CGMO 2003 Problem 2

There are 47 students in a classroom with seats arranged in 6 rows $\times$ 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 $S.$