## 10885 - Martin the Gardener

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Antonio Ocampo
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### 10885 - Martin the Gardener

Hi guys

I don

misof
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Antonio Ocampo
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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
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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
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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.
If only I had as much free time as I did in college...

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

Cosmin.ro
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I think he means all points are on a circle.

Antonio Ocampo
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I'm so frustrated

gush
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....
I've tested that the distances between them are integers. But I still got WA. Why?
Last edited by gush on Thu Aug 11, 2005 10:56 am, edited 1 time in total.

Cosmin.ro
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Maybe 3 colinear points, have you tested that?

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

little joey
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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
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gush, and when you get AC, please don't forget to remove the numbers from your post. Thanks.
If only I had as much free time as I did in college...

gush
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ok

kp
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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?