There is a math story that starts out, Two Jews on a Train going".  By
the end of the story, one of the gentlemen has figured out exactly
where the other was coming from and other data more or less by using
deductive reasoning.  I DID NOT FIND THIS STORY IN ADAM BIRO's book. 
I would like to have the entire progression of thinking that goes on
in this story.

Eddie

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Request for Question Clarification by efn-ga on 07 Sep 2004 21:31 PDT

Is this the story?

http://www.nikhilkhade.com/articles/2004/4/448/

--efn

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Clarification of Question by eddiet-ga on 08 Sep 2004 22:41 PDT

This is exactly what I was looking for.  Many thanks. Ironically,
someone sent me this same answer today.  Claim your reward and thanks
again.

Eddie

Hi Eddie,

I'm glad I was able to find the story you sought on this web page.

http://www.nikhilkhade.com/articles/2004/4/448/

The same story appears on several other pages with very similar
wording, usually classified as a Jewish joke.  Unfortunately, I could
not find the original source.

The search terms that led me to the page were:

two jews train deduction -biro

Regards,

--efn

This might be helpful:

"I remembered an old Jewish story about two Jews on a train in Russia.
One asks the other, ?Where are you going?? and the second replies, ?To
Kiev.? Whereupon the first says, ?You liar, you tell me you are going
to Kiev so I would think you are going to Odessa. But I know you are
going to Kiev, so why do you lie??" - Ulam, S. M., Adventures of a
Mathematician, Charles Scribner?s Sons, N.Y., 1976, p. 143.

Let us generalize the reasoning of the first speaker in the story.

Thought 1: ?If he says x1 it is because he wants me to think x2, but I
know he really means x1.?

Thought 2: ?But wait: he?s pretty smart. He knows that I will think
Thought 1, and he will try to fool me. So I know that if he says x1 he
really means x2.?

Thought 3: ?But wait: he?s even smarter than that. H knows that I will
think Thought 2, and he will try to fool me. So I know that if he says
x1 he really means x1.?

Thought 4: But wait: he?s even smarter than that. He knows...?

This sequence suggests the following school examination:
1. Solve problem 2.
2. Solve problem 3.
3. Solve problem 4.
   .
   .
   .

Given a sequence of Thoughts such as the above, is it meaningful to
ask what the speaker?s best strategy is? Any answer you give is
negated by the next Thought. We can say that, as with the example of
the examination, that we are dealing with paradoxes arising from
problems whose statements are never completed. The speaker assumes he
is simulating perfectly the second person?s thoughts. (We remark in
passing that he also assumes that intelligence implies the ability to
duplicate another?s line of reasoning, and then to ?outwit? it.
Thought (i) is always meta-Thought (i - 1).) It is interesting to
speculate on what the speaker?s reasoning would be if he knew that his
simulation of the second person?s thought were only correct some
percent of the time.

http://www.occampress.com/index_files/simparadox.pdf

This seems to be a variation of the old story of the travelling
salesman in the country who broke down, with a flat tyre and no
spare,on a lonely back road, late at night. Far in the distance he saw
a faint light. So off he goes to get some help. on the way he is
thinking about what he might say to the farmer, it being so late, to
convince the farmer to get out of his warm bed and lend him a jack. He
imagined that when he arrived at the farmhouse, all would be in bed
and all the lights out. Then he would knock on the door. The farmer,
who had to get up very early next morning for his chores, would wake
up and have to freeze getting to the front door. Then the salesman
would say " I`m broken down and need to borrow a jack". The farmer
would say " Why were you not more prepared for breakdowns when you
travel in the country". The salesman would say " If it was`nt for me
coming out to see you people, you would have to battle on without my
handy goods". Then the farmer said " You know you have woken me from a
nice sleep". And so on and on.
By the time he got to the farmhouse, walked up to the door and
reluctantly knocked. The farmer opened the bedroom window, and before
he could say anything, the salesman said. YOU CAN KEEP YOUR @#^*&^%$$
JACK!
....There is always that tendency to imagine the worst in people.
Happily, the opposite is true.