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2) The solution based on counting triads of intersecting lines. 1) E.g., if the figure doesn't include two triangles that I've erased...

On the subject of set sizes, it would benefit you to read about what Cantor did and how he approached the subject. IMHO, it has been...

I'm not sure what you mean here. 1) If an intersection is beyond the figure area, should it count as a possible triangle vertex or not...

I enjoyed thinking about it. Just for fun of finding an alternative approach.

IMHO, the desire for a non-"brute force counting" method is misguided here. The logic is so specialized and convoluted that it required...

I wrote a program to do brute force counting and its answer matches that of @bob012345 in post #15. I have not thoroughly examined the...

damn. this is hard to hear. @phinds was just a loved and core member for 15 years. Thank you so much for taking a bit of time to let us...

My deepest condolences. He will be missed.

Good afternoon, This is not Paul, but rather his son Robert. I am very sad to write here that my dad passed away on Saturday...

That seems logical. This is a treacherous problem. I would feel more confident of your logic if there was a simple, brute-force...

Here are my results;

Don’t forget these;

I think that even brute force counting would be challenging. And being confident that a mathematical method works would be very hard...

And 1-7-24 as well.

Using symmetry: 8 triangles per half-quadrant times 8?