Math, play the Hualong Dao game with the kids and tell me what you found out!

1. What I found

There is more than one solution that can make Cao Cao escape from Huarong Dao, and I want to find out the one with the least number of steps, because the least is the best.

2. Hualongdao Game

Hualongdao, an ancient Chinese game, is known as the "Three Incredible Intellectual Games" by foreign intellectuals along with Rubik's Cube and Independent Diamond Chess for its many variations and never-ending play. It is also synonymous with traditional Chinese educational toys such as tangrams and nine linked rings as "Chinese puzzles". Huarong Road game from the famous story of the Three Kingdoms, Cao Cao in the battle of Red Cliff by Liu Bei and Sun Quan's "Bitter Meat", "burning camps" defeated, forced to retreat to Huarong Road, and encountered Zhuge Liang's ambush, Guan Yu in order to repay Cao Cao's kindness to him, Ming forced to let the truth, and finally helped Cao Cao escape from Huarong Road. The game also features a new game called The Rise and Fall of Cao Cao.

The game is based on "Cao's defeat at Huarong Road, and Guan Yu's narrow path. The game follows the storyline of "Cao Cao's defeat at Huarong, and his encounter with Guan Gong on the narrow road. Only because of his kindness and righteousness, he let go of the golden lock to walk away from the dragon", and helps Cao Cao to escape through the exit by moving the pieces from his initial position to the center of the board at the bottom. You are not allowed to cross pieces, and you must try to move Cao Cao to the exit in the fewest number of moves. The biggest obstacle to Cao Cao's escape from Huarong Road is Guan Yu, who is standing on Huarong Road. Guan Yu and Cao Cao are of course the key to unlocking this game. The four Liu Bei soldiers are the most flexible and the easiest to deal with, and how to play their roles must also be fully considered thoroughly.

"Huarong Road" has a board with twenty small squares, representing Huarong Road. At the bottom of the board is a two-square-side exit for Cao Cao to escape. On the board*** there are ten different sized pieces representing Cao Cao, Zhang Fei, Zhao Yun, Ma Chao, Huang Zhong and Guan Yu, and four pawns. There are dozens of ways to set up the "Huarong Road", such as "Crossing the Sword and Standing on the Horse", "Close at Hand", "Passing the Five Passes", "Water Void", "Water Void", "Water Void", "Water Void", "Water Void", "Water Void", and so on. There are dozens of ways to play the game, such as "The Sword and the Horse", "Close at Hand", "Five Passes", "The Water is Vast", "The Swallow Comes Out of the Nest", etc. There are only two empty squares on the board, and the game is to move the pieces through these two squares to move Cao Cao out of Huarong Road in the least number of moves. This toy has attracted a lot of interest, and everyone tries to minimize the number of moves.

After decades of work by Chinese and foreign scientists such as Jiang Changying, Fujimura Yukizaburo, Shimizu Tatsuo, and Martin Gardiner, the solution to the game has been reduced from 87 moves more than sixty years ago to 81 moves.