The number of shipping possibilities in Homestuck has increased exponentially.

Let’s calculate how many there are!! as a FUN MATHEMATICAL EXERCISE.

Okay, first off, let’s establish the relationship types.

Humans: 1 type
Trolls: 4 types
Leprechauns: 9 types

Given that a) the fandom DOES have a tendency to apply troll shipping to humans as well, and b) for the sake of simplicity, I’ll just assume it’s possible to apply ALL of these shipping modes to ALL characters.

(Do note that this doesn’t take into account possible caliginous/ashen/etc. relationships in conjunction with leprechaun charms!)

Aight. So first of all, let’s establish the number of unique shipping types. The human, troll, and leprechaun concept of <3 overlap. This gives effectively 9 + 3 = 12 types of relationships. Of these, 11 are pairwise, while 1 is three-way. (This makes the assumption that all leprechaun shipping types are pairwise but I don’t really see any reason to assume otherwise at this point.)

So let’s do the pairwise ones first. In a previous analysis I said there were 165 characters; while an approximation, let’s stick with that.

So.

There are thus (165*164)/2! = 13530 ways to pick a pair of characters. And there are 11 types of pairwise relationships. This gives me 13530*11 = 148,830 possible pairwise ships.

Once again, for auspistices, we’re looking at (165*164*163)/2! = 2,205,390 possible ships.

So far so good! Now things get complicated:

there are 9 shipping types, all pairwise (presumably), for the leprechauns. Here’s the thing though: every pair can have more than one charm operating at once, from 1 charm to 9.

However, by this point, in our previous calculations, we’ve accounted for all the relationships that use only 1 charm. So we only have to do calculations for relationships with more than 1.

That gives us 8 more calculations to do:

13530*9*8/2! = 487,080
13530*9*8*7/3! = 1,136,520
13530*9*8*7*6/4! = 1,704,780
13530*9*8*7*6*5/5! = 1,704,780
13530*9*8*7*6*5*4/6! = 1,136,520
13530*9*8*7*6*5*4*3/7! = 487,080
13530*9*8*7*6*5*4*3*2/8! = 121,770
13530*9*8*7*6*5*4*3*2*1/9! = 13,530

Now, let’s add all those numbers up. We’re looking at

148,830 + 2,205,390 + 487,080 + 1,136,520 + 1,704,780 + 1,704,780 + 1,136,520 + 487,080 + 121,770 + 13,530

= 9,146,280 possibilities.

For reference, a series with only 1 type of pairwise relationship (traditional romance) would require 4,278 characters to pass this number.

HAPPY SHIPPING ALL

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