What's a boy to do?
 

An interesting problem was recently brought to my attention.

Let us say that you and I are standing next to a table on which I have
placed three boards identical in every respect except that each has a
different number painted on it.....1, 2, and 3, respectively.

I say to you that if you turn your back I will place a five dollar bill
under one of the boards and a slip of paper that says "you lose" under each
of the others. You then turn back to face the table and point to or name
the board you think has the five dollar bill under it. If you're right, you
win the five bucks.

We proceed. You pick, say, board number one. I say, "O.k., tell you what,
I like you so I'm going to make this easier for you," and I remove board
number three to show you that it has a "you lose" tag under it. Obviously,
the five dollars must be under one of the other two. "So," I say, "would
you like to stick with your original pick, or change your mind?"

It is a given that the game is not rigged in any way and you are not being
fooled by anything ambiguous or otherwise misleading in the description.

The question.......what should you do?

Wolfgang

What's a boy to do?
 

Wolfgang wrote:
An interesting problem was recently brought to my attention.

Let us say that you and I are standing next to a table on which I have
placed three boards identical in every respect except that each has a
different number painted on it.....1, 2, and 3, respectively.

I say to you that if you turn your back I will place a five dollar bill
under one of the boards and a slip of paper that says "you lose" under each
of the others. You then turn back to face the table and point to or name
the board you think has the five dollar bill under it. If you're right, you
win the five bucks.

We proceed. You pick, say, board number one. I say, "O.k., tell you what,
I like you so I'm going to make this easier for you," and I remove board
number three to show you that it has a "you lose" tag under it. Obviously,
the five dollars must be under one of the other two. "So," I say, "would
you like to stick with your original pick, or change your mind?"

It is a given that the game is not rigged in any way and you are not being
fooled by anything ambiguous or otherwise misleading in the description.

The question.......what should you do?

Assuming that I trust you, it doesn't matter. It's 50/50 chance
you can stick with your current pick or switch.

Given it's you, it REALLY doesn't matter since the $5 is probably
in your pocket.
- Ken

What's a boy to do?
 

Wolfgang wrote:
An interesting problem was recently brought to my attention.

Let us say that you and I are standing next to a table on which I have
placed three boards identical in every respect except that each has a
different number painted on it.....1, 2, and 3, respectively.

I say to you that if you turn your back I will place a five dollar bill
under one of the boards and a slip of paper that says "you lose" under each
of the others. You then turn back to face the table and point to or name
the board you think has the five dollar bill under it. If you're right, you
win the five bucks.

We proceed. You pick, say, board number one. I say, "O.k., tell you what,
I like you so I'm going to make this easier for you," and I remove board
number three to show you that it has a "you lose" tag under it. Obviously,
the five dollars must be under one of the other two. "So," I say, "would
you like to stick with your original pick, or change your mind?"

It is a given that the game is not rigged in any way and you are not being
fooled by anything ambiguous or otherwise misleading in the description.

The question.......what should you do?

Assuming that I trust you, it doesn't matter. It's 50/50 chance
you can stick with your current pick or switch.

Given it's you, it REALLY doesn't matter since the $5 is probably
in your pocket.
- Ken

What's a boy to do?
 

Wolfgang wrote:
An interesting problem was recently brought to my attention.

Ah yes, the famous Monty Hall Puzzle. Go ahead & tell 'em the answer;
they won't believe it anyway. g

Joe F.

What's a boy to do?
 

"rb608" wrote in message
ups.com...
Wolfgang wrote:
An interesting problem was recently brought to my attention.

Ah yes, the famous Monty Hall Puzzle.

Spoilsport.

Go ahead & tell 'em the answer;
they won't believe it anyway. g

Don't have to. You just did. :)

Wolfgang

What's a boy to do?
 

"Wolfgang" wrote in :


The question.......what should you do?

Wolfgang


If I recall correctly, you should change your mind. When you chose the
first, you had a 1/3 chance of being right, and nothing has changed that.
If you change your mind now, that gives you a 2/3 chance of being correct.
I'm pretty sure I'm dead wrong on that 2/3 number, though, but the chance
is more than 0.5. The key is that the removal process is not random.


--
Scott
Reverse name to reply

What's a boy to do?
 

Wolfgang wrote:
Don't have to. You just did. :)

Do not for a moment think that this entire body of flyfishermen & women
even approach the level of geekiness necessary to be familiar with the
MH puzzle and an extended discussion of the answer. Methinks anyone
who already did know of the puzzle recognized as I did; so I doubt I
spoiled it for anyone. But for those who would now go look it up by
name instead of figuring out the answer would probably fish pegged
beads anyway. :-)

Joe F.

What's a boy to do?
 

"Wolfgang" wrote in message
...
An interesting problem was recently brought to my attention.

Let us say that you and I are standing next to a table on which I have
placed three boards identical in every respect except that each has a
different number painted on it.....1, 2, and 3, respectively.

I say to you that if you turn your back I will place a five dollar bill
under one of the boards and a slip of paper that says "you lose" under
each of the others. You then turn back to face the table and point to or
name the board you think has the five dollar bill under it. If you're
right, you win the five bucks.

We proceed. You pick, say, board number one. I say, "O.k., tell you
what, I like you so I'm going to make this easier for you," and I remove
board number three to show you that it has a "you lose" tag under it.
Obviously, the five dollars must be under one of the other two. "So," I
say, "would you like to stick with your original pick, or change your
mind?"

It is a given that the game is not rigged in any way and you are not being
fooled by anything ambiguous or otherwise misleading in the description.

The question.......what should you do?

Wolfgang


I'd knock you in the head and take the money. If it wasnt under the
boards it would surely be in your pocket along with several other pieces
of folding money. Problem solved!
"a friend"

What's a boy to do?
 

"Wolfgang" wrote in message
...
An interesting problem was recently brought to my attention.

Let us say that you and I are standing next to a table on which I have
placed three boards identical in every respect except that each has a
different number painted on it.....1, 2, and 3, respectively.

I say to you that if you turn your back I will place a five dollar bill
under one of the boards and a slip of paper that says "you lose" under
each of the others. You then turn back to face the table and point to or
name the board you think has the five dollar bill under it. If you're
right, you win the five bucks.

We proceed. You pick, say, board number one. I say, "O.k., tell you
what, I like you so I'm going to make this easier for you," and I remove
board number three to show you that it has a "you lose" tag under it.
Obviously, the five dollars must be under one of the other two. "So," I
say, "would you like to stick with your original pick, or change your
mind?"

It is a given that the game is not rigged in any way and you are not being
fooled by anything ambiguous or otherwise misleading in the description.

The question.......what should you do?

Wolfgang

The obvious answer is to pick up board no.3, hit you over the head with it,
find the $5 ( plus any other spare change you have in your pocket) and
leave. 8~ ).

Bob Weinberger

What's a boy to do?
 

rb608 wrote:
Wolfgang wrote:
Don't have to. You just did. :)

Do not for a moment think that this entire body of flyfishermen & women
even approach the level of geekiness necessary to be familiar with the
MH puzzle and an extended discussion of the answer.

The thought never occurred to me. Trust me. :)

Methinks anyone
who already did know of the puzzle recognized as I did; so I doubt I
spoiled it for anyone. But for those who would now go look it up by
name instead of figuring out the answer would probably fish pegged
beads anyway. :-)

Precisely.......Google.

I bumped into this yesterday in a delightful little novel called "The
Curious Incident of the Dog In the Night-Time" by Mark Haddon. The
narrator, a 15 year old autistic boy named Christopher Boone, relates
his adventure as an amateur sleuth (ala his hero, Sherlock) and
runaway. He's something of a mathematical savant. As Haddon, through
Chrisopher, relates the story, the question was put to Marylin vos
Savant in "Parade" magazine by one Craig F. Whitaker of Columbia
Maryland. Wikipedia confirms this (while making it clear that this is
"a widely known statement" of the problem and thus, presumably, not the
first), so I assume that the quotes Haddon provides from responses to
Ms. Savant's answer, that you should always change your answer and pick
the final door, are also genuine:

"I'm very concerned with the general public's lack of mathematical
skills. Please help by confessing your error."--Robert Sachs, Ph.D.,
George Mason University

"There is enough mathematical illiteracy in this country, and we don't
need the world's highest IQ propagating more. Shame!"--Scott Smith,
Ph.D., University of Florida

"I am in shock that after being corrected by at least three
mathemeticians, you still do not see your mistake."--Kent Ford,
Dickinson State University

"I am sure you will receive many letters from high school and college
students. Perhaps you should keep a few addresses for help with future
columns."--W. Robert Smith, Ph.D., Georgia State University

"You are utterly incorrect...How many irate mathemeticians are needed
to get you to change your mind?"--E. Ray Bobo, Ph.D., Georgetown
University

"If all those Ph.D.'s were wrong, the country would be in very serious
trouble."--Everett Harman, Ph.D., U.S. Army Research Institute


I started this thread because it was a fascinating problem......not,
for me, so much because of the answer (which, naturally, I got wrong)
or because of the solutions (which I can sort of dimly
comprehend.....for about as long as I am looking at them), but because
it is such a truly beautiful illustration of the axiom that it ain't so
much what we don't know as what we know that ain't so that ****s us
up.....which is, in turn, a simply gorgeous paradox.

I posted the quotes included above because, of course, I knew that the
usual ****weasels would be incapable of resisting the temptation to
make asses of themselves yet again and thus append themselves to the
list. More of them would unquestionably have done so if you hadn't
netted kennie so quickly. :)

Wolfgang
"gravy" it's called......and i like it.