Three musketeers: The funda of buddy trios

One thing which has often struck me as odd is this unfailing, automatic tendency of mine to make friends in trios (including me, of course). No matter how many people I meet at various points of time in my life, I always end up having just two close friends from the whole batch, thus matching the combo of the classic three musketeers. Be it college, school, workshop, it almost always turns out to be three. Me-Addu-Gaddu; Me-Anubha-Tanmai; Me-Deepak-Atit (not all names could be included in sampling so those who are not mentioned are requested not to take it personally).
What is the funda behind this automatic selection process? Though I have pitiful knowledge when it comes to psychology, yet some brave attempts at delving into my mind have brought out some interesting explanation possibilities about the whole thing. Firstly, the number three has a certain rounded wholeness to it. You see one person - lonely. You see two persons - couple/best friends/ siblings/ enemies/ acquaintances - basically a little too many possibilities. But you see three smiling people together and bam! There's the balance we were looking for.
Being buddies-in-three also has the advantage of having a negotiator at hand whenever the need arises. In the event of a conflict between two gang members, there is always the third party who can put in efforts to solve the issue through tact, diplomacy, and appeasement. Of course, a precondition for this is that the third party involved here should have a certain degree of assertion in the trio, otherwise you will end up with two warring factions and a miserable figure stuck in the middle with nowhere to go.
Finally, there is the influence of the media and popular culture which may have a subtle role in popularizing the trio buddy business. Be it Charlie's Angels, Friends (3 guys, 3 girls, remember?), those million love-triangle rom-dramas, Harry Potter, Five Point Someone ... the message is simple: three means more fun.
But once again, I conclude with the warning to avoid simplifying my reflections down to a narrow message. Of course I am not advocating multiple calculations and manipulations while making friends. It is as much a natural process as falling in love. You don't plan to make friends, it just happens. Neither am I saying that only this combo works the best so all dissenters better find a third option to enjoy life. All I am trying to do is present my reflections on a particularly intriguing fact which has been revolving in my mind for quite some time now. Let's see if you agree ...