【正文】
IntroductionLights, which are popular in a very interesting game on the Internet in recent years, are defined as follows: In an n n grid board, every square have two states: white (open) and black (closed). When you click on any one of these squares with the mouse, the box and all its adjacent boxes change states. Namely, the black boxes bee the white boxes. At the edge of the board, the box can`t have the four adjacent boxes. Therefore, we only consider those existed boxes.using the method of algebra and mathematical modeling to give the mathematical modeling, based on the linear equations of finite field, Zhou Hao gave all the solutions for the case of n=, he used the Classification method of algebra to give the intuitive description of four equivalence classes of the game so that the players can immediately determine which type the “mess” is.Of course, before Zhou Hao, scholars added the control vector for a problem of PRG game on a similar light and analyzed and proved the problem by a mathematical model. After that, researchers made general promotion for a control problem in the RPG game and give a more prehensive solution.Furthermore, some foreign scholars used the dynamic programming methods to prove a variety of matrix reconstruction problems and also proved some plex results on reconstructing neighborhood binary matrix.The mathematical knowledge that Zhou Hao use to build the model on the control state issues of lights is relatively plicated.