Hi Lorenzo, 204 was the correct answer for Q1 from the book, but it didn't give the answer for the continued fraction.
I should of made it clear that I didn't have the answer for Q2, but the way it was written in the book made it seem like it was something obvious, which of course it isn’t. The only other clue supplied is that Ramanujan removed the 50 to 500 house constraint and provided a general solution (i.e. on an eight house street 6 is the answer (1+2+3+4+5)=(7+8)). Ken -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Lorenzo Costanzia di Costigliole Sent: Monday, July 26, 2010 7:18 PM To: Programming forum Subject: Re: [Jprogramming] The man who knew inifinity 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 2010/6/25 Lettow, Kenneth <[email protected]>: > 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> ". > > > > > > > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
