Puzzle cuboid

Abstract

A cubic puzzle assembled from a number of separable component pieces is disclosed. Each of the component pieces can be made of one, two or more cubes linearly arranged. Component patterns are provided on at least some of the six sides of a component piece so that when all component pieces are assembled into a single bigger cube, the component patterns on the sides of the component pieces form at least one combined pattern, but preferably, five or six different combined patterns on five or six faces of the bigger cube. In some embodiments, there are two or more correct combinations for a player to assemble the component pieces into the puzzle. The combined patterns preferably are easily recognizable, such as photographs, images of animals, likeness of a subject or landscape and the like.

Description

FIELD OF THE INVENTION

The present invention relates generally to a puzzle made up of many component pieces and, in particular, to a puzzle in a cube form with six faces having thereon six different patterns or images.

BACKGROUND OF THE INVENTION

A puzzle can be made up of many loose pieces. When all the loose pieces are assembled together, they form a cube or a ball, for example. Depending on the design of the loose pieces, the assembly can be very easy or very difficult. Such puzzles are always a fascination to a child as well as an adult.

SUMMARY OF THE INVENTION

The present invention provides a cubic puzzle assembled from a number of separable component pieces. Each of the component pieces can be made of one or two cubes, or three or more cubes linearly arranged. Each of the component pieces has six sides. Component patterns are provided on at least some of the six sides so that when all component pieces are assembled into a single puzzle cube, the component patterns on the sides of the component pieces form a number of different combined patterns on five or six faces of the puzzle cube. According to the present invention, there may be two or more correct ways or combinations to assemble the component pieces into a single cube so that the single cube assembled in each correct combination shows a different set of combined patterns on its faces. The combined patterns preferably are easily recognizable, such as photographs, images or likeness of animals, landscapes, human faces or the like.

Thus, the first aspect of the present invention is a puzzle which comprises:

a plurality of component pieces, each separable from another, wherein each of said plurality of component pieces is made up of one or more cubes such that each component piece has six sides, each side bound by four straight lines, wherein at least two of the sides are square sides, wherein the sides of the component pieces are provided with a plurality of component patterns, such that when all of the component pieces are assembled into one single body with eight vertices, twelve edges and six faces of equal area, the component patterns provided on the sides of the component pieces are arranged to form at least one combined pattern on at least one of the faces.

According to an embodiment of the present invention, when all of the component pieces are assembled into said one single body, each of the component pieces has at least three adjacent other component pieces, and when two of the component pieces are adjacent to one another, at least part of one of the six sides of one of said two component pieces is arranged to face at least part of one of the six sides of another of said two component pieces.

According to an embodiment of the present invention, the component patterns are provided on at least some of the six sides of some of the component pieces, such that when all of the component pieces are assembled in one of a plurality of combinations into said one single body, the component patterns provided on the sides of at least some of the component pieces are arranged to form a number of combined patterns.

According to an embodiment of the present invention, the component patterns are provided on at least some of the six sides of some of the component pieces, such that when all of the component pieces are assembled in one of a plurality of combinations into said one single body, the component patterns provided on at least some of the component pieces are arranged to form a number of different combined patterns, and each one of said different combined patterns is arranged to appear solely on one of the six faces. The plurality of combinations can be four different combinations.

According to an embodiment of the present invention, when all of the component pieces are assembled into said one single body, eight of the component pieces are arranged to locate at the eight vertices of said one single body, and three of the six sides of each of said eight of the component pieces arranged to appear on three of the six faces.

According to an embodiment of the present invention, at least some of the six sides of some of the component pieces on which the component patterns are provided include four of the six sides.

According to an embodiment of the present invention, at least some of the six sides of some of the component pieces on which the component patterns are provided have some portion of different images, from one to three images from a single puzzle solution and may include images from four different puzzle solutions.

According to an embodiment of the present invention, the number of different combined patterns is six.

According to an embodiment of the present invention, a puzzle can have at least two correct combinations, such that each of the different combined patterns as the result of a correct combination appears to be a predetermined design. The predetermined design is likeness of a subject or landscape, or an easily recognizable graphic pattern.

According to an embodiment of the present invention, each square side are bound by four straight lines of a unit length, and each of the twelve edges has an edge length substantially equal to three or more unit lengths, and the edge length is substantially equal to four unit lengths and said plurality of combinations includes four different combinations.

According to an embodiment of the present invention, each square side are bound by four straight lines of a unit length, and each of the twelve edges has an edge length substantially equal to three or more unit lengths, and the edge length is substantially equal to five unit lengths and said plurality of combinations includes at least four different combinations.

According to various embodiments of the present invention, some component pieces can be made up of one cube, some can be made up of two cubes, and some can be made up of three or more cubes in a linear arrangement.

According to an embodiment, the component pieces are configured to attract to each other with a magnetic material.

According to various embodiments of the present invention, each square side is bound by four straight lines of a unit length, and each of the twelve edges has an edge length substantially equal to three or more unit lengths, and the edge length is substantially equal to four or five unit lengths and said plurality of combinations includes four different combinations.

The second aspect of the present invention is a method for forming a puzzle, which comprises:

providing a plurality of component pieces, each separable from another, wherein each of said plurality of component pieces is made up of one or more cubes such that each component piece has six sides, each side bound by four straight lines, wherein at least two of the sides are square sides; and

providing a plurality of component patterns on at least some of the six sides of some of the component pieces, such that when all of the component pieces are assembled in one of a plurality of combinations into one single body with eight vertices, twelve edges and six faces of equal area, the component patterns provided on the sides of at least some of the component pieces are arranged to form a plurality of different combined patterns, and each one of each of the different combined patterns is arranged to appear solely on one of the six faces according to a predetermined design.

According to an embodiment of the present invention, at least some of the six sides of some of the component pieces include four of the six sides, and the plurality of different combined patterns include five different patterns.

According to an embodiment of the present invention, a magnetic material is provided in each of the component pieces so as to allow the component pieces to attract to each other.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows examples of component pieces.

FIG. 2 shows a 3×3×3 cuboid.

FIG. 3 shows a 4×4×4 cuboid.

FIG. 4 shows a 5×5×5 cuboid.

FIG. 5 shows examples of visible component pieces in a 5×5×5 puzzle cuboid.

FIG. 6a shows a plurality of component pieces for a puzzle, wherein some of the component pieces have been assembled.

FIG. 6b shows an exemplary puzzle cuboid completely assembled with three of the combined patterns visible.

FIG. 6c shows the same assembled puzzle cuboid having a different combined pattern visible.

DETAILED DESCRIPTION OF THE INVENTION

An aspect of the present invention is a puzzle assembled from a plurality of component pieces. The puzzle can be a cube that has six square faces; a rectangular prism that has four rectangular faces and two square faces; or a rectangular parallelepiped that has six rectangular faces.

In an embodiment of the present invention, the puzzle is in a cube form having six square faces of equal area and it can be referred to as a puzzle cuboid. The puzzle is made up of a plurality of component pieces. Each component piece can be a cube (single-cube piece), a two-cube piece, a three-cube piece, etc. (see FIG. 1). A cube is a smallest unit in a puzzle. All the cubes that make up a component piece are linearly arranged. Thus each component piece has six sides, each side bound by four straight lines, and at least two of the sides are square sides. A single-cube piece has six square sides. A two-cube piece has six sides, of which two are square in shape and four are rectangular. Each of the four rectangular sides has two squares. As disclosed herein, a square is the smallest surface that appears on a side of a component piece. The total number of visible squares on a two-cube piece is 10. A three-cube piece has six sides, of which two are square in shape and four are rectangular. Each of the four rectangular sides has three squares. The total number of visible squares on a three-cube piece is 14. Similarly, the total number of visible squares on a four-cube piece is 18. In general, the total number of visible squares on an n-cube piece is 2+4n.

In one embodiment of the present invention, all of the component pieces to be assembled into a puzzle are loose pieces such that each of the component pieces is separable from one other. When all of the component pieces are assembled into a single body, the single body is a bigger cube with eight vertices, twelve edges of equal length and six square faces of equal area. In general, there are a number of different combinations of the component pieces to form the single body. In any combination of which all the component pieces form a single body, any one of the component pieces must have a number of adjacent pieces, regardless where the component pieces are located. In a puzzle, some of the component pieces are located at the corner of the puzzle, some are located at the edges and some are located in the inner part of the faces (see FIG. 5). In some designs, some of the component pieces may be entirely located at the interior part of the puzzle and are completely invisible.

When two component pieces are placed adjacent to one another, at least part of one of six sides of one of the two component pieces is arranged to face at least part of one of the six sides of the another piece. As can be seen in FIG. 5, the component piece 19 is at least adjacent to the component pieces 11, 13, 17 and 18. As there are six different ways to place a component piece adjacent to another component piece, there are 36 different ways to place two component pieces next to each other. When putting three component pieces together, the possibilities increase to 6³ or 216. When putting ten component pieces together, the possibilities are 6¹⁰ or 60,466,176. In a 3×3×3 puzzle with 27 component pieces, there are 6²⁷ possibilities. In a 5×5×5 puzzle with 125 component pieces, there are 6¹²⁵ possibilities. These possibilities represent the search space or solution space in which solutions to the puzzle are sought.

In order to form a puzzle, at least some of the sides of a component piece are provided with a component pattern so that when all the component pieces are assembled into a single body in a correct combination, the component patterns that appear on a face of the single body form a combined pattern that is recognizable. In other words, if each of the combined patterns appears on a face is recognizable as a predetermined design, the puzzle is considered solved. A predetermined design can be as an image of a person, a photograph of animals or a scene, or a certain geometric pattern.

In a 3×3×3 puzzle as shown in FIG. 2, the puzzle or puzzle cuboid is made up of 27 individual cubes. Each cube has six squares (see FIG. 1), but the total number of visible squares on the six faces of the cuboid is 6×9 or 54. In each correct combination, the component patterns on the 9 squares on each face form a recognizable combined pattern. As shown below, a 3×3×3 cuboid may have 3 correct combinations to form 3 puzzles. However, because there is only one interior piece and six one-face pieces in a 3×3×3 stack, there are not enough sides that can be hidden in each puzzle. Thus, it may not be possible to have multiple puzzles or solutions in a 3×3×3 puzzle cuboid. A solution is a correct combination.

In a 4×4×4 puzzle as shown in FIG. 3, the puzzle is made up of 64 individual cubes. The total number of visible squares on the six faces of the cuboid is 6×16 or 96. A 4×4×4 puzzle cuboid is the smallest puzzle consisting of all single-cube pieces that can be configured for all image squares since each puzzle has eight interior pieces and twenty four one-face pieces that are adjacent to the eight interior pieces.

In a 5×5×5 puzzle as shown in FIG. 4, the puzzle is made up of 125 individual cubes. The total number of visible squares on the six faces of the cuboid is 6×15 or 150. As shown below, a 5×5×5 cuboid can have 4 or more correct combinations, depending on the number of the component pieces.

In one embodiment of the present invention, on some of the component pieces, at least four of the six sides are provided with four different component patterns, and three of these four sides must share at least one of the vertices. As such, when one of these component pieces is located at a corner of the single, assembled body, three of the different component patterns are visible to form part of a puzzle. The component patterns are chosen such that, in at least some of the combinations, the component patterns of the component pieces form at least five different combined patterns on five of the six faces, and each of the five different combined patterns is a predetermined design. The remaining sixth face can be blank or can be used to provide information about the puzzle, the logo, trademark and copyright and the like.

In one embodiment of the present invention, the combined patterns are photographs of different animals such as tiger, lion, zebra, elephant, cheetah and giraffe and the component patterns are different parts of those photographs. When the component pieces are assembled in a correct combination, six of the faces of the assembled body will separately show the tiger, the lion, the zebra, the elephant, the cheetah and the giraffe. With that correct combination, the puzzle is considered solved. In a puzzle with multiple solutions, a different set of photographs would appear on the six sides for each of the solutions.

It should be noted that, when all the component pieces are assembled into a big cube or cuboid 1, some component pieces are located at the corners of the big cube, some pieces are located at the edges, and some pieces are located in the inner part of the faces of the big cube. In the 5×5×5 cuboid as shown in FIG. 5, the component pieces are a mix of two-cube pieces and three-cube pieces (see FIG. 1). For illustration purposes only: the component pieces 11 and 17 are corner pieces; the component pieces 13, 14 and 18 are edge pieces; and the component pieces 12, 15, 16 and 19 are inner pieces. In a correct combination, only three sides of a corner pieces will have part of three different photographs, and only two sides of an edge piece has part of two different photographs. On an inner piece, only the visible side shows part of a photograph. Thus, there are still many unused sides on the component pieces. These unused sides can have different component patterns for making one or more puzzles. For example, photographs of six different animals such as cat, dog, rabbit, wolf, fox and pig can be divided into parts to be provided on the unused sides. When the component pieces are assembled in a different correct combination, six of the faces of the assembled body will separately show the cat, the dog, the rabbit, the wolf, the fox and the pig and another puzzle is considered solved.

FIG. 6a shows an example of a 5×5×5 puzzle with two-cube component pieces and three-cube component pieces, wherein some of the component pieces have been assembled into a partial cube. FIGS. 6b and 6c show two of the correct combinations or solutions in the same puzzle 1. In each correction combination, a set of different combined patterns will appear on different sides of the puzzle. In FIG. 6b, three of the combined patterns are photographs of a peacock, of a bear and of three horses. As can be seen in FIG. 6b, the combined pattern of the three horses is formed from twelve component patterns. In FIG. 6c, three of the combined patterns are photographs of a giraffe, of a lion and of three zebras.

As can be seen in FIGS. 6b and 6c, the assembled body of component pieces are arranged to have at least two different puzzles to be solved. In general, the assembled body can have a different number of puzzles to be solved, depending on the number of component pieces to be assembled into a single body. According to one embodiment of the present invention, a puzzle consists of a different image on a face of the cuboid, or six different images on six sides of the cuboid.

In a 4×4×4 puzzle made up of sixty four single-cubes as its component pieces, there are 64×6 or 384 squares on 64 cubes. The 4×4×4 cuboid has six faces, each of which has 4×4 or 16 squares. Thus, the cuboid has a total of 6×16 or 96 squares on its faces. Since each of the 64 cubes can be placed differently so that, out of 384 squares, only 96 squares appear on the faces of the cuboid. Thus, a 4×4×4 puzzle may accommodate 384/96 or 4 puzzles. A 4×4×4 puzzle can include component pieces of more than one cube. However, such a 4×4×4 puzzle may have only one solution.

A 5×5×5 puzzle may be made up of 125 cubes as its component pieces. However, it is possible to make two or more cubes into one component piece. For example, two cubes can be joined to make a two-cube piece, and three cubes can be joined to make a three-cube piece as shown in FIG. 1. In one embodiment of the present invention, a 5×5×5 puzzle is made up of 50 component pieces: 25 two-cube pieces and 25 three-cube pieces. It can be shown that, a 5×5×5 puzzle made up of 50 component pieces can accommodate 4 puzzles with 24 images. A 5×5×5 puzzle has six faces and each face has 5×5 or 25 squares. Thus, the cuboid has 6×25 squares on its faces. Since each of the two-cube pieces is made up of 2 individual cubes, the total number of individual cubes in the 25 two-cube pieces is 50. Likewise, each of the three-cube pieces is made up of 3 individual cubes, and the total number of individual cubes in the 25 three-cube pieces is 75. Thus, the total number of individual cubes in such a 5×5×5 puzzle cuboid is 50+75 or 125.

A two-cube piece has two ends of 1 square each and four sides of two squares each. Thus, a two-cube piece has a surface equal to (2+4×2) or 10 squares. Likewise, a three-cube piece has a surface equal to (2+4×3) or 14 squares. In the 50 component pieces, 25 two-cube pieces have a surface of 250 squares and 25 three-cube pieces have a surface of 350 squares. Thus, the 50 component pieces have a total surface of 250+350 or 600 squares. Since each of the 50 component pieces can be placed differently so that, out of the 600 squares, only 150 squares appear on the faces of the cuboid. This means that the 5×5×5 puzzle can accommodate 600/150 or 4 puzzles with 24 different images. These images are also referred in this disclosure as combined patterns.

There are two components in the design of a puzzle cuboid. The first component is to determine a solution set of the component pieces and the second component is to match the images to the sides.

If a cuboid is made up of only single-cube pieces, the stacking is simple and the solution set may consist of one solution. This is because all the single-cubes are identical and all orientations of a single-cube are indistinguishable from each other. For example, a 4×4×4 cuboid made up of 64 single cubes is a one piece, one orientation puzzle with just one solution. However, if the 4×4×4 cuboid is made up of 32 two-piece cubes, the stacking of these component pieces into a cube has many different configurations. Thus, the first design component is to determine the possible configurations in which 32 two-cube pieces can be arranged in a 4×4×4 cube. As each of the two-cube pieces may be placed in one of three orientations, this is a problem on the order of magnitude of 3³².

If a 5×5×5 cuboid is made up of 25 two-cube pieces and 25 three-cube pieces, the first design component is to determine the possible configurations in which these two types of component pieces can be arranged in a 5×5×5 cube. As a two-cube piece may be placed in one of three orientations and a three-cube piece may be placed in one of three orientations, this is a problem on the order of magnitude of 6⁵⁰. The calculation of the order of magnitude here is the magnitude of the search space.

The search in the search space to find possible solutions is a mathematical problem known to a mathematician, and is not part of the invention. The present invention is mainly concerned with selecting the possible solutions in the search space in order to form a puzzle. In particular, the present invention provides a puzzle with multiple solutions by choosing the types of component pieces and using multiple identifiable sets of images to create a number of separate puzzle solutions.

In the search in the search space to find possible solutions for the arrangements of 50 pieces in a 5×5×5 puzzle (25 two-cube pieces and 25 three-cube pieces), only about 10.5 billion possibilities have been considered. In the search, there is evidenced in that the four solutions, while not the same, are all very similar. They are all derived from the same section of the search space.

Of these 10.5 billion possibilities, 319 were considered viable solutions, having a workable number of end pieces, edge pieces and corner pieces in the solution. These 319 viable solutions were combined in all possible sets of four puzzle solutions to see if they met the criteria necessary to make a complete working puzzle solution. The present invention uses the following constraints on the puzzle:

• • Four solutions must have 50 face ends of two cube pieces and 50 face-ends of three-cube pieces.
  • Four solutions must have 100 face sides of two-cube pieces and 100 face sides of three-cube pieces.
  • Four solutions must have an equal number of blank, or no-face, pieces and two-face side edge pieces.

There may be seven different combinations of these 319 viable solutions which would produce a workable four-puzzle solution to one puzzle cuboid. The combination of solution number 318, solution number 122, solution number 7 and solution number 319 was selected. The working solution combination is as follows:

	Solution Number
	318	122	7	319	Total
	2 Cube Ends	14	11	14	11	50
	2 Cube Sides	48	50	54	48	200
	3 Cube Ends	13	14	10	13	50
	3 Cube Sides	75	75	72	78	300
	2 Cube Blank	10	10	12	10	42
	2 Cube Edges	12	10	8	12	42
	3 Cube Blank	18	21	18	21	78
	3 Cube Edges	18	21	21	18	78

Finally, all of the pieces must be assigned a face address, or none, in each of the four puzzles. Thus, each square on each of the 6 sides of each of the 50 component pieces is assigned a sub-square of each of the 24 images included in the four puzzles with six sides each.

It should be understood that how a search is carried out in the search space to come up with a puzzle is not part of the claimed invention. It is possible that there are many different ways to carry out a search and the search result may or may not be the same as that described herein. In particular, the search as shown above is only used to illustrate one of the ways to find possible solutions for a 5×5×5 puzzle with 25 two-cube pieces and 25 three-cube pieces. It may be possible to form a 5×5×5 puzzle with a different mix of component pieces.

The cuboids as shown in drawings are only used to show a few examples of the puzzle cuboids. Other puzzle cuboids are also possible. For example, a puzzle can be is 6×6×6 cube or larger. A 6×6×6 puzzle has a total of 316 individual cubes. However, it is possible to build a 6×6×6 puzzle from 108 two-cube pieces to have 5 puzzle solutions as shown below:

6sides×36 image squares/side=216image squares/puzzle

108 two-cube pieces with 10 squares/piece=1080 total squares

1080/216=5

The approximate solution or search space=3¹⁰⁸

Thus, in general, a puzzle can be an N×N×N cuboid made up of N³ individual cubes, with N being a positive integer greater than 1. However, some of the cuboids may have only one solution. Depending on the integer N, a component piece in a puzzle can be a single-cube piece, a two-cube piece, a three-cube pieces, etc. Each of the component pieces has six sides, each side bound by four straight lines, at least two of the sides are square sides. The component pieces may be placed differently to form a cuboid. In an assembled cube, some of the component pieces are located at the corners of the cuboid and they are referred to as corner component pieces. On a corner component piece, three of its six sides can be seen. Some of the component pieces are located on the edges of the cuboid and they are referred to as edge component pieces.

On an edge component piece, two of its six sides can be seen. Among the other component pieces, some are totally hidden from view and some have only one visible side (see FIG. 5). In order to form a puzzle, a component piece located at a corner of the cuboid must have three different component patterns on its sides and a component piece located at an edge must have two different component patterns on its sides. In order to form two puzzles, a component piece located at a corner of the cuboid must have at least four component patterns. Thus, in general, in a puzzle cuboid that has more than one puzzle to be solved, at least four of the six sides of some of the component pieces are provided with four different component patterns. As such, when all of the component pieces are assembled into a single body with eight vertices, six edges and six faces in a certain combination, the component patterns of the component pieces form at least five different combined patterns, each of which appears on each of at least five of the six faces. Each of the combined patterns can be an image of an animal, for example. Accordingly, the component patterns provided on the component pieces are part of the different images.

In an embodiment of the present invention, all the component pieces are separable from each other, wherein each of the component pieces is made up of one or more cubes in a linear arrangement such that each component piece has six rectangular sides and at least two of the rectangular sides are square, with each side being bound by four straight lines.

In one embodiment of the present invention, the component pieces can be held together with magnets or other holding forces for assembly purposes. Nevertheless, the component pieces are separable for one another.

To be a brain teaser, a puzzle will preferably have more than one solution. As disclosed above, an N×N×N puzzle or puzzle cuboid, with N being 4 or greater, may have four or more solutions or correct combinations for assembling all the component pieces into a single body. However, although a 2×2×2 or 3×3×3 puzzle cuboid may have only one solution, the assembly of the component pieces into a single body may also be appealing to some players. Furthermore, a puzzle cuboid, when assembled, will preferably have five or six combined patterns appear on its faces. Some players, especially those of very young age, may find a simple puzzle cuboid interesting. For example, a puzzle cuboid may have the combined pattern appearing on one or two of the six faces—with other faces being blank, for example.

It should be noted that the main aspect of the present invention is to provide a puzzle in a cube-form assembled from a number of separable component pieces. The mathematical analysis of the possible solutions, including the search in the search space, is only used to illustrate how the aspect of the present invention can be achieved. There may be different ways to search in the search space that would come up with the similar or different solutions. However, the mathematic analysis is not part of the claimed invention.

Thus, although the present invention has been described with respect to one or more embodiments thereof, it will be understood by those skilled in the art that the foregoing and various other changes, omissions and deviations in the form and detail thereof may be made without departing from the scope of this invention, which is defined by the description in the specification as well as the appended claims.

Claims

1. A puzzle comprising: a plurality of component pieces, each separable from another, wherein each of said plurality of component pieces is made up of one or more cubes such that each component piece has six sides, each side bound by only four straight lines, wherein at least two of the sides are square sides, wherein the sides of the component pieces are provided with a plurality of component patterns, such that when all of the component pieces are assembled into one single body with eight vertices, twelve edges and six faces of equal area, the component patterns provided on the sides of the component pieces are arranged to form at least one combined pattern on at least one of the faces.

2. The puzzle according to claim 1, wherein when all of the component pieces are assembled into said one single body, each of the component pieces has at least three adjacent other component pieces, and wherein when two of the component pieces are adjacent to one another, at least part of one of the six sides of one of said two component pieces is arranged to face at least part of one of the six sides of another of said two component pieces.

3. The puzzle according to claim 1, wherein the component patterns are provided on at least some of the six sides of some of the component pieces, such that when all of the component pieces are assembled in one of a plurality of combinations into said one single body, the component patterns provided on the sides of at least some of the component pieces are arranged to form a number of different combined patterns.

4. The puzzle according to claim 1, wherein the component patterns are provided on at least some of the six sides of some of the component pieces, such that when all of the component pieces are assembled in one of a plurality of combinations into said one single body, the component patterns provided on at least some of the component pieces are arranged to form a number of different combined patterns, and wherein each one of said different combined patterns is arranged to appear solely on one of the six faces.

5. The puzzle according to claim 4, wherein when all of the component pieces are assembled into said one single body eight of the component pieces are arranged to locate at the eight vertices of said one single body, and three of the six sides of each of said eight of the component pieces are arranged to appear on three of the six faces.

6. The puzzle according to claim 4, wherein said plurality of combinations includes four different combinations.

7. The puzzle according to claim 4, wherein said at least some of the six sides of some of the component pieces include four of the six sides.

8. The puzzle according to claim 7, wherein said number of different combined patterns is six.

9. The puzzle according to claim 4, wherein said plurality of combinations comprise at least two correct combinations, such that each of said different combined patterns appears to be a predetermined design.

10. The puzzle according to claim 9, wherein the predetermined design is likeness of a subject or a landscape.

11. The puzzle according to claim 9, wherein the predetermined design is a recognizable graphic pattern.

12. The puzzle according to claim 4, wherein each square side are bound by four straight lines of a unit length, and wherein each of the twelve edges has an edge length substantially equal to four unit lengths and said plurality of combinations includes four different combinations.

13. The puzzle according to claim 4, wherein each square side are bound by four straight lines of a unit length, and wherein each of the twelve edges has an edge length substantially equal to five unit lengths and said plurality of combinations includes at least four different combinations.

14. The puzzle according to claim 1, wherein each of at least some of the component pieces is made up of one cube.

15. The puzzle according to claim 1, wherein each of at least some of the component pieces is made up of two or more cubes.

16. The puzzle according to claim 1, wherein each of at least some of the component pieces is made up of two or more cubes in a linear arrangement such that, in said each of at least some of the component nieces, two and only two of the six sides are square sides.

17. The puzzle according to claim 1, wherein the component pieces are configured to attract to each other with a magnetic material.

18-20. (canceled)

21. The puzzle according to claim 1, wherein each square side is bound by four straight lines of a unit length, and each of the twelve edges is a straight line of N unit lengths and said plurality of component pieces comprise N×N×N component pieces, with N being a positive integer.

22. The puzzle according to claim 1, wherein some of said plurality of component pieces are made up of two cubes and some are made up of three cubes in a linear arrangement.

23. The puzzle according to claim 1, wherein each cube has six unit-square sides, and all of said plurality of component pieces are made up of two or more cubes in a linear arrangement such that each of said plurality of component pieces has two and only two unit-square sides.