Insight on Ramanujan’s Puzzle

Dr. R. Sivaraman

House Number Puzzle; Pell’s Equation; Continued Fraction; Convergents.

One of the most significant mathematicians of India, of 20th century was Srinivasa Ramanujan. He posed several interesting puzzles as his notebook jottings. The entries of his notebooks were today considered to be mathematical treasures. During the period when Ramanujan stayed at Trinity College of Cambridge University, England his Indian friend posed a interesting puzzle which Ramanujan had solved immediately. In this paper, I will introduce that puzzle and provide the way as how Ramanujan could have accomplished the solution in a flash.

[1] S. Ramanujan, Manuscript Book 1 of SrinvasaRamanujan, First Notebook, Chapter VIII, 66 – 68.
[2] Bruce C. Berndt, Ramanujan’s Notebooks Part II, Springer, Corrected Second Edition, 1999
[3] S. Plouffe,Identities inspired by Ramanujan Notebooks II , part 1, July 21 (1998), andpart 2, April 2006.
[4] G. H. Hardy, P.V. SeshuIyer, B.M. Wilson, Collected Papers of SrinivasaRamanujan, New York, Chelsea Pubishing Company, 1962.
[5] S.R. Ranganathan, Ramanujan: The man and the mathematician, Asia Publishing House, 1967.
[6] R. Kanigel, The man who knew infinity, Abacus, December 1992.
[7] P.K. Srinivasan, Memorial Volumes I and II, Letter and Reminiscences of Ramanujan, 1968.
[8] P.K. Srinivasan, Creativity of Ramanujan, Association of Mathematics Teachers of India, Chennai.
[9] R. Sivaraman, Recognizing Ramanujan’s House Number Puzzle, German International Journal of Modern Science, 22, November 2021, pp. 25 – 27.