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Constructive proof: Consider a person P who won the greatest number of matches. (If there is a tie for most, choose any of them.) This person is a dominant player. If P is not a dominant player, then some person Q beat P and every person P beat. But this is more people than P beat, contradicting the choice of P as the player with the most victories.


Unique solution? Group A: Group B: And finally:


There may be other solutions, but: Step 1: Step 2: Step 3: Step 4: Original Incorrect Answer - Oh boy, am I dumb. Here is one solution, there may be others: Next steps:


I think they must be These letter pairs EDIT: looks like this answer has a lot in common with @hexomino's earlier answer. I guess it couldn't be helped though.


So one key rule we must satisfy is that However, this does not tie in with the title so I thought a better fit would be the following


As many have mentioned, there is no "inside the box" answer to the problem. Depending on the exact statement of the problem, there may be trick answers. For example, as stated, the lines may not touch, but there is no rule against a line going through another circle in the middle of its route.


I know it is optimal:

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