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SIMPLE GEOMETRIC CHESS
The simple geometric chess is a standardized version of the standard geometric chess, in which the geometric meanings of the chess pieces are removed and replaced by simple numbers while the form of playing remains unchanged.
Each side has 9 chess pieces with a value from 1 to 9, which can be combined with the standard geometric chess into a set of double chess pieces. In addition to the nine chess pieces to play, there is an additional chess piece, called G piece, as in the standard geometric chess. The original chess pieces are arranged as shown in Figure 2.1.
Fig 2.1: Layout of chess pieces on the simple geometric chess board
a. Piece “1”: piece "1" is denoted by 1 or 1 square dot.
b. Piece “2”: piece "2" denoted by 2 or 2 square dots.
c. Piece “3”: piece "3" is denoted by 3 or 3 square dots.
d. Piece “4”: piece "4" is denoted by 4 or 4 square dots.
e. Piece “5”: piece "5" is denoted by 5 or 5 square dots.
f. Piece “6”: piece "6" is denoted by 6 or 6 square dots.
g. Piece “7”: piece "7" is denoted by 7 or 7 square dots.
h. Piece “8”: piece "8" denoted by 8 or 8 square dots.
i. Piece “9”: piece "9" denoted by 9 or 9 square dots.
Initially, piece G displays a G-shape, when one side wins a match, its piece G is flipped over to show the star. Therefore, piece G just recognizes the score for the side which wins in the matches.
In a simple geometric chess, to gain the score, the player must arrange the appropriate chess pieces into straight, even, triangular or square segments.
a. General notes
* Only consider the points for the side which has just done the move.
* A geometric form that is considered valid and scored for the side that has just ended the move must have the following characteristics:
+ Strictly follow the layout rules that are suitable for the geometric shapes shown below.
+ Chess pieces for arranging must be composed of pieces of both sides.
+ The number of pieces of the side which has the later move must be greater than or equal to that of the competitor.
* To make it easy to see, the illustrations in the next section refer only to the pieces involved in the puzzle and ignore the remaining chess pieces on the chess board.
b. Straight line (1 - 2 points)
+ A straight line must be made up of 3 or more pieces.
+ The chess pieces shall be placed on the horizontal, vertical or diagonal lines of the chessboard.
+ Distance between two consecutive chess pieces is always equal.
+ Pieces involved in straight line alignment must be consecutive numbers, arranged in the order of increasing or decreasing.
* Figure 2.2 illustrates three straight lines 4-5-6; 1-2-3; 5-6-7-8. These evenly spaced segments are generated by sequential numbers and are arranged in any direction (from the left to right, right to left, bottom to top, or right).
Fig 2.2: Straight lines with equal distance
* Straight line spacing consisting of 3 pieces is calculated 1 point, from 4 pieces or more are calculated 2 points.
* In addition to the chess pieces to join the straight line evenly spaced out, if on the straight line, there are other chess pieces positions, it is called "Stop piece". Figure 2.3 illustrates the existence of “Stop piece" in straight line alignment. In the straight lines 1-2-3 in the figure 2.3, piece 6 is known as “Stop piece”. In the straight lines 5-6-7 below figure 2.3, piece 4 is known as Can piece. When “Stop piece” appears, the straight line is not recognized.
Fig 2.3: Appearance of “Stop piece” when arranging the straight line with equal distance
c. Triangular layout (1 point)
When arranging the triangle, the player must identify three vertices of the triangle, at each vertex, there must be a positioning chess piece, three chess pieces in three vertices are consecutive numbers, the symmetry of the triangle must lie on the horizontal, vertical or diagonal lines of the chessboard. Triangular triangles are calculated 1 point.
+ Figure 2.4 illustrates triangular layout with three consecutive numbers. In order from the top down, there are three triangles: 4-5-6; 1-2-3 and 5-6-7.
Fig 2.4: Triangular layout with 03 chess pieces
+ In addition to three vertices of the triangle, if the triangles have other chess pieces to be positioned (called as Stop piece), then the triangle is not considered valid. As mentioned in Figure 2.5, Piece 1 is called Stop piece for the triangle 5-6-7.
+ The chess pieces located in the inside of the triangle are not Stop piece. As mentioned in Figure 2.5, Piece 5 is not Stop piece for the triangle 1-2-3.
Fig 2.5: Stop piece and non-Stop pieces in the triangular layout
d. Square layout ( 2 points )
When in the square layout, the player must determine four vertices of the square, at each vertex, i must have positioning chess pieces, four chess pieces at four vertices are consecutive numbers, the right side of the right square shall be lie on the horizontal, vertical or diagonal lines of the chessboard.
The square is arranged in 4 consecutive numbers, read in either reverse order or counterclockwise rotation. Square is calculated 2 points. Figure 2.6 illustrates how to make square layout.
Fig 2.6: Square layout with chess pieces
+ In addition to four tops of the square, if there are other chess pieces on the sides of the square, the square is not considered valid.
+ The chess pieces on the inside of the square are not Stop pieces.
+ Figure 2.7 illustrates the existence of Stop piece and non – Stop pieces in the square
Fig 2.7: Stop pieces and non-Stop pieces in the square
e. Polymorphic layout
In many cases, when we move a chess piece to a new location, we can create two or more basic geometric shapes - then we have a polymorphic sort. Thus, the polymorphic layout is a composite of individual shapes.
* When making the polymorphic layout, the maker must follow the following principles:
+ Each separate shape when separated must be a valid shape.
+ Individual pairs can share one or two pieces together.
+ Score is calculated as the total score of individual shapes.
* Figure 2.8 illustrates how polygons are arranged.
Fig 2.8: Polymorphic layout
+ As mentioned Figure 2.8, when the red side moves piece 5 to C7, it creates two valid triangles, the triangle 4-5-6 and triangle 5-6-7. With this move on the red side is calculated 2 points (each triangle is calculated 1 point).
+ As mentioned in 2.8, when the black side moves piece 2 to H3, it will produce a straight line 1-2-3 and 1 square 2-3-4-5 in perfectly valid way for scoring. These two basic shapes share piece 2 and piece 3. With this move, the black side gains three points, including one point for the line equidistant and two points for the square.
* Figure 2.9 illustrates two more examples of polymorphic layout.
Fig 2.9: Polymorphic layout
+ Like chess pieces in Figure 2.9, when the red side moves piece 2 to B8, it immediately creates two valid straight lines with points of 1-2-3 and 2-3- 4-5. With this move, the red side is added 3 points.
+ Like chess pieces in Figure 2.9, when the red side moves piece 6 to G3, it creates a triangle 5-6-7 and the straight line 6-7-8. With this move, the red side is added 2 points.
a. Repeating layout
Fig 2.10: Repeating layout
Figure 2.10 illustrates the straight line 1-2-3, consisting of 2 black pieces and 1 red piece, this line is created if the black side makes the last one, it is calculated 1 point and the red side creates it, neither sides have points. After a 1-2-3 straight line is available, if the black side moves piece "1" or "2" to another position, the red side does not move piece "3" from its position in the next move, then the black side has the right to move piece "1" or "2 back to its original location to re-establish a straight line 1-2-3 to gain the point.
This repeating layout is not only true for straight line layout, but applies to all cases of layout in simple geometric chess and standard geometric chess.
b. Do not create the shape by moving Stop pieces
In the geometric chess, valid geometric shapes are made up of three or more pieces. Among the pieces to be included is a move that has just arrived. Cases of shaping by moving Stop piece are not considered valid.
Fig 2.11: Do not create the shape by moving Stop pieces
In Figure 2.11, we see that piece "9" is in the middle of straight line 1-2-3, if the black side moves piece "9" out of its position, they are not scored for the straight line 1-2-3 just created.
The principle of not scoring by moving Stop piece is not only true for straight lines, but also for all forms of standard and simple geometric chess.
c. Avoid confusion in polymorphic layout
* In a simple geometric chess, when arranging a square, it is possible to create triangular triangles in that square, but these triangles are not counted but only for square. In Figure 2.12, it is supposed that the red side making the late move creates a 5-6-7-8 square, they are only given 2 points for that square, not plus the points of the triangle 5-6-7.
* When making a straight line (in a simple & standard geometric chess) with 4 or more pieces, it is possible to create evenly spaced segments consisting of 3 overlapping triangles on the same line but it is only calculated for the longest straight line. In Figure 2.12, it is supposed that the red side makes the late moves in a straight line1-2-3-4, it is only given two points for this line, not plus points of the line equidistant from 1-2-3.
Fig 2.12: Avoid confusion in polymorphic layout
The above cases are not known as polymorphic layout. When forming polymorphs, pairs of adjacent shapes use only one or two pieces. There are no polymorphic layouts where pairs of adjacent shapes share the same three or more pieces.