Klotski

Klotski

Huarongdao is an ancient Chinese folk puzzle game. With its changeable and never tired of playing, huarongdao, together with Rubik's cube and independent diamond chess, is called "the three miracles of the intelligence game world" by foreign intelligence experts. It is also synonymous with traditional Chinese educational toys such as Tangram and jiulianhuan, which is called "China's problem". According to the notes of Zizhitongjian, "from this way to Huarong.". Huarong Road was originally a place name in ancient China. It is said that Cao Cao was defeated here. At that time, Huarong Road was a swamp, so Cao Cao's army had to cut grass to fill the land, and many soldiers were buried alive.

By moving the pieces, Cao Cao was helped to move from the initial position to the bottom and middle of the chessboard and escape from the exit. It is not allowed to cross the chess pieces, but also try to use the least number of steps to move Cao Cao to the exit. The biggest obstacle for Cao Cao to escape from Huarong Road was Guan Yu. Guan Yu immediately went to Huarong Road, where one man was in charge and ten thousand men were not allowed to open. Guan Yu and Cao Cao are of course the key to solving this game. The four Liu Bei soldiers are the most flexible and easy to deal with. How to play their role should be fully considered. "Huarong Road" has a chessboard with 20 small squares, representing Huarong Road.

Game history

Game source

Huarongdao game is based on the famous story of the Three Kingdoms. Cao Cao was defeated by Liu Bei and Sun Quan in the battle of Chibi, and was forced to retreat to huarongdao. Then he met Zhuge Liang's ambush. In order to repay Cao Cao's kindness, Guan Yu forced Cao Cao to escape from huarongdao. The game is in accordance with the principle of "Cao deceives the soldiers and loses Huarong, meeting Guan Gong in a narrow way.". But the origin of the game is not "one of the oldest games in China" as people think. In fact, its history may be very short. The current style of Huarong Road is a patent applied by John Harold Fleming in the UK in 1932, and the solution of the horizontal knife is attached.

Related history

Huarong Road was invented by the Chinese, and the final solution was worked out by the Americans with a computer. However, the design principle of Huarong Road has not been clarified yet. At first, it was seen that it was on a chessboard composed of 20 squares, with a group of four small squares (Cao Cao), five two small squares (general five tigers) and four small squares (four soldiers). But Guan Yu is a horizontal two small squares, the other four will be vertical two small squares, so if Cao Cao is four, the four generals and Guan Yu can not be collectively referred to as two, the relationship of 1 * 2 * 4:20 can not be established. Another way is to regard Cao Cao as the fourth power, Guan Yu as the square, the four generals as the four 2, the four soldiers as the four 1, and the chessboard as the 20. But the final mathematical principle is still a mystery.

In his book exercise and recreation of scientific thinking, Jiang Changying said, "it is estimated that its history is only a few decades. There is no record of Huarong Road in the notes of former people. " Mr. Jiang himself saw the toy for the first time in the summer of 1943. At present, the earliest written record of huarongdao is science recreation published by Mr. Jiang in 1949.

According to Professor Lin Dekuan of Northwestern Polytechnic University, he saw children playing Huarong Road made of paper in the countryside of Chenggu County, Shaanxi Province in 1938.

In the 1950s, Mr. Xu Chunfang of Suzhou Normal University's "interesting mathematics" analyzed the huarongdao game in detail and gave a 100 step solution.

During the cultural revolution, huarongdao games were quite popular.

In 2002, Cui Lequan's "forgetting worries, clearing music -- ancient entertainment culture" introduced all kinds of games and toys in ancient China, including Tangram and nine links, but not Huarong Road.

It can be seen that before the discovery of new historical data, it is credible that the history of Huarong Dao is not more than several decades.

Huarongdao game belongs to slider game, which is to move something called "block" according to certain conditions within a certain range, and finally meet certain requirements. The origin of slider games can be said to be the "rearrangement of nine palaces" in ancient China. It should be produced in the era of Hetu Luoshu, which has thousands of years of history. In 1865, the game of "rearrangement 15" appeared in the west, especially the game of "14-15" launched by Sam Lloyd in 1878. Since then, a variety of slider games have emerged. L. W. hardy invented the pennant game and obtained a patent in 1909. Later, the red mane game appeared in France. It is conceivable that this game will spread to China and become a huarongdao game.

Research history

Xu Chunfang, a professor of mathematics at Soochow University, was the first person to study huarongdao systematically. In 1952, he made a detailed analysis of the game in "random talk on Mathematics" and summed up eight rules. The eight items can be summarized into the following four points:

1. The four soldiers must be together in pairs, not separated;

2. When Cao Cao, Guan Yu and the general move, there should be two small soldiers in front of them;

3. When Cao Cao moved, there should be two soldiers behind him to catch up;

4. In the above three conditions, each block can be moved locally (without hindering other places).

On this basis, Xu Chun Fang proposed a 100 step solution. The following is Mr. Xu's solution. Maybe due to different initial conditions, it only takes 98 steps.

Huarong Road has different starting points. According to the classification of the five rectangular blocks, except that it is impossible to place all five blocks vertically, there are one horizontal, two horizontal, three horizontal, four horizontal and five horizontal. Here are some examples.

Concrete solution

1. After decades of efforts by Chinese and foreign scientists such as Jiang Changying, Fujimura Yoshiro, Qingshui Daxiong and Martin gardana, the game solution has been reduced from 87 steps more than 60 years ago to 81 steps.

2. Thomas B. lenann, an American lawyer, found a new solution, which was published by Gardner in Scientific American in March 1964. There are 81 steps, which are called Gardner solution.

3. The fastest way of Huarong Road is 100 steps in China and 82 steps in Japan. Later, Americans used computers to find out the final solution by using the exhaustive method. There can be no faster solution. 81 steps. After finding the final solution by computer, the Americans joked with the Chinese that a famous American doctor named computer had found the final solution.

Other related

Besides its history, there are at least the following problems in the study of huarongdao game

1. How many starts are there;

2. Judge the solution;

3. The optimal solution is given;

4. Computer solution.

Therefore, Huarong Road is a mathematical game, which can exercise people's thinking and make people's thinking more active.

Both at home and abroad, there are some enthusiasts and researchers of huarongdao. In 1985, Mr. Jiang Changying initiated and organized the "huarongdao Research Association", and they achieved a lot of results. In particular, the former vice president of Beijing Institute of technology Qi Yao's network research can be said to completely solve the huarongdao game method. He studied 54 diagrams of various key states of a horizontal Huarong Road, found out the relationship between them and drew the diagram. So any horizontal Huarong Road can reach a critical state through a few steps, and the solution is given. He also drew diagrams for the two, three and four horizontal forms.

Using computer to solve huarongdao game, there is such a saying: "the contribution of the software hrde compiled by the author is the successful realization of a systematic searching algorithm, which can judge whether there is a solution to any layout placed by users in a short time. If there is a solution, then the least step of it is solved. Then, it will move the chessman on the screen in an animated way to show its operation method. You can also use a series of graphics to display the way of each step statically, which is convenient for users to observe and study carefully. Generally speaking, it takes only one or two minutes to solve a problem on the popular IBM 486 computer, and about ten minutes on the slower 286 computer. According to the principle of its algorithm, we can be sure that the result is absolutely credible. That is to say, the way it solves must be the least step of the layout. "

Huarong Road game has a lot of development, at home and abroad produced a lot of similar games. Such as push box game.

The game of pushing boxes appeared in computers. It originated from the warehouse family developed by Li Guozhao in Taiwan Province in 1994. Boxes can only be pushed, not pulled, and can only be pushed one at a time. The winning condition is to push all boxes to the destination. There are many kinds of box games on the Internet now.

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