Puzzles 3 & 4
| Puzzle
3 (Correct Answers and winners) Twelve of us met at Lake Elizabeth on a saturday to play cricket. As the noon approached we decided to pool in money and order Lunch. So each one of us contributed equally and ordered for a very costly lunch. The lunch got so delayed that some got bored and left. After the rest of us finished lunch, I found that I had to pay $9 from my pocket to cover evrything including tips. To my surprise I found that we had spent $41 per head which I am sure is too much under any circumstances.(after all, we ate more than what each of us paid for, since some guys had already left). Any way the question is How much was our original contribution and how many of us ate lunch. Rest assured that our contributions were only in Dollars and not in cents (i.e. No small change was used) |
| Puzzle
4 (Correct Answers and winners) A Problem Srinivasa Ramanujan, the famous 20th century Indian Mathematician solved ! This problem was first published in the English magazine 'Strand' in December 1914. A King's college student, P.C. Mahalanobis, saw this puzzle in the magazine, solved it by trial and error, and decided to test the legendary mathematician Srinivasa Ramanujan. Ramanujan was stirring vegetables in a frying pan over the kitchen fire when Mahalanobis read this problem to him. After listening to this problem, still stirring vegetables, Ramanujan asked Mahalanobis to take down the solution, and gave the general solution to the problem, not just the one with the given constraints. |
| The problem, stated in
simple language, is as follows: In a certain street, there are more than fifty but less than five hundred houses in a row, numbered from 1, 2, 3 etc. consecutively. There is a house in the street, the sum of all the house numbers on the left side of which is equal to the sum of all house numbers on its right side. Find the number of this house. Also find all solutions to this problem, without the above 50 and 500constraint. You may give any of the following: •A formula, an infinite series, a continued fraction, or a similar devise to generate all the solutions •A method with which one can find all the solutions up to any limit he/she wishes •A method to arrive at the next solution if all the previous solutions are known. And find all solutions where total number of houses is less than 10000. (Using a brute-force computer program is too trivial, so avoid it!) ---Umesh PN--- |