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Context: I was trying to solve some of the puzzles on this site, when it occurred to me to make a puzzle variant myself. I immediately could construct one with my additional rule. Making an interesting one was harder, but I succeeded. I was unsure whether this was actually fun to solve so I gave it to my test panel first. However, I know little more than the internet names of my contestants.

What I want you to figure out:

What are the real names of my top contestants?
What kind of game did I make?
Can you make such a puzzle for 10; can you for 11? 1 answer here is enough, bonus points for both answers.

Some information about my test panel:
Gold went to Anna. She is a real thinker, so it should not be a surprise that number 1 is all she is.
Victor ended second place. He is number two all the time. Well, except once, but that is beside the point.
Number 3 calls himself Ivan. He is unrelated to Anna and Victor. He is really into sudokus. He is a bit random but always ends up in the top 10.

Tactical tip from Anna: Divide and conquer, that is what I use.
Victor is a scrawny fanatic vegetarian; Ivan likes his meat and has a lot of meat on his body to show for it. Obviously that shows in what they stand for; I use that to make sure they do not cooperate against me.

enter image description here

Time for some hints to get started:

Look at Anna.

Did you notice the mathematics tag?

Note: This first multilayered puzzle of mine does not seem to attract answers or many votes. Maybe I am just impatient, but any partial answers will be appreciated, even if only for me to figure out what is blocking.

Some additional hints:

'Anna' is quite famous. Even if you don't know mathematics, you could easily look her up. Then find out why she seems to win all the time.

'Ivan' is even more famous, however you will need Anna to find him.

'Victor' is not famous at all. I now think this is a weakness in this puzzle, he is almost useless like this. I should have then given him a last name, if only to honor some people. Victor Bubbler, or better Victor Euler, but then I should have let him be number 1 most of the time.

New hint:

'Victor' is the square root of 2. The vegetarian <-> root link was a vague hint that this was correct. -Not that I expected this to be found before Anna was identified-

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    $\begingroup$ This seems as if it might want the [reverse-puzzling] tag. (On the face of it it certainly does, but in an [enigmatic-puzzle] all may not be as it seems.) $\endgroup$ – Gareth McCaughan Oct 15 '20 at 16:17
  • $\begingroup$ I think you are right, done. Still, following the clues is a bigger part than doing something with the emerging puzzle, so I'm not so sure. If it is solved, I'll appreciate an opinion about the labels. $\endgroup$ – Retudin Oct 15 '20 at 16:37
  • $\begingroup$ You may very well not want to answer this, but just in case it's meant to be more obvious than (to me) it is: Is the "sudoku" in the image intended to be an instance of the same type of puzzle as the one we're being challenged to identify? $\endgroup$ – Gareth McCaughan Oct 15 '20 at 16:54
  • $\begingroup$ No, the puzzle will emerge if the hints are understood/applied correctly $\endgroup$ – Retudin Oct 15 '20 at 17:11

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