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种树, Post Doc ranking

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楼主
发表于 2005-4-7 19:04:47 | 只看该作者 回帖奖励 |倒序浏览 |阅读模式

14 trees, 10 rows, each with 4 trees.
BTW, I found a new solution for 13-tree 9-row problem.  I'll post it later.
www.ddhw.com

 
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沙发
发表于 2005-4-7 20:44:07 | 只看该作者

回复:种树, Post Doc ranking(图)


 www.ddhw.com
No. 14 is only on one line. Well, I am not sure whether I can arrange to make 8, 12, and 4 be on one line.  It might need some boring computation, though it looks possible.
 
I guess higher than 13 or 14 is not so interesting.   And  PostDoc is not really higher than PHD.
www.ddhw.com

 
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板凳
 楼主| 发表于 2005-4-7 21:43:45 | 只看该作者

I don't think your strategy work


  I don't think your strategy work




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地板
发表于 2005-4-7 21:50:42 | 只看该作者

These three points can not be on one line?


  These three points can not be on one line?




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5#
发表于 2005-4-7 21:59:57 | 只看该作者

probably you want a tree at every intersection.


Then my contruction is surely wrong. www.ddhw.com
 
Maybe you can specify the problem strictly and mathematically. Thanks. www.ddhw.com
 
Anyway, it is kind of comlpicated.
www.ddhw.com

 
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6#
发表于 2005-4-7 22:08:02 | 只看该作者

More ranking


Assistant Professor: 15 trees, 12 rows, each with 4 trees
Associate Professor: 16 trees, 15 rows, each with 4 trees
Full Professor: 18 trees, 18 rows, each with 4 trees
www.ddhw.com

 
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7#
 楼主| 发表于 2005-4-8 05:19:20 | 只看该作者

for clarification


there should not be five trees in a row in any case, correct?
www.ddhw.com

 
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8#
 楼主| 发表于 2005-4-8 05:57:06 | 只看该作者

answers to assistant and associate profs prob


16 trees problem, it's 2 five stars overlapped, and put one tree at the center.
15 trees, remove one outer vertex.
www.ddhw.com

 
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9#
 楼主| 发表于 2005-4-8 06:17:13 | 只看该作者

pic for associate prof prob(图)


 remove any outer vertex to get answer for 15 trees
www.ddhw.com

 
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10#
发表于 2005-4-8 07:12:23 | 只看该作者

Honest, still not clear. But I can guess your poi


I think you mean one must plant a tree at each intersection and any line should  contain exactly  four trees. www.ddhw.com
 
 
The picture I drew satisfies the second condition but not the first.
www.ddhw.com

 
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11#
 楼主| 发表于 2005-4-8 07:31:38 | 只看该作者

It is clear now, i think i got the answe already


1. on any straight line, there can be no more than 4 trees.
2. it's not necessary to plant a tree on the intersection of two straight lines, where each of which contains eactly four trees.www.ddhw.com
 
your pic for 14 tree solution is not correct due to the point 1 above, not because of point 2 above.
www.ddhw.com

 
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12#
发表于 2005-4-8 07:42:05 | 只看该作者

Really? Then please check again


There are no five trees on one row. Maybe my picture is bad, but no. 14 is on the same line as 4, 12, and 8.  Trees 1, 4, and 14 are not on the same row. www.ddhw.com
 
As I said, I am not sure whether I can make 4, 12, and 6 be on the same row unless I do a careful computation, though it looks possible.
www.ddhw.com

 
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13#
发表于 2005-4-8 07:51:01 | 只看该作者

I only added one line and one point [:%]


based on my solution to the 13 -tree-on-9-row problem. Assuming that 8, 12, and 4 are on the same row, my solution should be correct. There are no five trees on any row. www.ddhw.com
 
 
www.ddhw.com

 
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14#
 楼主| 发表于 2005-4-8 18:33:24 | 只看该作者

reason


I think you put point 14 on a wrong place, thus causing the confusion.  14 is supposed to becolinear with 5, 9 13, and 8,12, correct?
www.ddhw.com

 
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15#
 楼主| 发表于 2005-4-8 19:09:35 | 只看该作者

answer:种树, Post Doc ranking(图)


www.ddhw.com
 This is for 13 trees.  Points ABCDE are random,  all the rest are determined by the intersections on AD and DE.  you have to be very precise in drawing the picture, since it used a property of similar triangle. For 14 trees problem, any tree on the line of BDC will generate a new row.
www.ddhw.com

 
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16#
发表于 2005-4-8 19:52:17 | 只看该作者

No. With 8, 12, and 4.


Obviously, 5, 9 13, and 8,12 are not colinear.   www.ddhw.com
 
If 14 were with 5, 9, 13, 4,  there is no point to put a new line. www.ddhw.com
 
Noet that except the line for 14, 4, 8, and 12, the picture is a solution for 13-9. No. 4 is the intersetion of three lines now.  
www.ddhw.com

 
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17#
发表于 2005-4-8 19:55:45 | 只看该作者

My solution for 14 trees is similar. There is an


tree on a single line.
www.ddhw.com

 
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18#
 楼主| 发表于 2005-4-8 20:54:17 | 只看该作者

if that is what you think


then your answer is wrong. 
based on your answer, here are three lines
1-2-3-4, 5-9-13-4, and 8-12-4-14
i don't think you can adjust your picture to make that happen.www.ddhw.com
 
line 1-2-3 and 5-9-13 don't have to meet on at the same point (4) on the line 8-12-14, actually it will most likely not happen
www.ddhw.com

 
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19#
 楼主| 发表于 2005-4-8 21:06:45 | 只看该作者

that is too big an assumption


  that is too big an assumption




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20#
发表于 2005-4-8 21:07:35 | 只看该作者

It will always happen. Please see my new post.


  It will always happen. Please see my new post.




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