Example: There are 6 apples in each of the three plates $A$, $B$, and $C$. The following 5 moves are made: $A$ plate remains unchanged, move 1 apple from one plate to another; $B$ plate remains unchanged, move 2 apples from one plate to another; $C$ plate remains unchanged, move 3 apples from one plate to another; $A$ plate remains unchanged, move 4 apples from one plate to another; $B$ plate remains unchanged, move 5 apples from one plate to another. In the end, each plate still has 6 apples. How were the apples moved?
Solve the following tables where $1,2,3,4,5$ represent 5 moves, and $A, B, C$ represent three plates. According to the problem, the numbers in Table 1 indicate the number of apples moved into or out of each plate during each move.

Since the number of apples moved in and out is equal during each move, just add a “ + ” sign before the number of apples moved in, and a “ - ” sign before the number of apples moved out, so that the algebraic sum of each move is 0. Since the number of apples in each plate remains unchanged after 5 moves, the algebraic sum of each plate is also 0. Starting from the 5th move, add “ + ” or “ - ” signs to make the column sums and row sums all 0, thus obtaining Table 2 and Table 3, which are the two solutions to this problem.