= Solution
The strongest donor belongs to the acid, $\alpha_1=3.5$, and the strongest acceptor to the <aminopyridine>, $\beta_2=8.5$. \b[The <cocrystal> pairs the strongest donor with the strongest acceptor], while the reciprocal amino-NH···<carbonyl> contact closes a complementary two-contact motif.
Using the simple favorable-contact score $\alpha\beta$, one heterodimer gives
$$
S_{\rm hetero}=\alpha_1\beta_2+\alpha_2\beta_1
=(3.5)(8.5)+(3.0)(5.5)=46.25.
$$
The self-associated comparison, normalized to the same two <molecules> and two <hydrogen bonds>, is half an acid <dimer> plus half an <aminopyridine> <dimer>:
$$
S_{\rm self}=\alpha_1\beta_1+\alpha_2\beta_2
=(3.5)(5.5)+(3.0)(8.5)=44.75.
$$
Thus
$$
\boxed{\Delta S=1.50=(\alpha_1-\alpha_2)(\beta_2-\beta_1)>0}.
$$
In a model where bond <free energy> contains $-\alpha\beta$, this is a favorable energy change. No bonds have been artificially added to one side of the comparison: both alternatives contain two contacts per acid/<aminopyridine> pair.
The calculation rationalizes the hydrogen-bond preference. It is not a complete <crystal> <free energy>: packing, additional contacts, <entropy> and possible <solvent> effects also matter. Without a specified calibration, the numerical score should not be promoted to a measured cocrystallization <free energy>.
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