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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?

I think that misses a triangle 1-24-20, for example, IIUC (see image in #2 above.)

It can be approached as a combinatorics problem. Mark the lines, e.g., Every three lines that intersect, make a triangle. There are 12...