@Discretelizard Thank you!!

I would love to contribute to the community. But, I don't want to contribute poorly. I've misinterpreted a user's question. And, by now he must be irritated of the constant pinging by my edits.

@Raphael I'm gaining step by step. Answering questions I believe I can answer. In the meantime, I'll keep practicing code and practice algebra and pre-calculus. This site is a benefit for me (and others) to actually read source material before answering a question. (And of course, knowing that my answer is correct before posting)

Ok, I'll proof-read my code just to make sure it does what intends to do. And, I'll transform it into pseudo-code with a good explanation.

@Raphael Seemed wrong to paste just code alone. Without explaining what it does. But, I'm familiar with python than math jargon.

Yes, this is true. What's obvious to you is not always obvious to others. Clearly, there's a spectrum of personality and thought patterns. An incompatible thought pattern is just like another language. I can't communicate abstract thoughts in a formal matter. It doesn't mean I'm smarter or dumber. It just means there's "no-clicking." I just wish, that when I'm expected to speak or write English. That language isn't so subtle. So I created literal pictures. And, for some reason, it didn't work.(confused why) If there was a race of aliens that were clones of me. We are missing the picture.

Was it a reader expecting a conventional vertice cover? I mean a sudoku puzzle is a graph. So it can be made into a vertice cover problem. Just tag the values with lines connecting values 1s together, 2 together etc. And finding the other lines completes the vertice cover(solve the puzzle)

Is it the title? Is it the long post? I mean clearly I've shown that sudoku can be a vertex cover problem. I even shown the search for them is at least as hard as Sudoku. I'm not sure why proof of contradiction is frowned upon. In math this can be considered formal(a proof of contradiction).