[Jprogramming] The man who knew inifinity

Tue Jul 27 07:18:10 HKT 2010

Hi everybody,
Not being a mathematician, I managed to solve only Q1 (using J, of
course!). While I won't unleash my unworthy messy code upon your dear
eyes, let's just say that the solution involved i."0 >: i. 500 for
enumerating all cases and (+/\ = +/\.)
So the solutions is: The Belgian lived in the 204th house, the total
number of houses being 288.
Now would someone please provide the answer to Q2?
Best regards
2010年6月25日 Lettow, Kenneth <KLettow at thomasnet.com>:
> Currently I am reading a book titled "The Man Who Knew Infinity
> <http://en.wikipedia.org/wiki/The_Man_Who_Knew_Infinity> " which focuses
> on the relationship between Hardy and Ramanujan
> <http://en.wikipedia.org/wiki/Srinivasa_Ramanujan>  while Ramanujan was
> attending Cambridge.
>>>> In the book, Mahalanobis
> <http://en.wikipedia.org/wiki/P._C._Mahalanobis> , a friend of
> Ramanujan's that was attending King's College, visits Ramanujan in his
> apartment and relates to him a story that he came across in Strand
> Magazine <http://en.wikipedia.org/wiki/Strand_Magazine> . The story was
> called "Puzzles at a Village Inn".
>>>> "Now here is a problem for you," Mahalanobis yells to Ramanujan in the
> next room.  "What problem?  Tell me," said Ramanujan.  And Mahalanobis
> read it to him.
>>>> "I was talking the other day," said William Rogers to the other
> villagers gathered around the inn fire, "to a gentleman about the place
> Louvain, what the Germans have burnt down.  He said he knew it well,
> used to visit a Belgian friend there.  He said the house of his friend
> was on a long street, numbered on this side one, two, three, and so on,
> and that all the numbers on one side of him added up exactly the same as
> all the numbers on the other side of him.  Funny thing that!  He said he
> knew there was more than fifty houses on that side of the street, but
> not so many as five hundred.  I made mention of the matter to our
> parson, and he took a pencil and worked out the number where the Belgian
> lived.  I don't know how he done it."
>>>> Through trial and error, Mahalanobis figured it out in a few minutes.
> Ramanujan figured it out too, but with a twist.  "Please take down the
> solution," he said, and proceeded to dictate a continued fraction that
> wasn't just a solution to the problem, but rather the solution to the
> whole class of problems implicit in the puzzle.
>>>> Mahalanobis was astounded.  How, he asked, had Ramanujan done it?
> Ramanujan replied, "Immediately I heard the problem it was clear that
> the solution should obviously be a continued fraction; I then thought,
> Which continued fraction?  And the answer came to my mind."
>>>> Q1:  What was the house number where the Belgian lived?
>> Q2:  What was the continued fraction that Ramanujan found?
>>>> FYI, this story appears on pages 214-215 of "The Man Who Knew Infinity
> <http://en.wikipedia.org/wiki/The_Man_Who_Knew_Infinity> ".
>>>>>>>> ----------------------------------------------------------------------
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