7 Trees, 6 Rows, 3 Per Row?

Question

Can you arrange 7 trees so that there are 6 rows of 3 trees? It is entirely possible.

Note: A tree can be part of more then one row, for example a if you arranged a 3x3 square (9 trees) the tree in the center is part of 4 rows.

Rows are usually horizontal but in this case they can be horizontal, vertical, or diagonal.

Joel Rondeau · Answer 1 · 2014-10-27T03:22:59.580

18

An equilateral triangle with 3 trees at the corners, 3 trees at the midpoints and one tree in the center.

Each side has 3 trees. Each altitude has 3 trees.

enter image description here

edited Oct 27 '14 at 03:22

answered Oct 26 '14 at 21:31

Joel Rondeau

7,540
1
30
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Could you please provide a picture? – warspyking Oct 26 '14 at 21:34
Picture added, seems a bit too late. – Joel Rondeau Oct 27 '14 at 03:23

Ole Tange · Accepted Answer · 2014-10-26T22:18:07.113

8

7 trees - 6 lines

(Joel Rondeau's solution would look like this:

With lines: 125, 137, 146, 247, 345, 567. A more symmetric solution than mine)

edited Oct 26 '14 at 22:18

answered Oct 26 '14 at 21:36

Ole Tange

516
2
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That's slightly off... – warspyking Oct 26 '14 at 21:41
How? Please show how this solution is wrong? Could it be there are more solutions that you are not aware of? – Ole Tange Oct 26 '14 at 21:55
Now it looks good. Your solution with numbers didn't line up properly. – warspyking Oct 26 '14 at 22:50
@OleTange it was possibly a bit confusing because in the diagram you've drawn your cross section has been lined up correctly. – Nick Coad Nov 10 '14 at 05:50

score 8 · Answer 3 · answered Oct 27 '14 at 00:24

8

this is my solution...

and this is done by euler line which i studied in high school.

euler line

enter image description here

answered Oct 27 '14 at 00:24

Numberknot

3,042
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21
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Tangentially related: the Fano plane, the Transylvanian lottery problem, and the board game fire and ice (played on a Fano plane of Fano planes). – Oct 27 '14 at 01:17

score 1 · Answer 4 · edited Sep 03 '18 at 05:58

1

North pole, south pole and 5 along the equator...10 rows :-)

edited Sep 03 '18 at 05:58

F1Krazy

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answered Sep 03 '18 at 00:40

sriram sathyamoorthy

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Hello and welcome to PSE :) Congratulations on your very first answer but it is a bit too unclear. Perhaps giving a picture of your answer will be better. Nevertheless, I encourage you to write and answer puzzles in this site. Don't forget to visit the Help Center (https://puzzling.stackexchange.com/help) and check out other puzzles. Happy Puzzling :D – Kevin L Sep 03 '18 at 02:33
1

That's definitely an interesting answer, as it uses the third dimension (and the original question didn't specify the trees must be on a plane). What does confuse me is that with 5 trees on the equator, there are only 5 lines that join each equatorial tree with the poles (N. Pole -> Equator -> S.Pole), so I'm a bit lost as to how you get 10 lines, unless you've double counted something. One way around this would be to arrange 4 of the 5 equatorial trees such that you can make a straight line from Equator -> N. Pole -> Opposite Equator, and mirror it with the other pole, giving 9 lines in all. – Phylyp Sep 03 '18 at 03:06
there are 5 trees on the equator..1,2,3,4,5..so 123, 234, 345, 451 and 512 are 5 more lines..similarly 1NP2 is a line, 1NP3 is another, so is 1NP4..also 1SP2, and so on (any longitude is a straight line).. i think this will mean there are a total of 30 such lines – sriram sathyamoorthy Sep 26 '18 at 08:22
While clever, I'm not sure if spherical geometry is in the spirit of the answer – qwr Jun 02 '22 at 05:14
I know it's not in the spirit...but I did follow the letter, or rather the line of the puzzle :-) Sriram Sathyamoorthy – sriram sathyamoorthy Aug 29 '22 at 02:58

7 Trees, 6 Rows, 3 Per Row?

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