One fine day I happened to mistakenly enter my father's boss's office room. Once I introduced myself and apologized he welcomed me but after knowing I had just written my standard X board exams, he started to bombard me with a series of puzzles and mathematical questions that afternoon as if it was punishment I had to endure for being in the wrong room at the wrong time. Also I sensed he was using me as a guinea pig to test the current schooling standards. I managed to tackle, all his question, but for one. I eventually cracked it that evening and the complete process made me move a notch up in my understanding of mathematics and made me realize how a puzzle can be one of the best teaching methodology. Since then I have asked many this puzzle and have in most cases got the answer in quick time. Much quicker than I managed.
What I will do now is state the puzzle here without further delay and wait for some weeks to get answers from whoever cares to read this post. Most likely some of you have come across it and and I am expecting some participation. In the process of solving the question, each of you, I am sure, will understand the wider implication of this puzzle and would agree to me when I say it could be a good starting point when one introduces a particular of branch of mathematics to students.
I have been asked to weight all weights up to 100. That is I might be asked to weight, lets say 49 kg or any integer weight under 100 (including). What would be the least number of weights I should have and which ones.
It's possible I was not able to frame the question in best possible way. Let me know if you have any queries.