2. 65 Mary scored above 80 points on the American middle school math test, and she told John her score. John can correctly deduce how many questions Mary answered correctly. If Mary's score were slightly lower but still above 80, John would not be able to deduce it. What did Mary score?
[Solution] Given $S=30+4 C-\omega>80$.
Our problem is to find the smallest such $S$, with its corresponding $C$ being unique.
First, note that when $C$ increases by 1 and $\omega$ increases by 4, the value of $S$ remains unchanged, but it must satisfy
$$
(c+1)+(\omega+4) \leqslant 30 \text {, }
$$

which means
$$
c+\omega \leqslant 25 \text {. }
$$

Therefore, when $c+\omega \leqslant 25$, the value of $c$ for the same $S$ cannot be uniquely determined, so it must be
$$
c+\omega \geqslant 26,
$$

only then is it possible for $c$ to be uniquely determined.
Secondly, there should also be $\omega \leqslant 3$,
otherwise, if $\omega \geqslant 4$, $\omega$ can be reduced by 4 and $C$ reduced by 1, still keeping $S$ unchanged (since from $S>80$, $\omega \geqslant 4$ we can get $c \geqslant 13$, which is also possible).
Thus, to make $S$ as small as possible, we should minimize $C$ and maximize $\omega$ within the range
$$
\left\{\begin{array}{l}
c+\omega \geqslant 26 \\
\omega \leqslant 3
\end{array}\right.
$$

For this, $\omega$ should be 3 and $c$ should be 23, at which point
$$
S=30+4 \times 23-3=119,
$$

which means Mary scored 119 points.