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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...

I would consider that to be automating a "brute force counting" method. IMO, although it is not what the OP asked for, it is still an...

It's true of any music genre that time lets us remember the good ones and forget about the tons of mediocre/bad ones. Our memories are...

Use the "I dislike this", thumb down, every time you see them post. It has had a corrective effect on what is offered to me.

We have many threads on AI, which are mostly AI/LLM, e.g,. ChatGPT, Claude, etc. It is important to draw a distinction between AI/LLM...

https://en.wikipedia.org/wiki/MoM-z14 Any photon with energy above 24.6 eV is going to ionize any atom. K, L X-rays would certainly...

A countable union of countable sets is countable. This means when you say hey I've got infinity infinities, that's gotta be a bigger...