as illustrated in fig1 the game board 1 has two visually distinguishable sections , x 2 and y 3 . section x 2 consists of 32 defined square spaces and section y 3 consists of 49 defined square spaces . fig2 illustrates the process of finding the integers located in the spaces of section y 3 . the space containing the integer − 20 18 of section y 3 is used as an example . the integer − 20 18 is found by adding the eight integers contained in the spaces of section x 2 located perpendicular and at forty - five degree angles to the space containing the integer − 20 18 . those eight integers in section x 2 , located perpendicular and at forty - five degree angles to the space containing the integer − 20 18 that are preceded by a +/− symbol , are added as positive integers and those integers preceded by a −/+ are added as negative integers . therefore , the integer − 20 18 in section y 3 is derived by the process of adding the integers : 1 15 , 21 16 , 1 17 , − 3 10 , − 8 11 , − 21 12 , − 8 13 , − 3 14 of section x 2 this expression ( 1 + 21 + 1 +− 3 +− 8 +− 21 +− 8 +− 3 ) is equal to − 20 . this process is done to each of the 49 square spaces of section y 3 determining all of the integers contained therein . fig3 illustrates the process of movement in this game . a playing piece in section y 3 can only be moved to a new space when the difference between the integer contained in that space and the integer contained in the piece &# 39 ; s current space is created . this is done by placing the pieces located in section x 2 on an integer or integers that create the difference between the two spaces in section y 3 . in this example the arrow piece 8 is moved in section x 2 onto the space containing the integer −/+ 13 , making it possible for square piece 5 to move from the space containing the integer − 21 to the space containing the integer − 8 in section y 3 . arrow piece 8 a is moved in section x 2 onto the space containing the integer −/+ 5 , making it possible for square piece 5 a to move from the space containing the integer − 21 to the space containing the integer − 16 located in section y 3 . arrow piece 9 is moved in section x 2 onto the space containing the integer +/− 5 , making it possible for circle piece 4 to move from the space containing the integer 14 to the space containing the integer 9 in section y 3 . arrow piece 9 a is moved in section x 2 onto the space containing the integer +/− 3 , making it possible for circle piece 4 to move from the space containing the integer 9 to the space containing the integer 6 in section y 3 . fig4 illustrates the movement ability of each type of piece . the circle piece 4 can move horizontally and vertically anywhere within section y 3 providing no other piece is blocking its path . the square piece 5 can move horizontally and vertically anywhere within section y 3 and can jump over a piece or pieces blocking its path in those directions . the triangle piece 6 can move horizontally , vertically , and diagonally anywhere within section y 3 providing that there is no other piece blocking its path . diamond piece 7 is able to move horizontally , vertically , and , diagonally within section y 3 and can jump over a piece or pieces blocking its path in those directions . arrow pieces 8 and 8 a can be placed on any space within section x 2 containing the symbol −/+ or a zero . arrow pieces 9 and 9 a can be placed on any space within section x 2 containing the +/− symbol or a zero . fig5 shows the preferred starting positions of each piece of each player &# 39 ; s set of playing pieces . player one &# 39 ; s set of pieces is illustrated as white and player two &# 39 ; s pieces are illustrated as black . the diamond piece 7 is placed in section y 3 on the spaces containing the integers 40 for player one ; the diamond piece 7 a is placed in section y 3 on the space containing the integers − 40 for player two . the triangle pieces 6 and 6 a are placed in section y 3 on the spaces containing the integers 29 and 29 for player one ; the triangle pieces 6 b and 6 c are placed in section y 3 on the spaces containing the integers − 29 and − 29 for player two . the square pieces 5 and 5 a are placed in section y 3 on the spaces containing the integers 21 and 21 for player one ; the square pieces 5 b and 5 c are placed in section y 3 on the spaces containing the integers − 21 and − 21 for player two . the circle pieces 4 , 4 a , 4 b , are placed in section y 3 on the spaces containing the integers 14 , 14 , and 20 for player one ; the circle pieces 4 c , 4 d , 4 e , are placed in section y 3 on the spaces containing the integers − 14 ,− 14 , and − 20 for player two . the arrow pieces 8 and 9 are placed in section x 2 on one of the spaces containing the integer zero , for both player one and player two ; the arrow pieces 8 a and 9 a are placed in section x 2 on the other space that contains the integer zero , for both player one and two . fig6 illustrates the object of the game which is to place one &# 39 ; s alike pieces located in section y 3 on spaces containing integers that when added together equal zero . in this example of a winning situation , circle piece 4 is on a space containing the integer 6 , circle piece 4 a is on a space containing the integer 5 and circle piece 4 b is on a space containing the integer − 11 . square piece 5 is on a space containing the integer 0 and square piece 5 a is on a space containing the integer 0 . triangle piece 6 is on a space containing the integer 5 and triangle piece 6 a is on a space containing the integer − 5 . diamond piece 7 is on a space containing the integer 0 . each of the alike pieces are on spaces containing integers that when added together equal zero , which is the preferred winning condition of the game . the game board 1 is made of a material such as : wood , plastic , marble , cardboard or any other suitable material . if possible it is preferred that the game board 1 can be folded in half , from its square shape into a triangle , wherein the crease is along the spaces containing the integer zero . alternatively , it may be made to fold into a triangle with the crease along the opposite diagonal or in half into a rectangle . the game board 1 may also be a divisible board , which could be taken apart and put together . it is preferred that each of the two players are assigned a set of 10 pieces . 3 of which are distinguished as circles , 2 of which are distinguished as squares , 2 of which are distinguished as triangles , 1 piece distinguished as a diamond , and 2 pieces distinguished as arrows . the two sets of playing pieces must be visually distinguishable . it is preferred that the playing sets are distinguished by color . the preferred color scheme is to have one player assigned pieces that are distinguished as being black and the other player having pieces that are distinguished as being white . it is possible that the displays applied to the faces of the pieces are differentiated from each other into shapes other than circles , squares triangles , diamonds , and arrows . alternatively , characters such as numerals , alphabets , colors , marks or symbols , patterns or designs , which are different from each other , may be applied to the faces of the pieces . it is preferred that the aforementioned playing pieces are cubes made out made out of a transparent glass or acrylic material , allowing the players to view the integers located on the board through each piece . alternatively , the pieces may be made out of a material such as paper , cardboard , wood , metal or a synthetic resinous material such as plastic or the like . the pieces are preferably distinguishable by paint , ink , vinyl decal or the like , which is preferably applied to four of the faces of the cubes . the regulations of the game are as follows : 1 ) each player is given a set of pieces that is either white or black . the player that is using the white pieces , positions his pieces in the preferred position , on the positive integers , located in section y 3 as shown in fig5 . the player that is using the black pieces , positions his pieces in the preferred position , on the negative integers , located in section y 3 as shown in fig5 . the playing pieces which start in section x 2 , may only be moved within section x 2 and the pieces which start in section y 3 may only be moved within section y 3 . 2 ) the player starting on the side containing positive integers and using the white set of pieces makes the first move . 3 ) a player moves by using his two pieces , signified by arrows , which move within section x 2 , to create an integer which is the difference between two integers in section y 3 , enabling a piece in section y 3 to move . this is done by placing the arrow piece on the space containing the desired integer or using the arrow pieces in combination to create a number . each arrow piece may be used together or apart once per turn . the arrow pieces may be moved anywhere in section x 2 on that player &# 39 ; s side of the board . this process of movement is illustrated in fig3 . 4 ) at the beginning of a player &# 39 ; s turn , the player may choose to use the integer or integers , which were used in section x 2 , the turn before , again . the player may only use each integer once , in combination or apart , no matter how they were used during the previous turn , to move a piece in section y 3 . the player may choose to discard this opportunity and whether a player uses it or not , he / she gets to make a new move . 5 ) each piece &# 39 ; s movement ability is illustrated in fig4 . 6 ) a player wins the game when he / she has positioned his / her alike pieces , played within section y 3 , on integers that when added together equal zero . as illustrated in fig6 . 7 ) a player must make a move if it is possible . if it is not possible for a player to make a move , he / she loses his / her turn . 8 ) an optional rule may also be applied , wherein if a player positions his / her circles , squares , triangles or diamond on an integer or integers that when added together equal zero , the other player loses the opportunity to use the integers he / she placed his arrow pieces on the turn before , in his upcoming turn . 9 ) an alternative to rule # 8 wherein this rule is applied and continued only when the player who went second makes his / her first positioning of alike pieces to equal zero or when the player who went first positions two types of his / her alike pieces on integers that when added together equal zero . 10 ) an alternative to rule # 6 wherein the winning positioning is achieved by placing one &# 39 ; s pieces located within section y 3 , whether or not they are alike , on integers that when added together equal zero . 11 ) an alternative to rule # 7 wherein if a player is unable to make a move he / she loses the game rather than his turn . 12 ) an alternative to rule # 2 wherein the player using the black pieces goes first . it is to be understood that the embodiments herein described are merely illustrative of the application of the principles of the invention . reference herein to details of the illustrated embodiments are not intended to limit the scope of the claims , which themselves recite those features that are essential to the invention .
this is a novel two - player board game which uses addition and subtraction to initiate the movement of a player &# 39 ; s pieces . the game is comprised of two sections ; each section consists of a plurality of spaces containing integers . the interior section is comprised of opposite sides separated by zeros , one side containing negative integers and the other positive . pieces are provided to each player for separate use in the exterior and interior sections . movement is initiated by positioning pieces in the exterior section on spaces whose integers produce a difference of two integers found in the interior section , thus enabling pieces to move from one space to another . the object of this game is to be the first player with all his / her pieces positioned within the interior section on spaces whose integers when added together equal zero .