This problem looked so intimidating, but your solution was pealing it like an onion. It's a really nice presentation. Maybe a nitpick: to reason why there are only a draw between p_i and p_{i+1} is argued with a small triangle (A and B), but those patterns can be generalized to longer chains. Other than that this is a brilliant and enjoyable to follow answer :D
I am very happy that you liked the solution :D I planned (and forgot) to say that if p_i, p_j draw for j >= i+2, then p_i, p_{i+1}, p_j must form a sub tournament (A) since p_i and p_j can only draw with each other by the previous argument. Unfortunately, my example with j = i+2 wasn't very general which is why I agree that an explanation of the general approach would have been advantageous. Thanks for the feedback :)
This problem looked so intimidating, but your solution was pealing it like an onion. It's a really nice presentation. Maybe a nitpick: to reason why there are only a draw between p_i and p_{i+1} is argued with a small triangle (A and B), but those patterns can be generalized to longer chains. Other than that this is a brilliant and enjoyable to follow answer :D
I am very happy that you liked the solution :D
I planned (and forgot) to say that if p_i, p_j draw for j >= i+2, then p_i, p_{i+1}, p_j must form a sub tournament (A) since p_i and p_j can only draw with each other by the previous argument. Unfortunately, my example with j = i+2 wasn't very general which is why I agree that an explanation of the general approach would have been advantageous. Thanks for the feedback :)