“Well, there must’ve been some sort of love triangle,” said a second-year witch named Samantha Crowley (she never answered when asked if there was any relation). “The question is, which ways was it going before it all went wrong? Who was in love with who—and whether or not that person loved them back—I don’t know how many possibilities there are—”
“Sixty-four,” said Sarah Varyabil, a blossoming beauty who probably should’ve been Sorted into Ravenclaw or Hufflepuff instead. “No, wait, that’s wrong. I mean, if nobody loved Malfoy and Malfoy didn’t love anyone then he wouldn’t really be part of the love triangle… this is going to take Arithmancy, could you all wait two minutes?”
Makes sense. Six possible one-directional (A loves B, B loves A, etc) relationships that can be either present or not, so 2^6 = 64. Each person has 3 graphs where they’re disconnected but the others are not (A loves B, B loves A, A and B love each other), and one where there are no connections at all. 64 − 3*3 − 1 = 54.
4, actually, since “nobody loved draco and draco loved nobody”, we’re left with Hermione and Harry, which leaves a mere two one-directional options. 2^2=4.
“Draco loves nobody and nobody loves Draco” isn’t a given, it’s a subset of possible “love triangle” conditions which can be ruled out on the basis of their invalidating the love triangle premise. Configurations in which either Harry or Hermione neither love nor are loved by anyone would also be excluded.
Svsgl-sbhe.
Makes sense. Six possible one-directional (A loves B, B loves A, etc) relationships that can be either present or not, so 2^6 = 64. Each person has 3 graphs where they’re disconnected but the others are not (A loves B, B loves A, A and B love each other), and one where there are no connections at all. 64 − 3*3 − 1 = 54.
There’s thirteen kinds of Triang Relations (warning: TV Tropes), but that counts, for example, both love Draco the same as both love Harry.
4, actually, since “nobody loved draco and draco loved nobody”, we’re left with Hermione and Harry, which leaves a mere two one-directional options. 2^2=4.
“Draco loves nobody and nobody loves Draco” isn’t a given, it’s a subset of possible “love triangle” conditions which can be ruled out on the basis of their invalidating the love triangle premise. Configurations in which either Harry or Hermione neither love nor are loved by anyone would also be excluded.