2 A class has 47 students, and the classroom used has 6 rows, with 8 seats in each row. The seat located in the $i$th row and the $j$th column is denoted as $(i, j)$. For the new semester, the seats are to be rearranged. If a student's original seat is $(i, j)$ and the new seat is $(m, n)$, then the student's movement is denoted as $[a, b] = [i-m, j-n]$, and the sum $a+b$ is called the student's position number. The total sum of all students' position numbers is denoted as $S$. Find the difference between the maximum and minimum possible values of $S$. (2003 Girls' Mathematical Olympiad Problem)
2. The value $i+j$ is called the characteristic value of the cell $(i, j)$. The number of positions a student can move to is the difference between the characteristic values of the cells before and after the move. Let the sum of the characteristic values of all cells be $M$. Introduce parameters: Let the initial empty cell be at $(x, y)$, and after the adjustment, it is at $(p, q)$. Then, the sum of the characteristic values of all students initially is $M-(x+y)$, and after the adjustment, it is $M-(p+q)$. Therefore, 
$$\begin{array}{l}
S=M-(x+y)-[M-(p+q)]=p+q-(x+y). \ S_{\max }=6+8-(x+y), S_{\min }=1+1-(x+y), \\
S_{\max }-S_{\min }=[6+8-(x+y)]-[1+1-(x+y)]=14-2=12.
\end{array}$$