Sutta Question about 4 ways of debating There is a sutta where the Buddha discusses four ways a debate can go between two people: a person could be hard to convince, causing either torment to the speaker but not the listener, torment to the listener but not the speaker etc.. the Buddha makes the final point that it is always worth undertaking the discussion so long as there is a possibility of coming to an understanding, if not, heed mindfulness. What is the reference please?
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.