Problem 314

sivakd · Post by **sivakd** » Thu Dec 16, 2010 2:26 am

Wow, only 25 solvers so far. Looks like the toughest problem of this season.

I want to make sure I understand the following correctly

"The wall must be a closed series of straight lines, each line running from post to post."

If I have a slanting line from point a to b, does it have to be like a staircase so that it touches the nearest posts? Either way, I am no where close to solve this, but want to make sure I spend time on the right interpretation.

orj · Post by **orj** » Thu Dec 16, 2010 9:26 am

I thought as long it is a wall between two posts, it would meet the criteria. If not, you could not get past the 125 limit i guess.

Anyone trying to solve it with an integral?

hk · Post by hk » Thu Dec 16, 2010 9:59 am

Any straight segment is fine as long as its endpoints are posts.

arpit_tarang · Post by **arpit_tarang** » Thu Dec 16, 2010 6:48 pm

Hmm i was thinking maybe taking the area as a circle which extends outside the square might do the job. Although i'm still a noob at this

. But i am getting a nice value of the ratio around ~131.7, but that's on taking a circular boundary... i've yet to make a straight-lined approximation.

Lord_Farin · Post by **Lord_Farin** » Fri Dec 17, 2010 8:01 pm

This forum is not for discussing solving strategies. Please refrain from posting anything that might spoil the solving fun for others.

foumou · Post by **foumou** » Thu Dec 23, 2010 1:44 pm

In my opinion, part of the description of question is a little vague. For example,

"251001 posts have been placed in a rectangular grid with 1 meter spacing. The wall must be a closed series of straight lines, each line running from post to post."

Does this mean that we divide the square in a grid of 1x1 boxes? Probably not, because if every post had size 1 then we would need more than 251001 posts to fill the square. I still don't get it. Also, "Each line that runs from post to post" refers to a line that can run only through the ending points of each post or even through the middle of it.

I would appreciate any clarification on these issues. Also, congrats to those who have already solved it.

hk · Post by hk » Thu Dec 23, 2010 2:35 pm

You can look up what is meant by a post using this link:
http://dictionary.reference.com/browse/post?r=75
You should have the first meaning:

"a strong piece of timber, metal, or the like, set upright as a support, a point of attachment, a place for displaying notices, etc.
"

foumou · Post by **foumou** » Thu Dec 23, 2010 2:54 pm

Thank you for letting me know that there are dictionaries, but I just asked how these posts are used in the description of the problem since it is a little bit unclear. Anyway, thnx for your time, I think I have found the solution.

hk · Post by hk » Thu Dec 23, 2010 3:02 pm

Well, I thought that if the meaning of the word post was clear there wasn't any ambiguity anymore.
But one never knows.

foumou · Post by **foumou** » Thu Dec 23, 2010 3:04 pm

I understand, I just got confused for a minute but now I get the whole picture. Thnx

Muckle_ewe · Post by **Muckle_ewe** » Fri Nov 18, 2011 7:34 pm

Anyone care to look at my working and give me any hints as to how to improve. I'm currently accurate to 2 decimal places (know the numerical answer from ages ago when I first joined and wanted to solve this). I don't have a code as such since I've sort of tried to solve it with pencil/paper and just by looking at a plot of matlab but I can send the coordinates of the posts (not too many of them).

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