there is a coursemate of mine at uni who has a very awkward personality and I'd like to type him correctly. at present, the most likely hypothesis seems to be INTP, but I'm not that sure.
since his personality is quite similar to mine, I'll make quite a few comparisons between him and I (INTJ), so please keep that in mind.

1)he's as lazy as hell, and always groans about having to come to school, or how long it takes to go there, and sometimes skip school just to stay at home to sleep.

2)he's very smart, and has great logico-mathematic skills (better than mine, admittedly, but he has been taking maths and physics for far more years than I have), whereas his linguistic skills seem to be lacking (can't phrase his thoughts clearly and has a narrow vocabulary), beside being worse at describing things.

3)in social situations, he's more reserved than me, still when he turns on, he does thing I'd never do (such as making fun of himself or smirking like an idiot)
moreover, he posts stupid stuff on fb (such as pictures in which he sticks his tongue out or in which he's dressed like an idiot)

4)he's quite reserved and secrets useless info, whereas I am willing to share trivial info with my acquaintances (if anything just to brag about how smarter than them I am)

5)he's no plan for his future, whereas I made mine eons ago. for instance, he decided to enroll chemistry just a few months before uni's start, whilst I decided it like 10 years before. moreover, he's no idea about what to do next.

6)he seems to be more spontaneous than me, and he is absolutely unable to understand what his interlocutor is thinking (unlike me, who can predict his moves like hell)

7)when he speaks, he inferes his thoughts inconsciously, whereas I do it consciously, thus he happens to offend people more easily.

8)our humor style is quite different: whilst I tend to make fun of other people by caustic comments, he makes absolutely idiotic puns with words which cause frequent pity laughs.

9)we both like to discuss about philosophic topics, but his point's are more "standard" (he often quotes famous authors whose works he studied at high school), whereas I developed my system of beliefs all by myself through my living experience and mind.

10)if he disagrees with someone, he's quite likely to back down and hush, whilst I'd fight back until interlocutor admits being wrong.

11)he's much less interessed in people: he never inquires about people interests and demographics, whereas I do in order to be able to manipulate them.

12)even if he is more of a loner than me, he seemingly has more friends because of his more agreeable and submissive nature. in fact, he can cope with being with stupid people, whilst I can't, since I feel the urge to correct them :\

13)even though he's supposedly a thinker, his reasoning skills seem to be more shallow: he doesn't unravel a topic as deeply as I do, and is content with superficial answers. for instance, a few days ago we were talking life's meaning, and, albeit we both agreed that a single person's life has no point, we differed on the point of view about humanity: he thinks that humanity is irrelevant even as a whole because once we're dead all our interests in this world stop, whereas I argued that individuals are just cells of a body whose purpose is to gather knowledge. really, he's very shallow and has no big picture perspective.

14)he seems to be more interested in ideas rather than in their applications: thus he is interested in literature, philosophy and art, whereas I think that's trivial and we should focus more on the present world in order to understand what patterns are going on in it and how to affect it.

15)he's zero control over his physical needs, as he often needs to eat, piss, sleep and stuff, whilst I can cope with refraining from satisfying my physical needs much better, for instance fasting if I am working in order not to waste time.

16)he's way more playful and easy-going than me, and he finds it hard to stay serious. in spite of this, he is able to focus way more than me, especially on boring things like maths or physics.

I know that this info is quite subjective and narrow, but keep in mind that the overall INTP characteristics (such as being, a loner, smart, good at side-thinking and so forth) are present, so I just pointed out the main differences between him and me.