The aim of this study is to figure out the optimization of survival probability of the generals in the card game "Legends of the Three Kingdoms". First, based on combinatorics and probability theory, the PASCAL program was performed to analyze the probabilities of success when several popular generals perform their special skills in the game. The results are as follows: Second, seven typical generals, including Zhou Tai, Zhang Jiao, Zhen Ji, Lu Xun, Ma Chao, Xiahou Dun, and Guo Jia, were chosen, and their abilities including attacking and defense were arbitrarily quantified according to a model constructed in the present study. The scores are as follows: Card-drawing Changing Attacking Defense Blood-selling Zhen Ji 5.62 Zhou Tai 1.04 Ma Chao 1.68 Xiahou Dun 1.19 Guo Jia 3.36 Lu Xun 3.55 Zhang Jiao 2.55 The abilities of different generals were sorted, and by comparison with the statistical record online, the reliability of the model was proved. Thus, the irrationality of the game is identified in this study, and we recommend the game designer to modify the abilities of some generals and to obtain an optimized value according to the output of the model, by which the game would be more popular.

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Lights Out is a video game, which was released by Tiger Toys in 1995. Generally, there are 3×3, 4×4, 5×5, 10×10 grids of games. Under the normal circumstances, it’s easy to deal with some special configurations manually. However, the possibility of solving the randomly-generated configuration by hand is small, for it’s a bit difficult to find the law. Out of interest and enthusiasm about the game, our team reads some reference and gathered four mathematic methods to solve the game. What’s more, we extend the methods to m×n games, the cycling game, the lit-only game and N-color game. We independently propose a method to classify all configurations in the game for 5×5, which can also be extended to general cases. We also put forward the issues about N-order hexagon games, and provide some feasible solutions.

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In a class of mathematic competition in our school, Mr. Yang explained for us a problem in 2006 Iranian Maths Olympics (Example 1) and the problem of the 176 in Medium Mathematics 2006.4.At the end of which he raised a question that whether we can make up an inequality chain, which interested us very much. So with the instruction of Mr. Yang, we obtained Theorems 1-6 by means of Bottema 2009 which is mdae by Professor Yang Lu ,a researcher of Chinese Academy of Social Sciences ), computers and calculators. And in this line, we considered that whether they could be extended to situations of high power. After making great endeavors, we endeavor Theorem 7. Finally, we thought about whether it could be extended to high dimensional situation and obtained the creative Theorem 8. The objective of this paper is to further study a type of inequalities of the sum of equal powers of right triangle’s 3 edges to the and has successfully obtained a series of inequalities to the power of 3 to 6 and some of higher order, among which some inequalities of lower order have been proved true by means of the software of Bottema 2009 that developed by Doctor Yang Lu, who is a researcher of Chinese Academy of Science. And we have obtained the inequalities about ndimensional simplex. Meanwhile we studied the application of these inequalities in mathematical competitions and teaching. In the last section, we also proposed two conjectures of more generality,among which conjecture 2 is about n dimensional simplex, for those who are interested in it. The study of this type of problems is beneficial to mathematical competitions and researches of primary and advanced mathematics. As for the application of these theorems, we can discover their value in geometries like right-angled triangle, rectangle,round,ellipse, hyperbola,cube, hypocycloid,right-angled triangular pyramid, globe, ellipsoid, hyperboloid of two sheet, elliptic cone and so on. We can also study about their value in teaching and competitions. In the end, we proposed more general conjectures while the second discusses about situations of n dimensional simplex and both of which are for those readers who are interested in it. This type of problems is beneficial for competitions and study of primary and advanced mathematics. Highlight：We systematically study the inequality of the sum of 3 right-angled triangular sides（Theorems1-6）and extend them to the right-angled tetrahedron and propose some difficult conjectures. Innovation：We get some inequalities of the sum of 3 right-angled triangular sides of high order (4 and above(Theorem 7))，and extend them to the n dimensional space (theorem 8)，and proposed conjectures in n dimensional space (conjecture 1,2) with creative methods .