种树, Post Doc ranking

sean9991 · 发表于 2005-4-7 19:04:47

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.

怀疑1 · 发表于 2005-4-8 21:07:35

It will always happen. Please see my new post.

sean9991 · 发表于 2005-4-8 21:06:45

that is too big an assumption

sean9991 · 发表于 2005-4-8 20:54:17

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.

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

怀疑1 · 发表于 2005-4-8 19:55:45

tree on a single line.

怀疑1 · 发表于 2005-4-8 19:52:17

Obviously, 5, 9 13, and 8,12 are not colinear.

If 14 were with 5, 9, 13, 4, there is no point to put a new line.

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.

sean9991 · 发表于 2005-4-8 19:09:35

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.

sean9991 · 发表于 2005-4-8 18:33:24

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?

怀疑1 · 发表于 2005-4-8 07:51:01

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.

怀疑1 · 发表于 2005-4-8 07:42:05

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.

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.

sean9991 · 发表于 2005-4-8 07:31:38

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.

your pic for 14 tree solution is not correct due to the point 1 above, not because of point 2 above.

怀疑1 · 发表于 2005-4-8 07:12:23

I think you mean one must plant a tree at each intersection and any line should contain exactly four trees.

The picture I drew satisfies the second condition but not the first.

sean9991 · 发表于 2005-4-8 06:17:13

remove any outer vertex to get answer for 15 trees

sean9991 · 发表于 2005-4-8 05:57:06

16 trees problem, it's 2 five stars overlapped, and put one tree at the center.

15 trees, remove one outer vertex.

sean9991 · 发表于 2005-4-8 05:19:20

there should not be five trees in a row in any case, correct?

fzy · 发表于 2005-4-7 22:08:02

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

怀疑1 · 发表于 2005-4-7 21:59:57

Then my contruction is surely wrong.

Maybe you can specify the problem strictly and mathematically. Thanks.

Anyway, it is kind of comlpicated.

怀疑1 · 发表于 2005-4-7 21:50:42

These three points can not be on one line?

sean9991 · 发表于 2005-4-7 21:43:45

I don't think your strategy work

怀疑1 · 发表于 2005-4-7 20:44:07

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.

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种树, Post Doc ranking

It will always happen. Please see my new post.

that is too big an assumption

if that is what you think

My solution for 14 trees is similar. There is an

No. With 8, 12, and 4.

answer：种树, Post Doc ranking（图）

reason

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

Really? Then please check again

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

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

pic for associate prof prob（图）

answers to assistant and associate profs prob

for clarification

More ranking

probably you want a tree at every intersection.

These three points can not be on one line?

I don't think your strategy work

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