Question

Shown below is a number puzzle. Only one piece can be slid horizontally or vertically in one move. What is the least number of moves required to bring the piece with number 10 to the empty position x?

Hint:

When solving sliding puzzles, focus on reversing the order of moves needed to shift the target piece to the desired position, and aim to minimize unnecessary shifts.

Answer 1

To move the piece numbered 10 to the empty position \(x\), the sequence of moves required is as follows:
1. Move adjacent pieces systematically to free up the path for the piece numbered 10.
2. Considering the current configuration, a total of 13 moves is required to slide the piece numbered 10 into the empty position \(x\).
Each move shifts one piece either horizontally or vertically toward its target position, ensuring that the empty slot \(x\) is aligned with the desired path.
Conclusion: The least number of moves required is 13.