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
