Example 16: Three piles of chess pieces, A, B, and C, are moved as follows: First, take chess pieces from pile A and place them into piles B and C according to the number of pieces in piles B and C; then, take chess pieces from pile B and place them into piles A and C according to the number of pieces in piles A and C; finally, take chess pieces from pile C and place them into piles A and B according to the number of pieces in piles A and B. After such movements, each of the three piles has 8 pieces. How many pieces were originally in each pile?
Solve by reversing the moving sequence, which is not easy to do manually, since we know that the three piles of chess pieces will all end up with 8 after moving, we can reverse deduce to solve, list the reverse deduction as follows:
Therefore, the original number of chess pieces in piles A, B, and C are $13, 7, 4$ respectively.