15 Digital Problem _ backtracking method

15 Digital problems

In the 1878, the nation's greatest Enigma expert, Sam Loyd, invented 15 digital puzzles. The puzzle consists of a square box and 15 square sliders numbered 1,2,...,15, each of which is 1/4 of the length of the box, so that they can be spelled in the form shown on the left side of the edges, leaving a space. Each time you can move a slider adjacent to a space to a space (so you can move sliders 12 and 15 to a space in the left figure), and the original position of the slider changes to a new space. The left and right graphs are very close to each other, so whether you can start with the state of the left graph and then turn to the right figure after a few steps. Sam Loyd A reward for the "1000 Dollar Award for the first person to solve the problem."

The rules of the game are easy to understand, so the problem has aroused the interest of many different classes of people, but no one has ever got the 1000 dollars. In fact, this particular 15-digit problem is not solvable, but in many cases it can be transformed from a layout A to another layout B.