santhoshsram wrote:And I just picked a conveniently large number 100, it can be 200, 300 or whatever.
See my point?
Unless we assume that both last year and this year the entire garden was packed with cabbages we won't be able solve it as mentioned. In other words, we are assuming there is no empty space in the garden. Is that ok? Because if we do not assume that, we can pick another answer choice.
I mean, just imagine a really really large square garden that is large enough to fit X cabbages as well as X+211 cabbages.
first of all, it's not as easy and simple as you imagine. Shankar also solved for answer and Mitch came with breaking factors of prime. I stopped at the eve and decided unclear.
There is one major constraint in this problem, and it's name is
cabbage (
one sq.foot area). Each cabbage is one, whole, unit and you could not count these as half cabbages or 1/3 cabbages. Therefore, even if theoretically you can have X+216 in the garden, practically you may have only Integer A^2- Integer B^2 = 216. This is resolved in expert's Mitch answer with great elegance. If you account for constraint cabbage is integer and then figure the way for T^2-L^2=216, you are done.
it's very precise and clear now, the answer is A.
looked up the last post by expert.
@Mitch, even if the question doesn't convey each cabbage occupies 1*1 sq.ft, it tells the dimensions of each cabbage, which is again whole unit (must be integer) and gathered together the cabbages form some area. This area will be construed by individual cabbages (say scattered within the square shaped garden) and aggregated will make some area. We are interested in area and it's composite sides. We are not measuring the areas of garden portions packed from end-to-end. We measure areas.
