October 2018

[a1call]

Yes that is true.
So I have wasted my time as well as anyone's who has listened to me.
They have no one to blame but themselves. They should have known better by now.

[a1call]

So assuming that maximizing the actual number of cells will yield a solution faster, the optimum grid would be L1xL2=5x120=600 with 121x6=726 actual cells.

[Batalov]

Originally Posted by a1call

So assuming that maximizing the actual number of cells will yield a solution faster, the optimum grid would be L1xL2=5x120=600 with 121x6=726 actual cells.

You cannot have more than one coordinate with two points present. (Easy to prove. Two simple steps: draw two parallel lines, put two points on each. Now draw triangles and consider their areas. They will form two pairs of equal values.)
Therefore you cannot use L1 or L2 < 9.

[a1call]

That is very clever. I had not thought of that. Thank you for the correction.

[a1call]

Originally Posted by KangJ

Any of two segments cannot be parallel.

You were way ahead of me there pal.

[science_man_88]

Originally Posted by Batalov

You cannot have more than one coordinate with two points present. (Easy to prove. Two simple steps: draw two parallel lines, put two points on each. Now draw triangles and consider their areas. They will form two pairs of equal values.)
Therefore you cannot use L1 or L2 < 9.

You also have, that the average of two x (resp. y) coordinates on any perpendicular lines can't be the x or y coordinate of the line it's perpendicular to.

[Dr Sardonicus]

Originally Posted by Batalov

You cannot have more than one coordinate with two points present. (Easy to prove. <snip>)
Therefore you cannot use L1 or L2 < 9.

KangJ beat you to it here with a more general statement:

Any of two segments cannot be parallel.

Same argument applies.

[Batalov]

Mine was a responce to a specific thing:

the optimum grid would be L1xL2=5x120 ...

Yes, I could have just responded - "read the thread". Right?
You think it would have been obvious to the intended audience?

I don't think so. It it was, they wouldn't have written what they have.
Hence, repetition is the mother of learning.

[LaurV]

A similar mistake I did before (in the above post which I deleted overwrote, I was wondering why the former posters started their lists from 10, haha, then immediately I realized how stupid I was). Of course you can't have parallel lines and moreover, you can't have any symmetric figure (i.e. quadrilateral or higher), either if the symmetry is a dot or a line (the dot symmetry is actually a particular case of parallel lines, but the line symmetry is not, when the line passes through two of the points, think something like a deformed rhombus, or "kite").


Edit: puzzle: how "long" a solution with 10 lines needs to be? (this can be actually "computed" by hand very easy).

[Batalov]

Found one!

[bsquared]

Originally Posted by Batalov

Found one!

Congrats!!

It has proven to be pretty difficult to go the final inch... but I hope to join you soon.