Polycube Games, Systems, and Methods

Abstract

Polycube-based puzzles are disclosed. Three-dimensional Sudoku-like puzzles using polycubes of various sizes and dimensions, where the cubes making up each polycube have visually identifiable features on all sides such that sets of polycubes can be created to facilitate the Sudoku-like puzzle game. Polycube-based puzzles using sets of polycubes arranged in different configurations where each side of a resulting combination of a set of polycubes has no repeated visual identifier.

Claims

1. A puzzle, comprising: a set of polycubes, wherein each polycube of the set of polycubes has a defined shape; wherein each polycube of the set of polycubes comprises a set of cubes, and wherein each cube of the set of cubes has a unique visually identifiable attribute on all exterior sides; and wherein the set of polycubes are arranged together to create a larger polycube such that the larger polycube does not repeat any of the visually identifiable attributes on a given side.

2. The puzzle of claim 1, wherein the visually identifiable attribute is at least one of a color, a shape, and a symbol.

3. The puzzle of claim 1, wherein the unique visually identifiable attribute is selected from a set of at least three unique visually identifiable attributes.

4. A puzzle, comprising: a set of polycubes, wherein each polycube of the set of polycubes has a defined shape; wherein each polycube of the set of polycubes comprises a set of cubes, and wherein each cube of the set of cubes is has a unique visually identifiable attribute on all exterior sides; and wherein the set of polycubes are arranged together to create a larger polycube such that the larger polycube does not repeat any of the visually identifiable attributes on any row or column of a side of the larger polycube.

5. The puzzle of claim 4, wherein the unique visually identifiable attribute is selected from a set of at least three unique visually identifiable attributes.

6. The puzzle of claim 4, wherein the visually identifiable attribute is at least one of a color, a shape, and a symbol.

7. The puzzle of claim 4, wherein the larger polycube is a cubic polycube.

8. The puzzle of claim 4, wherein the set of polycubes comprise a Soma Cube puzzle.

9. The puzzle of claim 4, wherein each polycube of the set of polycubes is a cubic polycube, and wherein the larger polycube is arranged as a square.

10. The puzzle of claim 9, wherein each cubic polycube comprises eight cubes.

11. The puzzle of claim 9, wherein each cubic polycube comprises four pairs of cubes, wherein each pair of cubes have the same unique visually identifiable attribute on all exterior sides.

12. The puzzle of claim 11, wherein each side of the cubic polycube comprises cubes having different unique visually identifiable attributes.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0024] FIG. 1 shows a T-shaped polycube.

[0025] FIG. 2 shows a Sudoku-like pattern formed by four polycubes put together.

[0026] FIG. 3 shows an exploded view of a polycube

[0027] FIG. 4 shows another T-shaped polycube.

[0028] FIG. 5 shows an exploded view of four polycubes.

[0029] FIG. 6 shows an L-shaped polycube.

[0030] FIG. 7 shows a cubic polycube.

[0031] FIG. 8 shows a variety of different polycube configurations.

[0032] FIG. 9 shows a cubic polycube comprised of the polycubes shown in FIG. 8.

DETAILED DESCRIPTION

[0033] The following discussion provides example embodiments of the inventive subject matter. Although each embodiment represents a single combination of inventive elements, the inventive subject matter is considered to include all possible combinations of the disclosed elements. Thus, if one embodiment comprises elements A, B, and C, and a second embodiment comprises elements B and D, then the inventive subject matter is also considered to include other remaining combinations of A, B, C, or D, even if not explicitly disclosed.

[0034] As used in the description in this application and throughout the claims that follow, the meaning of “a,” “an,” and “the” includes plural reference unless the context clearly dictates otherwise. Also, as used in the description in this application, the meaning of “in” includes “in” and “on” unless the context clearly dictates otherwise.

[0035] Also, as used in this application, and unless the context dictates otherwise, the term “coupled to” is intended to include both direct coupling (in which two elements that are coupled to each other contact each other) and indirect coupling (in which at least one additional element is located between the two elements). Therefore, the terms “coupled to” and “coupled with” are used synonymously.

[0036] In some embodiments, the numbers expressing quantities of ingredients, properties such as concentration, reaction conditions, and so forth, used to describe and claim certain embodiments of the invention are to be understood as being modified in some instances by the term “about.” Accordingly, in some embodiments, the numerical parameters set forth in the written description and attached claims are approximations that can vary depending upon the desired properties sought to be obtained by a particular embodiment. In some embodiments, the numerical parameters should be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. Notwithstanding that the numerical ranges and parameters setting forth the broad scope of some embodiments of the invention are approximations, the numerical values set forth in the specific examples are reported as precisely as practicable. The numerical values presented in some embodiments of the invention may contain certain errors necessarily resulting from the standard deviation found in their respective testing measurements. Moreover, and unless the context dictates the contrary, all ranges set forth in this application should be interpreted as being inclusive of their endpoints and open-ended ranges should be interpreted to include only commercially practical values. Similarly, all lists of values should be considered as inclusive of intermediate values unless the context indicates the contrary.

[0037] A polycube is a solid figure formed by joining one or more equal cubes face to face, as seen in FIG. 4. Polycubes can take on many different shapes, depending on the number of cubes within the polycube. Polycubes of the inventive subject matter can include 3, 4, 5, 6, 7, 8, or 27 cubes. This application describes a specific type of polycube that was designed for Sudoku-like puzzles.

[0038] One application of the inventive subject matter is a Sudoku-like puzzle based on polycubes that have a unique property. Each of the cubes within the polycube has a unique attribute (e.g., the same color, symbol, or sets of colors and symbols on each of its exterior sides). The cubes, e.g., cubes 101, 102, 103, and 104 of polycube 100 cannot be twisted or repositioned, and the cubes of a polycube always have the same relative position to the other cubes of the same polycube.

[0039] In an embodiment of the inventive subject matter, a polycube can be rotated or flipped in three dimensions, allowing the user to position it however they like in their attempt to solve a puzzle. The set of cubes within the a polycube can include three or more visual identifiers (e.g., colors, symbols, or shapes). In these embodiments, the goal of the puzzle is to assemble the polycubes so that each visual identifier appears no more than once in each row or each column, as seen in FIG. 2.

[0040] As seen in FIG. 3, polycubes are assembled by using a set of cubes 301, 302, 303 and 304, where each side of the cube is the same (e.g., the same color, symbol, feature, character, etc.). To create a polycube as seen in FIG. 1, cubes 301, 302, 303 and 304 are connected together into a solid block or polycube, where the cubes are fixedly aligned to each other. All neighboring cubes should be fully aligned so that they are orthogonal to each other, with each cube completely covering the sides of its neighboring cubes that are closest to it.

[0041] The inventive subject matter lends itself to several puzzles that can be made using a set of Polycubes. For example, a Tetracube is a Polycube comprising four cubes. One possible shape of Tetracube is a T, as seen in FIG. 4. If each of the four cubes in the T-shaped polycube are different colors, there are 12 distinct blocks that can be created. Four such T-shaped polycubes can be arranged as seen in FIG. 5, and placed so that each color appears once in every row and once in every column, as seen in FIG. 2.

[0042] Another possible shape of Tetracube is an L, as seen in FIG. 6. If each of the four cubes in the L-shaped polycube are different colors, there are 24 distinct versions that can be created. It can be challenging to find a way to arrange those Tetracubes into a 4×4×4 arrangement where each color appears once in every row and once in every column on each of the 6 sides of the resulting cube. The remaining eight pieces can then be placed in two separate 4×4×1 arrangements where each color appears only once in every row and column (similar to a Sudoku puzzle where a number cannot be repeated in a row or column).

[0043] In one embodiment of the inventive subject matter, polycube blocks are in the shape of a cube (e.g., 2×2×2, 3×3×3, or 4×4×4). From herein we may refer to that shape as a Cubic Polycube, to differentiate it from the subcubes which are its components. A 2×2×2 Cubic Polycube having eight total cubes using four different colors is seen in FIG. 7. The cubes of the polycube in FIG. 7 come in four different colors, with two cubes of each color. A 2×2×2 cubic polycube can be created by following these steps: (1) place one of each color in a 2×2×1 polycube, and (2) above each cube of the polycube, place the second cube that shares the same color (3) then switch each cube on the top row with the one that is diagonal to it. The resulting pattern can be seen in FIG. 7.

[0044] Thus, when the 2×2×2 cubic polycube as seen in FIG. 7 is completed, each colored cube within the polycube is diametrically opposite its corresponding colored cube in the polycube. Every cube within the polycube in FIG. 7 has three neighboring cubes that are orthogonal to it, and 3 more cubes that are diagonal to it. There is only one cube that it doesn't share a side with, and that is its corresponding color on the diametrically opposite corner. For example, cube 702 is diametrically opposite to cube 705, cube 703 is diametrically opposite to cube 704, and cube 701 is diametrically opposed to cube 706.

[0045] The resulting polycube is a 2×2×2 cubic polycube where each of the four colors appear once on every side as seen in FIG. 7, with each side having a unique arrangement of colors. Since a cube has six sides, and each side can be rotated four different ways, the Cube allows 24 distinct ways to position the four colors. Thus, no matter how a user wants to position the four colors, this 2×2×2 cubic polycube has a side that can be rotated into a desired position.

[0046] For such a puzzle to be solvable, the colors of each cube within a polycube must be properly chosen. In general, any N×N number of cubic polycubes should use 2*N distinct colors, where N is greater than two. Divide the 2*N colors into two teams, with N colors in each team. Assign an order to each of the colors in both teams. Each of the colors in each team should be placed into two pairs. One pair should be with the color that comes after it in the ordering, and one pair should be with the color that comes before it in the ordering. Each Cubic Polycube then takes one pair from each team. As each cubic polycube in a set of N×N polycubes for this type of puzzle should be different from one another, each Cubic Polycube should take a different a different combination of pairs.

[0047] For example, if there are 16 blocks and eight colors, we can label the colors on one team 1, 2, 3, 4 and the colors on the other team A, B, C, and D. The four pairs from the first team will be (1,2), (2,3), (3,4), (4,1), and the four pairs from the second team will be (A,B), (B,C), (C,D), (D,A). The resulting colors for the Cubic Polycubes will then be AB12, AB23, AB34, AB41, BC12, BC23, BC34, BC41, CD12, CD23, CD34, CD41, DA12, DA23, DA34, and DA41.

[0048] When there are 16 cubic polycubes to be formed into a 4×4 grid having 8 colors, there is an alternate method to choose the colors of the blocks which gives the same results. The colors are grouped into four pairs, where each cube chooses only one color from each pair. If the 8 colors are labeled 1, 2, 3, 4, A, B, C, D and the pairs are (A,C), (B,D), (1,3), and (2,4) it will produce the same 16 Cubic Polycubes.

[0049] In some embodiments, the puzzle could include nine cubic polycubes and six colors, 16 cubic polycubes and 8 colors, 25 cubic polycubes and 10 colors, and 36 cubic polycubes with 12 colors. Each of the above can also be formed into three-dimensional cube puzzles by adding multiple copies of the same cubic polycubes. For example, if you take 3 complete sets of the 9 cubic polycubes, you can place the 27 cubic polycubes into a 3×3×3 box that forms a Sudoku-like pattern on every side.

[0050] Another version of the puzzle involves 9 cubic polycubes and 9 colors, where each cubic polycube is a 3×3×3 of color cubes. The cubic polycubes must be designed so that no color appears more than once on each side. There are different configuration that can assure that property, with some of them leading to harder puzzles. In the harder version of the puzzle, for each of the 9 cubic polycubes, the center cube of each of the six sides is a different color. In an easier version, every cubic polycube has the same color in the center of each of its six sides.

[0051] In another embodiment, a version of the puzzle involves 4 cubic polycubes and 6 colors, where each cubic polycubes is a 3×3×3 polycube with six distinct colors on each side, and no color appearing more than once in any row of column. There is also a three-dimensional version with 8 cubic polycubes that are 3×3×3×3 and contain 6 colors. The solution requires placing the 8 cubic polycubes into a 2×2×2 box, with each side forming a Sudoku-like pattern on the colors.

[0052] In another embodiment, a puzzle has 8 cubic polycubes with 4 colors and 4 symbols, where each cubic polycube is a 2×2×2 with the properties described above. For each cubic polycube, every color is paired with a different symbol, so that every appearance of the color on the cube will also have that symbol. Every side of every cubic polycube has all 4 colors and all 4 symbols, but each of the 8 cubes will have somewhat different pairings between the colors and symbols. For instance, if one cubic polycube has A1, B2, C3, D4, the next cubic polycube may have A1, B4, C3, D2, where 1, 2, 3, 4 represent colors and A, B, C, D represent symbols. The goal of the puzzle is to assemble the 8 Cubes into a 2×2×2, so that for all 6 sides, each color and each symbol appears only once in each row and once in each column.

[0053] The Soma Cube is a solid dissection puzzle invented by Piet Hein. The present invention allows one to make variant of the Soma Cube called “Soma Sudoku” that can be more challenging for experienced puzzle solvers. It involves giving each of the cubes in the polycubes of the Soma pieces one of 3 colors, and requiring the solved Cube to have a Sudoku-like patterns on every row and column of every side. An example of the Soma Sudoku pieces can be seen in FIG. 8, and the solved cube can be seen in FIG. 9. There are 240 distinct solutions of the classic Soma cube puzzle. There is only one pattern that can support a solution to the Soma Sudoku, but there are four ways to position it. Therefore, for each of the 240 Soma solutions there are 4 ways to color the 26 exterior cubes so that each of the 6 sides of the solved cube form a Sudoku-like pattern where each of the three colors appear once on every row and once on every column. There will be 9 cubes with the first color, 9 cubes with the second color, and 8 cubes of the third color. It is recommended to give the interior cube of the solved puzzle that third color, so that people can't analyze the color distribution to know the color of the interior cube.

[0054] The exterior 26 cubes of a solved Soma Cube can also be assigned 9 colors such that each color appears only once on each side. There will be 8 colors that have 3 cubes each, and one color that only appears twice. It is recommended to assign that color to the one interior cube, so that each of the 9 colors appear on an equal number of cubes.

[0055] Other dissection puzzles include Diabolical Cube, and Bruce Bedlam's Bedlam Cube. All such puzzles can be used to create new puzzles by assigning a color to each of the cubes of the polycubes of the pieces, similar to the manner described above with the Soma Cube.

[0056] Thus, specific compositions and methods of polycube games have been disclosed. It should be apparent, however, to those skilled in the art that many more modifications besides those already described are possible without departing from the inventive concepts in this application. The inventive subject matter, therefore, is not to be restricted except in the spirit of the disclosure. Moreover, in interpreting the disclosure all terms should be interpreted in the broadest possible manner consistent with the context. In particular the terms “comprises” and “comprising” should be interpreted as referring to the elements, components, or steps in a non-exclusive manner, indicating that the referenced elements, components, or steps can be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced.