2. 79 In a game, scoring is as follows: answering an easy question earns 3 points, and answering a difficult question earns 7 points. Among the integers that cannot be the total score of a player, find the maximum value.


[Solution] Let the set of natural numbers that cannot be the total score be $S$. Among the first 12 natural numbers, only $1,2,4,5,8,11$ belong to $S$.

Since $7=2 \times 3+1,3 \times 5=7 \times 2+1$, when the sum of several 3s and 7s $n \geqslant 12$, one 7 can be exchanged for two 3s, or five 3s can be exchanged for two 7s, making the composed sum number increase by 1. Therefore, natural numbers greater than 12 do not belong to $S$. So
$$
S=\{1,2,4,5,8,11\} \text {. }
$$

The maximum value sought is 11.