Sudoku (sometimes spelled Su Doku) puzzles are numerical logic puzzles that use a nine-by-nine grid of squares. The squares are grouped into nine regions, each containing nine squares in a three-by-three grid. The puzzle, which is predetermined by the game creator, includes numbers in some of the squares, with the goal of the game being to fill in the empty squares so that the numbers 1 through 9 appear just once in every row, column, and region of the puzzle.
The puzzle's origin dates back to the 18th century, when Swiss mathematician Leonhard Euler invented a puzzle called Latin Squares. The modern day Sudoku puzzle originated in 1979 when a grid titled “Number Place” was published in an American puzzle magazine. By the early 1980's, the puzzle was renamed Sudoku (which means “single number”) and appeared in several Japanese magazines. In 2004, the first Sudoku puzzle was published in a London newspaper.
Sudoku puzzles were originally available only in printed form, appearing in newspapers, magazines, and books. Recently, however, Sudoku board games and computer games played on desktop computers, cell phones and arcade style devices have begun to appear on the market.
United States Patent Publication No. 20070267813 discloses a three dimensional Sudoku game which is played in a manner akin to a Rubik's cube, by having a player solve the cube by manipulating conjoined cubiform elements having numbers on each side. Another type of three-dimensional Sudoku puzzle, made up of nine Sudoku puzzles layered on top of each, other was also published in the Weekend supplement of The Daily Telegraph on May 21, 2005 as the “Dion Cube puzzle.” In this game, each plane through the cube formed a valid puzzle.
The present invention is a three dimensional, Sudoku-like game having faces which are joined to form a three-dimensional shape, such as a cube, in which the solutions to individual Sudoku puzzles played on each face are constrained by the numbers or other symbols occupying cells in an adjoining face of the game. All of the individual Sudoku puzzles of the present game must therefore be played together as a larger, single puzzle.
In one embodiment, the present game is a three-dimensional game having at least 6 faces, wherein each face comprises 4 sides, each of the 4 sides comprising an edge shared with a different face, wherein:
In the foregoing embodiment, the symbols are preferably numbers, and N is preferably 2, 3, or 4.
A three-dimensional Sudoku game according to the present invention can also comprise:
a plurality of faces, each face comprising a plurality of sides, wherein each of the sides comprises an edge shared with a different face;
a plurality of cells on each face, wherein the cells of each face are arranged in rows and columns, each row and each column of the face comprising N cells, wherein N is a whole number greater than 1, thereby forming an array of N2 cells on each face of the game; and
N regions on each face, each region comprising N rows of N cells each and N columns of N cells each,
wherein each cell includes no more than one symbol in a non-repeating series of symbols, each symbol in the series of symbols appearing only once in each row, each column, and each region of a face, and a first cell of a first face of the game and a second cell of a second face must include the same symbol if the first cell and second cell are adjacent.
The symbols are preferably an ordered series of numbers, and N preferably is selected from the group consisting of 4 and 9 in this embodiment. Each cell is also preferably in the form of a square, and each row of a face is arranged perpendicularly to each column of the face. The faces in this embodiment can each be in the form of a square and be arranged to form a cube. The present game is preferably in three-dimensional physical form, but can also be displayed in two dimensions, such as on a computer screen or piece of paper. If the game is in physical form, it can be formed from a rigid planar material such as paper or cardboard which is folded into a three-dimensional object, with each face of the object comprising a face of the game.
The present invention can further comprise a method of playing a three-dimensional Sudoku game, comprising the steps of:
providing a plurality of faces which form at least part of a polyhedron, each face comprising a plurality of sides and N regions, each region comprising N rows of N cells each and N columns of N cells each, wherein N is a whole number greater than 1;
assigning a different symbol from a group of N2 non-repeating symbols to each cell in each row of each face;
assigning a different symbol from the group of N2 non-repeating symbols to each cell in each column of each face; and
assigning a different symbol from the group of N2 non-repeating symbols to each cell in each region of the face,
wherein at least a first face and a second face of the polyhedron are joined at an edge, and adjacent cells on the first face and the second face are assigned the same symbol from the group of N2 non-repeating symbols.
A further embodiment of the present invention can comprise a method of generating a three-dimensional Sudoku game in which each cell of the game can comprise a symbol from a predetermined set of symbols, wherein each symbol of the set appears only once in each row, column, and region of a face of the game, comprising:
(a) generating a plurality of faces, each face comprising N2 cells, the cells are arranged into rows of N cells and columns of N cells;
(b) assigning a top edge, a bottom edge, a right edge, and a left edge to each cell;
(c) mapping each cell such that the top edge of a cell is the bottom edge of an adjacent cell in a column and such that a right edge of the cell is the left edge of an adjacent cell in the row;
(d) randomly selecting a previously unselected cell of a face of the game and randomly assigning a symbol to the cell from the predetermined set of symbols, thereby generating a randomly assigned cell containing the symbol, the symbol must be different from other symbols contained in other cells in the same row, column and region as the randomly assigned cell, and when the randomly assigned cell shares an edge with a second cell on a different face of the game, the randomly assigned cell and the second cell must comprise the same symbol;
(e) selecting a remaining cell in the game and determining whether the remaining cell can comprise only one valid choice of symbols, and if so, assigning the valid symbol to the remaining cell to generate a nonrandomly assigned cell, and removing the valid symbol from the set of predetermined symbols assignable to other cells in the same row, column and region of the nonrandomly assigned cell; and
(f) repeating steps (d) and (e) until a symbol from the predetermined set of symbols has been assigned to each cell of the game, thereby generating a solved game.
As used herein, the following terms and variations thereof have the meanings given below, unless a different meaning is clearly intended by the context in which such term is used.
“Adjacent,” with respect to cells of the present game, refers to a logical association between two cells which is usually depicted by a physical and/or visual association between the two cells, such as a shared boundary.
“Cell” refers to a physical or visually displayed area on a face of the present game for retaining and displaying a number or other symbol.
“Column” refers to an ordered series of cells on a single face of the present game which intersects with other ordered series of cells on the same face designated as rows. The columns on a face are non-intersecting. Typically, rows and columns are laid out on a grid comprising parallel rows and parallel columns, with the rows being perpendicular to the columns.
“Computer-readable medium” refers to an electronic, magnetic, optical, or other physical device or structure that can contain and/or store a computer program. Examples of such media include magnetic computer disks, optical disks, random access memory (RAM), read-only memory (ROM), and erasable programmable read-only memory (EPROM or Flash memory).
“Corner” refers to a logical association between three cells of the present game, and is generally depicted physically and/or visually as the point at which three or more faces of the present game meet.
“Edge” refers to a side formed at the joining and/or intersection of two faces of the present game.
“Face” refers to a group of cells associated with each other in rows, columns, and regions according to Sudoku rules. A face of the present game is generally a physical or visually depicted surface of a cube, and comprises a Sudoku puzzle.
“Polyhedron” refers to a three-dimensional shape whose faces are polygons.
“Random” in the context of the present method of generating a three dimensional Sudoku game means having no specific pattern, arrangement and/or predictable outcome. It is to be understood that the selection of a first cell of a game to which a symbol or value is to be assigned in the present method may be predetermined in a particular embodiment of the game, i.e. the same cell of a face may be consistently selected when generating puzzles, and/or the same symbol may be assigned in this first selection step, without departing from the randomness of this step, as the puzzle comprises no pattern or arrangement prior to such selection step.
“Region” refers to a square block of cells on a face of the present game having N2 cells, where N is at least 2, and is typically 2 or 3. In a nine-by-nine Sudoku cube game there are nine regions on each face of the game having nine cells each, while in a four-by-four game there are four regions on each face having four cells each.
“Row” refers to an ordered series of cells on a single face of the present game which intersects with another ordered series of cells on the same face designated as a column. The rows on a face are non-intersecting.
“Side” refers to a peripheral portion (outer boundary) of a cell or a face of the present game, as the case may be. The side of a face of the present game is comprised of the sides of adjacent cells. The side of a cell or face is joined at each end to another peripheral portion of the cell or face, and such sides are preferably depicted as being straight, though this is not required.
“Sudoku puzzle” or “Sudoku game” refers to a puzzle in which N4 non-repeating symbols (usually numbers, with N typically being 2 or 3) must be placed into an associated group of cells so that each row, column, and region in which the cells are arranged contains only one of the symbols. The symbols used are typically an ordered series of numbers, e.g. the numbers 1-4 for a puzzle having four rows and four columns on each face. As used herein, such symbols are sometimes referred to as having a “value” without limiting the type of symbol being referred to.
As used herein, the term “comprise” and variations of the term, such as “comprising” and “comprises,” are not intended to exclude other additives, components, integers or steps. The terms “a,” “an,” and “the” and similar referents used herein are to be construed to cover both the singular and the plural unless their usage in context indicates otherwise.
In the present game, each face of the game comprises a puzzle solvable using the rules of Sudoku games, typically using traditional Sudoku rules. As in traditional Sudoku, a face of the present game comprises N regions with each region having N rows of N cells each and N columns of N cells each, with N being a number greater than 1. Typically, N is 4 or 9, though other values are possible, and the square root of N is typically a whole number. Game play using this configuration of cells under traditional Sudoku rules is as follows:
1. A single, different symbol from a group of N non-repeating symbols (usually an ordered series of numbers) must be assigned to each cell in each row of the face;
2. A different symbol from the same group of N non-repeating symbols must be assigned to each cell in each column of the face; and
3. A different symbol from a group of N non-repeating symbols must be assigned to each cell in each region of the face.
In view of these rules, duplicate symbols are not permitted in any column, any row, or any region of a face. Each face will comprise one or more symbols which are pre-assigned to cells on that face (following the rules above) prior to the start of game play by a user, and typically each region will comprise one or more symbols which are pre-assigned to cells of that region of the face.
In addition to the foregoing rules, additional rules apply to adjacent cells 40 on different faces of the present game 1. In particular, cells 40 on different faces 10 of the present game 1 which are adjacent to each other must be the same. The present game 1 comprises a plurality of faces 10 which are arranged such that each side of a face 10 borders a side of another face of the game at an edge 4. Each cell on a first face which has a side on that edge is adjacent to a cell on the second face which has a side on that edge, and such adjacent cells on the first and second face (i.e., on faces whose sides share a common border or edge 4) must hold the same symbol. An example of this rule is demonstrated for example in
A corollary of this rule is that when more than two cells 40 are adjacent to each other, the same symbol must be assigned to all such adjacent cells. This occurs at corners, such as the corner 6 formed in
In alternative embodiments, the present game can employ rules used in variants of a traditional Sudoku game. For example, in the variant known as “Greater Than Sudoku,” cells are filled with an ordered series of symbols (usually numbers), and a relationship between the symbols in adjacent cells is specified with respect to which of the symbols can be greater than the other (i.e., appearing later in the ordered series of symbols). The relationship between such adjacent cells is usually specified graphically with symbols such as “>” or “<.” Traditional Sudoku rules as well as the additional rules for the present game specified above also apply when such variant games are played.
The present game 1 can exist in a variety of forms, e.g. in physical or virtual form, and can also comprise a variety of shapes. The game is played on the surfaces (faces) of a polyhedron, such as a cube. Preferably, all surfaces of the game can be viewed by a player of the present game, either by physical manipulation of a game embodied in a physical object or by manipulation of a virtual object displayed on a screen. However, in some embodiments only a subset of the faces of a polyhedron on which the present game is played are viewed by a player.
The cells 40 of the present game 1 retain symbols, such as numbers, which can be in physical or virtual form. In physical embodiments of the present game the cells 40 comprise a physical space, while in electronically enabled embodiments cells will generally comprise a visually displayed area (such as an area displayed on a monitor or touch screen). Cells generally have four contiguous sides and are typically square in configuration, as shown e.g. in
The side 41 of a cell 40 of the present game 1 is used as a referent, to indicate an association between the cell and another cell of the game. A side 41 of one cell 40 which is associated with another side of a second cell is described herein as being adjacent to the second cell. In the illustrated embodiments, this association is usually depicted by a shared boundary between a first cell and second cell. For example, in the embodiment shown in
In the present game, cells 40 typically have four sides 41, and for ease of depiction are illustrated as a four-sided planar shape, generally a square. The four sides 41 of a cell 40 in such embodiments are termed herein the top side 43, bottom side 44 (positioned opposite the top side 43), right side 45, and left side 46 (positioned opposite the right side 45), as illustrated in
Each face 10 of the present game 1 is in the form a polygon whose outer periphery is composed of a finite sequence of line segments, i.e. sides 20. Faces 10 of the present game 1 are typically planar and in the form of a square or other parallelogram.
The present game 1 can be embodied in a number of different forms, but most commonly will comprise either a three dimensional physical object or an image of such an object generated by a computer program. In one embodiment, the faces of the game are formed from a substrate, such as paper, cardboard, or plastic, which is sufficiently rigid to be able to form a polyhedron on which the present game can be played. In this embodiment, the cells and pre-assigned numbers or other symbols of the game are preferably printed onto the substrate. The substrate can for example be planar and can be initially formed as a blank, after which it is folded into a cube or other shape for game play. Alternatively, the game can be formed from a material that is molded into a desired polyhedral shape.
An embodiment of the present game 1 in physical form is illustrated in
Alternatively, the present game 1 can be implemented in electronic form by a computer or other electronic device capable of generating a visual display comprising the present game 1. In this embodiment, the game can be embodied in instructions contained in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer or other processor-containing system that can execute the instructions. In this embodiment, the game is preferably rendered in a three-dimensional manner (even though the display screen itself may only be capable of displaying a flat or two-dimensional image). Such an image can also preferably be rotated or maneuvered in three dimensions, i.e. such that all the faces of the present three-dimensional game can be visualized.
In one embodiment, the present game 1 is presented and solved using a mobile communications device, such as a mobile phone. Mobile communications devices have wireless data transmission and reception functionality (typically using radio frequencies to send and receive data) and a user input device, such as a keypad or a touch screen. The data transfer capability allows a mobile device to receive new puzzles, for example after previously received puzzles are solved by a user. In preferred embodiments the input device is a touch screen, a display that enables the user to interact with the mobile communications device by touching areas on the screen.
In another embodiment, the present game can be illustrated or displayed in two dimensional form, either on paper or on a display screen. In this embodiment, the game is solved by applying the rules of the present game only to the displayed faces, and can resemble for example the faces shown in
As described above, each face of the present game 1 comprises a matrix of rows and columns determined by the size of the puzzle. For purposes of the following discussion, the cells of the rows and columns of each face are numbered from 1 to a number N. As shown in
As is common in a variety of programming languages, in a preferred embodiment of the puzzle generation process the cells of the matrix of cells are just pointers to the memory locations for individual cells. Cells can be referred to in many programming languages as “objects,” and this “pointer to an object” concept can be used in the next step 104.
In the second step of
During remapping, some cells are forced to be mapped in reverse order (N−1) so it is important to understand the direction in which the cells are described. Given the layout of faces described above, e.g., in connection with
When considering each edge, in addition to the order that the cells appear on the edge, once the faces are wrapped around the cube, some edges are inverted in relation to edges on other faces that they line up with. For example, the right side 25 of the top face 13 maps to the top side 23 of the right face 15, however cell number 1 of the right face 15 is cell N of the top face 13, so careful consideration must be given to the direction of each mapping. As this mapping is used to change the pointers in the matrix to point to common memory locations, care must be given to map these cells in a particular order to ensure all pointers are properly accounted for in the mapping.
Table 1 below illustrates the order that each edge should be mapped to ensure that no cell pointers are lost. When this mapping is complete the number of cells considered in a nine-by-nine game is reduced from four hundred eighty-six cells to three hundred eighty-six by overlapping the common edges and corners. Likewise, when generating a four-by-four game, the number of cells considered is reduced from ninety-six cells to fifty-six.
Step 106 of
Solving Sudoku puzzles preferably involves reducing the number of valid choices that there may be for any given cell. In the present process, a list of valid choices for each cell 40 is maintained, and whenever a value is selected for a cell, any other cell in the puzzle that is affected by this selection will have that value removed from its list of valid choices. In step 106, it is advantageous to select a cell from the face in the game with the most open cells (i.e. cells that do not yet have only a single valid choice), and to select on this face the cells having the fewest number of valid choices. In order to accomplish this, it is first necessary to create a list of cells that have the least number of valid choices. If ten cells all have only two numbers as valid selections and no cells have one number as a valid selection then a random cell will be selected from these ten cells with two valid choices.
In the beginning of the process, all cells will have N valid choices, so a random cell is chosen and set to a random value, as described in step 108. In step 110, the value chosen needs to be removed from all cells that are in the same row, column and region as the selected cell. If the cell is on an edge or corner, then any rows, columns and regions on other faces need to be updated, since adjacent cells must comprise the same value, pursuant to the rules of the present game 1. This value is therefore also removed from the list of possible values available to cells that are in the same row, column and region as such adjacent cells.
In step 112, exclusive choices are processed, i.e. remaining cells for which there is only one valid choice are identified. An exclusive choice is an artifact of the way the puzzle is solved, and minimizes the number of random choices the computer will make in coming up with a solution. The first time through the game generation loop no exclusive choices will be found, but it is important to put this step into the process so that exclusive choices can be accounted for.
To identify exclusive choices, each face in the game is preferably processed sequentially, and the validity of each number or other symbol used in the game is tested in each remaining cell (i.e. each cell to which a symbol has not yet been assigned) to see if the cell can be identified as one that has a single valid choice. If one is identified, then it is processed as in step 110 to assign the single valid value to this cell and then remove this value as a valid choice from all concerned cells in the puzzle.
Once cells with only a single valid choice of symbols are removed from the puzzle, the process returns to step 106. Once there are no remaining cells to be solved, the puzzle is checked for validity by applying the Sudoku rules to every row, column and region in the puzzle. If the puzzle is not valid for any reason, then the process is repeated until a valid puzzle is generated.
In step 116, the final step of generating the three dimensional Sudoku puzzle, any cells that were randomly generated in creating the puzzle are retained, i.e. are shown in the puzzle, and all of the cells whose values are set pursuant to the rules of the present game are discarded or hidden from view and are thus not visible to a user of the present game 1. This step generates a puzzle to be solved by such a user which has only one solution.
Although the present invention has been described in considerable detail with reference to certain preferred embodiments, other embodiments are possible. The steps disclosed for the present methods, for example, are not intended to be limiting nor are they intended to indicate that each step is necessarily essential to the method, but instead are exemplary steps only. Therefore, the scope of the appended claims should not be limited to the description of preferred embodiments contained in this disclosure. All references cited herein are incorporated by reference in their entirety.
The present application claims the benefit of priority from U.S. Provisional Patent Application No. 61/232,419, filed Aug. 8, 2009 and entitled THREE DIMENSIONAL SUDOKU CUBE PUZZLE, the entire disclosure of which is hereby incorporated by reference in its entirety.
Number | Date | Country | |
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61232419 | Aug 2009 | US |