Rules and Features of tetta

For convenience, we explain the rules with 4*4 squares only in the following.

1. Learning the graph - Introduction to the graph of game in the following

   

   The whole graph is called a square, which is composed of 4*4 = 16 cells. The cells are separated with white lines. There are 2 shapes in them. The top-left one is a color rectangle (including black one, invisible). The bottom-right one is a color triangle ( including black one, invisible). Color rectangles and triangles have 4 colors each (including black one, invisible). Each color occurs 4 times each, total 4*4 = 16 color rectangles and triangles. The combinations of color rectangles and triangles in cells are all distinct. Rectangles and triangles have 4 colors each, total 4*4 = 16 cells of distinct color combinations. Each square has a black cell, which is swapped with the other cells (Refer to the following explanation). The perpendicular 4 cells are called a column and the horizontal 4 cells a row.

2. How to play - Introduction to how to play in the following

   Image 1 Square from the start	Image 2 Each of the 6 cells in the same column or row (marked white) can be swapped with the black cell	Image 3 Select one of the six cells in the left image (marked white)
   Image 4 Result after swap	Image 5 Each of the 6 cells in the same column or row (marked white) can be swapped with the black cell	Image 6 Select one of the six cells in the left image (marked white)
   Image 7 Result after swap	Image 8 Each of the 6 cells in the same column or row (marked white) can be swapped with the black cell	Image 9 Select one of the six cells in the left image (marked white)
   	...
   Image 10 Result after swap	And so on

3. Objectives - It explains the permutations of squares to complete in the following. The game is completed when any permutation in the following is achieved.

   Rule 1 Column-Row
   Image 1 Color rectangles in each column have distinct colors and in each row the same color. Color triangles in each column have the same color and in each row distinct colors.	Image 2 Color rectangles in each column have the same color and in each row distinct colors. Color triangles in each column are distinct colors and in each row the same color.
   Rule 2 Column/Row-Latin
   Image 3 Color rectangles in each column have distinct colors and in each row the same color. Color triangles in each column have distinct colors and in each row distinct colors.	Image 4 Color rectangles in each column have the same color and in each row distinct colors. Color triangles in each column have distinct colors and in each row distinct colors.
   Image 5 Color rectangles in each column have distinct colors and in each row distinct colors. Color triangles in each column have the same color and in each row distinct colors.	Image 6 Color rectangles in each column have distinct colors and in each row distinct colors. Color triangles in each column have distinct colors and in each row the same color.
   Rule 3 Graeco-Latin
   Image 7 Color rectangles in each column have distinct colors and in each row distinct colors. Color triangles in each column have distinct colors and in each row distinct colors.

4. Comparisons of features of tetta and other intelligent games

   Features	tetta	N-Puzzle	Rubik's Cube	Sudoku	Tetris	Chess	Go	Contract Bridge	Poker
   1. Complexity of rules	**	*	*	**	**	***	**	*****	***
   2. Start	Random	Random	Certain permutations	Certain givens	Blank	Fixed positions	Blank	Random	Random
   3. End	Complete certain permutations	Complete only one permutation	Same colors of six faces	Fill out the square according to the rules	Stack to the top	Checkmate or stalemate	Fill out the board and decide the winner	Show up all cards and decide the winners	All players except one fold, or compare the hands to decide the winner
   4. Complexity of variance	The higher order the more complex	The higher order the more complex	The higher order the more complex	The higher order the more complex	**	*****	The higher order the more complex	****	**
   5. Chance	No	No	No	No	*	No	No	***	*****
   6. Players	1+	1+	1+	1+	1+	2	2	4	2+
   7. Relationship between players	Everyone competes with each other	Everyone competes with each other	Everyone competes with each other	Everyone competes with each other	Everyone competes with each other	Two players play against each other	Two players play against each other	Two sides (two players per side) play against each other	Everyone competes with each other
   8. Competition on calculation	The lower order the more suitable	The lower order the more suitable	Only order of 2 is suitable	Depends on the difficulty	*	Only	Only	Only	Only
   9. Competition on reaction	The higher order the more suitable	The higher order the more suitable	Order of 3 or above is suitable	Only order of 3*3 or 4*4 is suitable	***	No	No	No	No
   10. Computer time	Maybe very much when AI is used	Maybe very much when AI is used	Maybe very much when AI is used	Maybe very much when AI is used	*	Maybe very much when AI is used	Maybe very much when AI is used	Maybe very much when AI is used	*
   11. Replay to learn	Yes	Yes	Yes	No	No	Yes	Yes	Yes	No
   12. Educational function	Coordinate geometry, combinatorics, algebra	Coordinate geometry, combinatorics, algebra	3D coordinate geometry, combinatorics, algebra	Coordinate geometry, combinatorics	Coordinate geometry, combinatorics, algebra	Coordinate geometry, combinatorics, algebra, game theory	Coordinate geometry, combinatorics, algebra, game theory	Combinatorics, probability, game theory	Combinatorics, probability, game theory

   Remarks:

   1. Complexity of rule

   It refers to the difficulty of understanding rules.

   2. Start

   It refers to the state of game start.

   3. End

   It refers to the state of game end.

   4. Complexity of variance

   It refers to the consequences of each move of player. the 19*19 go may be the most complex of all games.

   5. Chance

   It refers to that the player is affected by hidden information.

   6. Players

   It refers to the suitable number of players.

   7. Relationship between players

   It refers to the relationship between players. "Compete with" means that the players are opponents but they cannot interfere with each other with moves. "play against" means the players are opponents but they can make bad interference to each other with moves.

   8. Competition on calculation

   It refers to that the opponent players compete on more complete calculation.

   9. Competition on reaction

   It refers to that the opponent players compete on shorter time of reaction to some situations.

   10. Computer time

   It refers to the computrer time which the game costs.

   11. Replay to learn

   It refers to that the player can record the gameplay and replay it for learning.

   12. Educational function

   It refers to that the game can be an example of education. Here list only educational functions of mathematics.

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