Three in a row puzzler

[lightjedi39]

How would I arrange seven objects, such that can you can draw exactly 6 straight lines through any 3 of the objects?

Below is an example which shows 5 objects that you can draw exactly 2 straight lines through any 3 objects:

X       X
    X
X       X

I need to figure out something like this for 7 objects and exactly 6 lines. Thank you for any help!

 

[stapel]

The example you include, with the five X's, does not allow straight lines through "any" three of the X's. For instance, you can't draw a straight line through the three X's that exclude the right-hand column.

What are the exact (word for word) instructions?

Thank you.

Eliz.

 

[lightjedi39]

3 in a row

the first part of the message is the exact wording and my diagram of the X's didn't look correct in my post, so imagine an X with one object (point) at the end of each line (4 points) and the fifth point is the intersection of the two lines, which makes an X, so the two lines pass through 3 points, so this problem asks draw 7 points or objects that you can draw exactly 6 lines through three of the points. I hope this helps clarify.

 

[soroban]

Hello, lightjedi39!

That is a very poorly worded problem . . . "any three" ?
. . . Think about it.

I believe you're trying to describe the classic "Orchard Problem".
\(\displaystyle \;\;\)"Plant seven trees so that there are six rows with three trees each."

      A
       .\     .
          \           B
        .   \     /  .        .
              G     .                 .
         .  /   \  .                          .
          C . . . D . . . . . . . . . . . . . . . . . E
           .     .
            .   .
             . . 
              F

Draw line \(\displaystyle AB\) extended.
Draw line \(\displaystyle CD\) extended to intersect \(\displaystyle AB\) at \(\displaystyle E.\)

Draw line \(\displaystyle AC\) extended.
Draw line \(\displaystyle BD\) extended to intersect \(\displaystyle AC\) at \(\displaystyle F.\)

Diagonals \(\displaystyle AD\) and \(\displaystyle BC\) intersect at \(\displaystyle G.\) . . . There!

[It's a diagram from Desargues' Theorem.]


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

You want a challenge?

We can plant nine trees and make eight rows of three trees each.

      o   o   o

      o   o   o        Easy!

      o   o   o

Now plant nine trees to make ten rows of three trees each.


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

And a real classic . . . older than dirt!

Plant ten trees in five rows with four trees each.

 

[lightjedi39]

Thanks Soroban, I appreciate the help

 

[Schmyd]

I kind of came up with one of the previous solutions, except it looked more like a Christmas Tree.

Ignore the statement on the bottom.. was teasing the Girlfriend at her college.