Question 158
There are 47 students in a classroom with seats arranged in $6$ rows $ imes$ $8$ columns, and the seat in the $i$-th row and $j$-th column is denoted by $(i, j)$. Now, an adjustment is made for students' seats in the new school term. For a student with the original seat $(i, j)$, if his/her new seat is $(m, n)$, we say that the student is moved by $[a, b] = [i-m, j-n]$ and define the position value of the student as $a+b$. Let $S$ denote the sum of the position values of all the students. Determine the difference between the greatest and smallest possible values of $S$. (posed by Chen Yonggao)