however the modified second problem appears to
converge to 2 hours.

What would have been a fast and impressive proof at an interview
situation?

The expected value is a summation of the probability times the length of time for each and every combination of choices. All you need is for one choice combination to not result in escaping (theoretically you could always select either entry 2 or 3) and the expected time value will be infinite.

Phil H

Well, no.

Back to school.

Ex 1. Go to a simpler cave with only door 1 and door 2.

Ex 2. Go to a cave with only door 1 and door 3.

If you make it out, go to the original cave...

T.
.

Relevant Pages

  • Re: statistical problem - cave teaser
    ... I was at a job interview today and I was asked a brain teaser that I ... exit 1 takes you out of the cave system in one hours time ... exit 2 returns you to the starting cavern after an hour ...
    (sci.stat.math)
  • Re: statistical problem - cave teaser
    ... exit 1 takes you out of the cave system in one hours time ... exit 2 returns you to the starting cavern after an hour ... what is the expected time for escaping the cave system? ...
    (sci.stat.math)
  • statistical problem - cave teaser
    ... I was at a job interview today and I was asked a brain teaser that I ... exit 1 takes you out of the cave system in one hours time ... exit 2 returns you to the starting cavern after an hour ...
    (sci.stat.math)