Sutta Question about 4 ways of debating
There are 4 related suttas, but they may not fit your description precisely.

Pañhapuccha Sutta (AN 5.165) describes 5 types of motivations for asking questions:


Stupidity and bewilderment
Evil desires and greed
Contempt
Desire for knowledge
'If, when asked, he answers correctly, well &amp; good. If not, then I will answer correctly [for him].'


The last type of motivation for questioning usually applies to the Buddha and Arahant teachers toward their students.

Pañha Sutta (AN 4.42) describes 4 ways of answering questions:


There are questions that should be answered categorically [straightforwardly yes, no, this, that].
There are questions that should be answered with an analytical (qualified) answer [defining or redefining the terms].
There are questions that should be answered with a counter-question.
There are questions that should be put aside. 


Kathavatthu Sutta (AN 3.67) describes 4 types of persons who are fit and unfit to talk with:


A person who does not answer a question with the type of answer that is fitting to it (based on AN4.42), is unfit to talk with.
A person who, in his answer, does not stand by what is possible and impossible, doesn't stand by agreed-upon assumptions, doesn't stand by teachings known to be true, doesn't stand by standard procedure, then he is unfit to talk with.
A person, when asked a question, wanders from one thing to another, pulls the discussion off the topic, shows anger &amp; aversion and sulks, then he is unfit to talk with.
A person, when asked a question, puts down [the questioner], crushes him, ridicules him, grasps at his little mistakes, then he is unfit to talk with.


A person who is fit to talk with, is the opposite of the above.

The Buddha concludes the purpose of teaching and discussing, as quoted by Samana Johann in his answer:


  For that's the purpose of discussion, that's the purpose of counsel,
  that's the purpose of drawing near, that's the purpose of lending ear:
  i.e., the liberation of the mind through no clinging.


The Kesi Sutta (AN 4.111) describes the four approaches the Buddha has towards a student:


Gentleness or mild training.
Harshness or harsh training.
Both gentleness and harshness, or both mild and harsh training.
Give up teaching the student for whom the 3 methods above do not work.