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
