I already specified the monoid part of these monoidal preorders before stating the first puzzle. The puzzles ask what's the preorder part: that is, when does one complex count as \\(\le \\) another. This depends on what reactions we allow.

Yes, we can think of a complex

\[ a \text{H} + b \text{O} + c \text{H}_2\text{O} \]

as a multisubset of the set \\( \\{\textrm{H}, \textrm{O}, \textrm{H}_2\textrm{O} \\} \\). Alternatively, and perhaps less stressfully, we can think of it as an ordered triple \\( (a,b,c) \\) of natural numbers. The monoid operation is just the usual addition of these triples.

Yes, we can think of a complex

\[ a \text{H} + b \text{O} + c \text{H}_2\text{O} \]

as a multisubset of the set \\( \\{\textrm{H}, \textrm{O}, \textrm{H}_2\textrm{O} \\} \\). Alternatively, and perhaps less stressfully, we can think of it as an ordered triple \\( (a,b,c) \\) of natural numbers. The monoid operation is just the usual addition of these triples.