The Joy of playing with numbers.

                                                       Kunal A. Borse      I will start with a little anecdote from the life of mathematician Srinivasa Ramanujan. Once a friend visited him, while Ramanujan was cooking in his kitchen. His friend was solving a puzzle from the 'Strand' magazine, but he just could not crack it. So he read it out to Ramanujan. The puzzle goes as follows-    'Find the numbers x and y, given that                              1+2+3+......+(x-1)+x=x+(x+1)+.....+y and 50<y<500.'   Much to his friend's amusement, Ramanujan, still busy with his cooking, answered correctly within a moment. "The value of y must be 288 while that of x must be 204,'' ...

The Weirdest coincidence . Kunal .A. Borse      While thinking about the ‘Kaprekar constant (6174) ’, I came across another constant. The following constant is defined for a four digited number. The process to be followed is described below. We take a random four digited number, say ‘abcd’ (in decimal form). Then we arrange its digits in an ascending and descending order, and divide both these into two 2 digited numbers, and perform the following. Let a>b>c>d without loss of generality, abcd -ab and cd dcba- dc and ba We calculate       (ab)^2 +(cd)^2 – (dc)^2 – (ba)^2 We do the process again after getting the result until we keep getting the same result. On getting a three digited number, we consider it to be four digited by adding a zero to the left. What I observed was that we always get the number 1782 or 0 after performing this operation. It is quite easy to see that 1782 again gives 1782 on subjecte...