From: kanad@quip.eecs.umich.edu (Kanad Chakraborty)
Subject: Re: Help me with MH puzzle, also, a new puzzle.
Organization: University of Michigan EECS Dept., Ann Arbor
Date: Sun, 3 Jan 1993 22:26:29 GMT

In article <1i7cb6INNe0@mirror.digex.com> adric@access.digex.com (William Johnson) writes:
>Damn.  Someone help, please.  I know people are sick of this one, but....
>
>I see two lines of reasoning, and the one I intuitively feel is correct
>is not the one that logically seems correct.
>
>Reasoning one:  Once Monty shows you a door, the remaining two are one right
>	and one wrong, making the choice 50/50.

If there are 2 possibilities to an issue (e.g. 2 doors as in this case)
it is not necessarily true that they are equally _probable_. Monty 
doesn't just show _a_ door, he uses his knowledge of what's behind each
door to show you a _wrong_ door, _after_  he has seen your initial choice.
Therefore, the third door is in some sense related to the one you initially
chose -- it is one of the 2 _remaining_ doors such that the _other_ one 
was known, and then shown, to be a wrong door by Monty.  Yea, I know this is
a lousy way to explain it but I hope you get the point. 

Matters would have been quite different however, if the problem were as
follows : Suppose you have 3 doors. Monty knows what's behind each door,
and he opens a wrong door. _Then_, from the 2 remaining doors, you first
pick one -- and then Monty allows you the option of staying or switching.
In this case, obviously, your first reasoning is correct, and it's a
wash whether you stay or switch.

>Reasoning two:  Once you pick, you have a 2/3 chance of being wrong, and so
>	if one of the two wrong answers is shown, switching give you a 2/3
>	chance of being RIGHT.
>
 
Correct reasoning !

>Now I'm pretty sure two is correct, but I keep coming back to 1.  I can see
>2 as the correct answer, but I can't express the logic in a way that makes it
>comfortable.
>
>This reminds me of a puzzle I saw years ago in a Mensa test as follows:
>
>When playing Russian Roulette, each member has a revolver with 6 chambers
>and 1 bullet (may have been 2 bullets, I don't think it changes the answer,
>just the likelihood of death).  Each member then fires the gun twice into
>his/her own head.  Members may spin the revolver before each shot.  Which
>option gives the best chance of survival:
>	A) Spin shoot spin shoot
>	B) Spin shoot shoot
>	C) Shoot spin shoot
>	D) Shoot shoot.
>
>Warning:  My speculations regarding this follow the CTRL-L, so if you don't
>want to see the (possibly flawed) answer, hit 'n' now.
>
>Ok, it seems obvious to me that the two options where you shoot twice
>without a spin in the middle are worst.  Because assuming you survive
>the first shot (because if you didn't, it's over), you have now reduced
>your chances of surviving the next chamber.
>
>But I don't see the difference between A and C, unless in case C you know
>in advance that where you put the bullet either was or was not in the
>next chamber to be fired.  This may have been the answer, but I don't think
>so, because reading their answer sheet, the probabilities weren't as clear
>cut as that.  Any suggestions?
>
>
>
>(Note, I am not a member of Mensa.  Also, I am new to this group, so if this
>has been posted before, I am sorry).
>
>Will.
>-- 
>Copyright (C) 1993 by William Johnson  All rights wronged, all lefts made
>adric@access.digex.com                     without benefit of turn signal.
>Will Johnson, 307 S. Reynolds St Box P-216, Alexandria, VA  22304
>"Tis better to have loved and lost than never to have included a quote in your .sig file."

Kanad