10885 - Martin the Gardener

Antonio Ocampo · Post by **Antonio Ocampo** » Sun Jul 31, 2005 9:56 pm

Hi guys

I don

misof · Post by **misof** » Sun Jul 31, 2005 11:03 pm

http://ginger.indstate.edu/ge/Graphs/GE ... rcle12.png

http://citeseer.ist.psu.edu/rd/76151371 ... 7every.pdf

Antonio Ocampo · Post by **Antonio Ocampo** » Sun Jul 31, 2005 11:25 pm

That paper is very hard for me

. What I feel is, if this is the expected way to solve the problem, then this is a maths problem instead of programming problem. Thx anyway

misof · Post by **misof** » Sun Jul 31, 2005 11:28 pm

Well, it was "Abednego's Mathy Contest", so one could expect math problems...

(And don't worry, the paper was too hard for me too, I found it during the contest but couldn't make a working solution... I plan to get back to this task once I have more time

)

Abednego · Post by **Abednego** » Mon Aug 01, 2005 8:54 am

No hard papers are required. The idea is very simple. I was very happy when 1 person solved this problem during the contest! He ended up in the 155'th place. :-)

The key observation is the following. Suppose that you know how to plant 13 trees at rational coordinates, so that the distance between each pair of trees is a rational number. Then you can simply multiply every coordinate by the common denominator of everything (coordinates and distances), and you will get integer coordinates and integer distances.

Now how do we solve the problem in rational numbers? That's not very hard at all. Here is a hint. We are not allowed to place 3 trees on the same line. If you add the restriction that no 4 trees are allowed on the same circle, then this is a famous unsolved problem. The largest number of trees that anyone knows how to place with the additional no-4-on-a-circle constraint is 6.

Cho · Post by **Cho** » Mon Aug 01, 2005 10:45 am

Hmmm.. It turns out that, for me, understanding misof's reference is easier than getting insight from Abednego's hint.

Cosmin.ro · Post by **Cosmin.ro** » Mon Aug 01, 2005 11:38 am

I think he means all points are on a circle.

Antonio Ocampo · Post by **Antonio Ocampo** » Tue Aug 02, 2005 5:23 am

I'm so frustrated

gush · Post by **gush** » Wed Aug 10, 2005 10:42 am

This is my answer:
....
I've tested that the distances between them are integers. But I still got WA. Why?

Cosmin.ro · Post by **Cosmin.ro** » Wed Aug 10, 2005 11:27 am

Maybe 3 colinear points, have you tested that?

gush · Post by **gush** » Wed Aug 10, 2005 11:55 am

All the points are on the same circle. So there should be no 3 points in the same line.

little joey · Post by **little joey** » Wed Aug 10, 2005 1:13 pm

gush, your values are OK and I just got AC with them.

Please make sure you send in a program that prints them, not just a text file that contains them.

Abednego · Post by **Abednego** » Wed Aug 10, 2005 6:05 pm

gush, and when you get AC, please don't forget to remove the numbers from your post. Thanks.

gush · Post by **gush** » Thu Aug 11, 2005 10:57 am

kp · Post by kp » Sat Aug 20, 2005 5:36 pm

So points should be on a cirle, but what's next?

Should I look for points like

x = R*cos(k*phi)
y = R*sin(k*phi)

k = 0..12

for some R and phi?

If yes then how can I find such R and phi?