*This is not a puzzle. So, for those of you who follow this puzzle blog, please bear with me for just one post. Interesting Math in this article though :P*
Most of my friends already read an article that I wrote more than an year back - "

Speak Up"

Here, inspired by the movie, The Beautiful Mind, I give a mathematical analysis of asking a girl out. Nice time it is. Feb 10. No plans for Feb 14 and I am sure this article makes me look even more geekier and all the more reason for me to believe that I will be alone, yet again. But what the hell, lets do it!

Note: This is not an independent analysis. There are many "mathematics sites" which does "similar" analysis.

@Consultants, correct me if I am wrong in my estimates. :P

Why is there a need to be selective?

From the age of 15, I guess there are approximately 3,600 girls I have liked (On average days, I don't see new girls. But going outside, I like about 30 girls. Saying that I go out once every week right …

Not possible.

ReplyDeleteLemma: If the gcd of all the pile sizes is a odd number (>1), then the objective isn't possible.

Proof: Assume that the common gcd of piles is n, an odd no > 1. Hence, both the operation will keep this invariance. As a result, you can never create a pile of size < n.

Now, the only operation you can do at {5, 49, 51} is (a).

But, 3| {51, 54}; 5|{5, 100} and 7|{49, 56}. Hence the desired piling isn't possible.

Thanx Shantanu.. Correct Solution :)

ReplyDeleteim not sure of my solution..

ReplyDeletethis is mine..

if after all such operations we get 105 single pebbled piles...

the last operation would be dividing a pile of 2 into 2 piles of 1 pebble.

in that way the proceeding from back

we get 52 piles of 2 pebbles and 1 single pebbled pile.There is no pile with equal number if pebbles as this 1 pebbles pile.

So this is not possible...

I am sorry.. I did not get this. Why is this not possible?

ReplyDeletei was not sure of my soln....

ReplyDeletelater after posting it, i came 2 know dat i was wrong...

:) chalega :P

ReplyDelete