Sunday, June 13, 2010

One puzzle that starts a story

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.

The question:
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.


Rajesh Kumar 'Nachiketa' said...
This comment has been removed by the author.
Rajesh Kumar 'Nachiketa' said...

you said, "One puzzle that starts a story" at the same time there are stories that leaves (at least some of the)listeners puzzled.This curiosity generates some researchers who dares to find the truth. we need such story-tellers (who can puzzle your mind) and audience (who can raise questions) to understand the true picture of nature through science (or otherwise).

Utpal said...

@Rajesh: Yes completely agree. By the way why didn't you put in the answer to the question? Anyways ... I was expecting more response to the article but that didn't happen. I will wait for some more time keeping in mind that presumably most have not visited the article for want of time.

Rajesh Kumar 'Nachiketa' said...

I am sorry, I gave the answer in the deleted comment.
The answer is:
ONE each weight of 1,3,9,27 and 81 kg.

Utpal said...

@Rajesh: That's an interesting answer. I have not verified it but I assume your have check it.

Now I understand that 2 you are weighting with (3-1).

Lets see the pattern .. the numbers are three times the previous numbers. Can you extrapolate this pattern and measure all weights to 1000 or more? Check it out.

By the way ... the answer I have is different. But if your answer is correct than we have something in our hands. I am excited with your answer. Will discuss mine later, understandably.

Rajesh Kumar 'Nachiketa' said...

Yes! i want to weigh 2 as 3-1 and 4 kg as 9-(3+1).
I think this sequence can be extended upto 1000. If fact 1,3,9,27 and 81 can weigh upto 121 kgs.
We can discuss your answer whenever you want.

ZEAL said...

thanks for the wonderful puzzle.

It was nice to see the calculations going on here.