WO2004004851A2

WO2004004851A2 - Multi-way puzzle

Info

Publication number: WO2004004851A2
Application number: PCT/GB2003/002841
Authority: WO
Inventors: Gavin Theobald
Original assignee: Gavin Theobald
Priority date: 2002-07-02
Filing date: 2003-07-01
Publication date: 2004-01-15
Also published as: GB2391821B; GB0315329D0; AU2003244826A1; WO2004004851A3; GB0215240D0; GB2391821A

Abstract

A jigsaw puzzle (10) having multiple solutions is described. In one embodiment, the puzzle has a set of pieces (11) that can be interconnected in a one arrangement to form a first image, and interconnected in a second distinct arrangement to form a second image on the reverse side of the pieces. Alternative embodiments are capable of being formed into three or more distinct arrangements, which may be of different shape. A method of forming the puzzles is also described.

Description

Multi -way puzzle

The present invention relates to the field of geometrical puzzles, and in particular to jigsaw puzzles having a variety of distinct arrangements.

The jigsaw puzzle has been popular for many years. The concept behind the jigsaw is simple and familiar, whilst puzzles of varying difficulty can be manufactured by adjusting the size and/or number of the pieces, or using images of differing degrees of complexity or repetition.

However, the traditional jigsaw is limited in complexity by the size of the completed puzzle, which must be small enough to assemble on a surface. In addition, the pieces must be large enough for a user to handle practically.

Thus there has been a need for jigsaw puzzles with increased difficulty of solution, whilst retaining the practicality of smaller puzzles.

Various double-sided jigsaws have been proposed in the past in order to provide an additional challenge to the user. Typically, this involves simply printing a second image on the reverse side of the first image. In this case, there is only one true arrangement of pieces whereby the puzzle is completed. That is, the puzzle has only one solution for both images.

An alternative puzzle is disclosed in US 5,368,301 to Mitchell. This arrangement is essentially a double-sided puzzle with two solutions: one for the image on the first side and one for the image on the second side. This puzzle is achieved by making almost all of the puzzle pieces congruent, thereby allowing the pieces to be interchangeable.

Although the puzzle of US 5,368,301 presents an increased challenge to the user, it has a number of drawbacks. Firstly, all of the pieces in the puzzle are identical, or have just two forms. This high degree of congruency results in many possible combinations of pieces being possible, presenting several different "non-solutions" to the user.

Additionally, the pieces in US 5,368,301 combine to form a solution with jagged edges. This arises as a result of the congruency of the pieces, and the fact that all edges of the pieces have connectors. The jagged edges of the resulting solutions are generally considered to be undesirable.

The triangular pieces of the puzzles in US 5,368,301 are either "left-handed" or "right-handed", again as a result of the congruency. This means that it will often be possible to determine which way up the pieces should face simply by their shape. It would therefore be desirable to provide a puzzle that obviates, or at least mitigates, some of the problems associated with the prior art.

It is one object of the invention to provide a puzzle that presents a greater challenge and/or stimulation to a user.

It is a further object of at least one embodiment of the invention to provide a double-sided puzzle with a distinct solution for each side.

It is a further object of the invention to provide a method of producing a multi-way puzzle.

Further objects and aims of the invention will become apparent from a reading of the following description.

According to the first aspect of the invention, there is provided a puzzle comprising: a plurality of pieces each having a first side and a second side, the first and second sides being provided with markings thereon, each piece comprising at least one engaging portion for allowing the piece to temporarily interlock with a corresponding engaging portion on an adjacent piece, the pieces being shaped such that they interlock in a first arrangement defining a first surface upon which the markings form a first image, and interlock in a second arrangement, distinct from the first, defining a second surface upon which the markings form a second image, wherein the pieces are formed in at least three different shapes. In this context, the term "shape" is intended to reflect the shape of the piece with connectors formed thereon. The basic form of all of the pieces may be the same; for example, the connectors may be formed on square pieces.

In addition, the term "image" should be construed broadly to cover photographs, drawings, patterns, labels, abstract shapes, and other graphical or artistic works including those generated by computer.

The first and second arrangements may comprise the same number of pieces .

The first and second arrangements may comprise exactly the same pieces.

The second arrangement may comprise a plurality of sub- arrangements, each forming a separate image.

The first arrangement may comprise a plurality of sub- arrangements, each forming a separate image.

The pieces may be shaped such that a third subset of the pieces interlock in a third arrangement, distinct from the first and second arrangements, defining a third surface upon which the markings form a third image.

The markings on a single piece may form part of any two of the first, second or third images.

Preferably, the markings on the first side of a piece form part of one of the images, and the markings on the second side of a piece form part of another of the images. The pieces may be shaped such that a fourth subset of the pieces interlock in a third arrangement, distinct from the first, second and third arrangements, defining a fourth surface upon which the markings form a fourth image .

The pieces may be shaped such that there are further subsets of pieces that interlock in further distinct arrangements, defining further surfaces upon which the markings form further images.

The first and/or second arrangements may be in the form of irregular polygons.

The first and/or second arrangements may be in the form of regular polygons.

The first and/or second arrangements may be in a form selected from the group consisting of: circles, triangles, rectangles, hexagons, octagons, dodecagons, and hexadecagons .

Preferably, the pieces include a first group of edge pieces forming a perimeter of one of the arrangements, and a second group of edge pieces forming a perimeter of another of the arrangements.

More preferably, the edge pieces form a smooth edge.

The first and second groups of edge pieces may share some of the pieces . The first and second groups may comprise the same number of edge pieces.

Alternatively, the second group may comprise fewer edge pieces than the first group, leaving a surplus of edge pieces.

Preferably, the surplus of edge pieces is used in the interior of the second arrangement.

According to a second aspect of the invention, there is provided a method of manufacturing a puzzle comprising the steps of: (i) defining a plurality of pieces, each having a first side and a second side; (ii) assigning each piece to a primary position in a primary arrangement and a secondary position in an secondary arrangement; (iii) allocating a first connector to a first piece, to later form an engaging portion; (iv) sequentially allocating additional connectors on each piece, the shape of the additional connectors being determined by connectors already formed on adjacent pieces in the primary and secondary arrangements.

Step (iv) of the method may comprise the sub-steps of: (a) allocating a second corresponding connector to a second piece, adjacent to the first piece when in its primary position, to later form an engaging portion for allowing the first and second pieces to temporarily interlock; (b) allocating a third corresponding connector to a third piece, said third piece being adjacent to the second piece when in its secondary position, to later form an engaging portion for allowing the second and third pieces to temporarily interlock in the secondary arrangement; (c) allocating a corresponding connector to a fourth piece, said fourth piece being adjacent to the third piece when in its primary arrangement, to later form an engaging portion for allowing the third and fourth pieces to temporarily interlock in the primary arrangement .

The method may comprise the additional steps of: (i) reiterating sub-steps (a) to (c) for subsequent pieces until a connector is formed with the first piece; (ϋ) selecting a further piece and repeating steps (iii) to (iv) until all pieces are connected; (iii) forming markings on the first and second sides of the pieces such that the pieces form images when arranged in their primary and secondary positions.

Preferably, the pieces form at least two images.

More preferably, the primary and/or secondary arrangements define two or more distinct image surfaces.

The method may include the additional step of: exchanging a pair of pieces and reallocating the connectors, starting from those connectors on the pair of pieces exchanged.

Preferably, some or all of the steps are carried out by a computer program.

The pieces of the puzzle may be cut by laser cutting techniques.

Alternatively, the pieces of the puzzle may be cut by die cutting.

According to a third aspect of the invention there is provided a method of manufacturing a puzzle comprising the steps of: (i) dividing a first image into a plurality of pieces defining a first arrangement; (ii) assigning each piece to a position in a second arrangement in the shape of a second image; (iii) allocating a first connector to a first piece, to later form an engaging portion; (iv) allocating a second corresponding connector to a second piece adjacent in the first image, to later form an engaging portion for allowing the two pieces to temporarily interlock; (v) allocating a third corresponding connector to a third piece, said third piece being adjacent to the second piece in the second arrangement, to later form an engaging portion for allowing the second and third pieces to temporarily interlock in the second arrangement; (vi) allocating a corresponding connector to a fourth piece adjacent to the third piece in the first arrangement, to later form an engaging portion for allowing the third and fourth pieces to temporarily interlock in the first arrangement; (vii) reiterating the steps (iv) to (vi) for subsequent pieces until a connector is formed with the first piece; (viii) selecting a second piece and repeating steps (iii) to (vii) until all pieces are connected; (ix) forming a second image in a rearranged configuration on the reverse side of the second arrangement.

According to a fourth aspect of the invention there is provided a puzzle manufactured by the method according to the second aspect.

According to a fifth aspect of the invention there is provided a puzzle comprising: a plurality of pieces each having a first side and a second side, the first and the second sides being provided with markings thereon, each piece comprising at least one engaging portion for allowing the piece to temporarily interlock with a corresponding engaging portion on an adjacent piece, the pieces being shaped such that a first subset of pieces interlock in a first arrangement such that the markings form a first image on a first surface, a second subset of the pieces interlock in a second arrangement, distinct from the first, such that the markings form a second image on a second surface, and a third subset of the pieces interlock in a third arrangement, distinct from the first and second, such that the markings form a third image on a third surface. The markings on a single piece may form part of any two of the first, second or third images.

The markings on the first side of a piece may form part of one of the images, and the markings on the second side of a piece form part of another of the images.

According to a sixth aspect of the invention there is provided a puzzle comprising: a plurality of pieces each having a first side and a second side, the first and the second sides being provided with markings thereon, each piece comprising at least one engaging portion for allowing the piece to temporarily interlock with a corresponding engaging portion on an adjacent piece, wherein the pieces are adapted to be arranged in three distinct arrangements, each arrangement forming an image.

According to a seventh aspect of the invention there is provided a puzzle comprising a plurality of pieces each piece comprising at least one engaging portion for allowing the piece to temporarily interlock with a corresponding engaging portion on an adjacent piece, the pieces being shaped such that they interlock in a first arrangement to form an image on a first surface, wherein the pieces include a first group of edge pieces forming a border of the first arrangement, and a majority of the edge pieces do not directly interconnect with adjacent edge pieces.

According to an eighth aspect of the invention there is provided a puzzle comprising: a plurality of pieces each having a first side and a second side, the first and the second sides being provided with markings thereon, each piece comprising at least one engaging portion for allowing the piece to temporarily interlock with a corresponding engaging portion on an adjacent piece, the pieces being shaped such that they interlock in a first arrangement such that the markings form a first image on the first side, and interlock in a second arrangement, distinct from the first, such that the markings form a second image on a second side, wherein the pieces are formed in at least three different shapes.

The first and second arrangements may comprise the same number of pieces.

The first and second arrangements may comprise exactly the same pieces.

Preferably, the pieces include a first group of edge pieces forming a border of the first arrangement, and a second group of edge pieces forming a border of the second arrangement. Most preferably, the edge pieces form a smooth edge.

The first and second groups of edge pieces may share some of the pieces .

In one embodiment, the second arrangement comprises a plurality of sub-arrangements, each forming a separate image. Alternatively, or in addition, the first arrangement may comprise a plurality of sub-arrangements, each forming a separate image.

The first and/or second arrangements may be in the form of irregular polygons. Alternatively, the first and/or second arrangements may be in the form of regular polygons .

The first and/or second arrangements may be in the form selected from the group consisting of circles, triangles, rectangles, hexagons, octagons, dodecagons, and hexadecagons, although this list is non-exhaustive.

The perimeters of the first and second arrangements may comprise the same number of edge pieces. Alternatively, the perimeter of the second arrangement may comprise fewer edge pieces. Conveniently, the surplus edge pieces may be used in the interior of the second arrangement.

According to a ninth aspect of the invention there is provided a method of manufacturing a puzzle comprising the steps of: (i) defining a plurality of pieces, each having a first side and a second side; (ii) assigning each piece to a primary position in a primary arrangement and a secondary position in a secondary arrangement; (iii) allocating a first connector to a first piece, to later form an engaging portion; (iv) allocating a second corresponding connector to a second piece, adjacent to the first piece when in its primary position, to later form an engaging portion for allowing the two pieces to temporarily interlock; (v) allocating a third corresponding connector to a third piece, said third piece being adjacent to the second piece when in its secondary position, to later form an engaging portion for allowing the second and third pieces to temporarily interlock in the secondary arrangement; (vi) allocating a corresponding connector to a fourth piece, said fourth piece being adjacent to the third piece when in its primary arrangement, to later form an engaging portion for allowing the third and fourth pieces to temporarily interlock in the primary arrangement; (vii) reiterating the steps (iv) to (vi) for subsequent pieces until a connector is formed with the first piece; (viii) selecting a second piece and repeating steps (iii) to (vii) until all pieces are connected (ix) forming markings on the first and second sides of the pieces such that when the pieces form images when arranged in their primary and secondary positions.

The pieces may form at least two images. The primary and/or secondary arrangements may comprise two or more distinct image surfaces.

The method may include the additional steps of: exchanging a pair of pieces and reallocating the connectors, starting from those connectors on the pair of pieces exchanged. Some or all of the steps may be carried out by a computer program.

The pieces of the puzzle may be cut by laser cutting techniques, or alternatively by die cutting.

There will now be described, by way of example only, various embodiments of the invention with reference to the following Figures, of which:

Figures la and lb show front and rear views of a puzzle in accordance with a first embodiment of the invention.

Figures 2a and 2b show front and rear views of the same puzzle, positioned in a second arrangement.

Figures 3a and 3b show an example of a two-way puzzle wherein the first and second arrangements have different shapes .

Figures 4a to 4j show an example puzzle at various stages of an example construction method.

Figures 5a and 5b show an example of a circular two-way puzzle in accordance with an embodiment of the invention.

Figures 6a and 6b show an example of a two-way puzzle in accordance with an embodiment of the invention, the puzzle having first and second solutions of different shapes.

Figures 7a to 7f show an example of a three-way puzzle arrangement in accordance with an embodiment of the invention. Figures 8a to 8f demonstrate the formation of odd and even cycles of connectors in an example three-way puzzle.

Figures 9a to 9f show an example of a complete three-way puzzle with a pair of odd cycles.

Figures 10a to lOf show the puzzle of Figures 9a to 9f after the odd cycles have been eliminated.

Figures 11a to lie show an example of a two-way puzzle, wherein one of the solutions comprises two sub- arrangements.

Figures 12a and 12b show a further example of two-way puzzle.

Figures 13a to 13f show an example of a three-way puzzle, wherein the pieces are diagonally cut.

Figures 14a to 14f show a further example of a three-way puzzle, with the three solutions being different shapes.

Figures 15a to 15f show the puzzle of Figures 7 to 10 with an alternative arrangement of connectors.

Figures 16a to 16h show an example of a four-way puzzle.

Figures 17a to 17i show the effect of exchanging two pieces on connection cycles.

Shown in Figure la is a puzzle, generally depicted at 10, comprising twelve pieces 11. On the front surface 14A of the puzzle, there is formed an image, in this case being the words "first image".

Each piece of the puzzle is planar, and comprises several connectors for forming engaging portions with corresponding connectors on adjacent pieces. Thus the pieces interlock to form a particular arrangement. Figure la shows the pieces arranged such that the puzzle is solved for the first image.

Figure lb shows the reverse side 14B of Figure la. Side 14B is also patterned, but the pieces do not form an image in this particular arrangement.

Figure 2a shows the same puzzle of Figures la and lb, arranged in an alternative manner. Figure 2a shows the rear surface 14B, with the pieces arranged such that the puzzle is solved for the second image (in this example simply the words "second picture".)

Arranging the pieces in the manner shown in Figure 2a rearranges the image on the first side 14A, to the pattern shown in Figure 2b.

Thus the puzzle has two distinct arrangements: one providing a solution for an image on a front side of the puzzle, and the other providing a solution for a second image on a rear side of the puzzle.

The above-described puzzle is a simple example of how the puzzle according to the invention may be embodied. However, the principles of the invention may be applied to provide many different puzzle arrangements. Figures 3a and 3b show a second embodiment of the invention having seventy-two pieces 11. The first arrangement, shown in Figure 3a, comprises pieces in a 8x9 pattern. The pieces are arranged such that a selected image (not shown) is displayed on the front surface 14A.

Figure 3b shows an alternative arrangement of the same seventy-two pieces as in Figure 3b. However, in this case, the pieces are arranged in a 6x12 pattern. The pieces fit together such that a second image (not shown) is formed on the rear surface of the puzzle.

Thus, once again, the puzzle has two distinct arrangements, each one providing a solution for an image on respective sides of the puzzle. However, in contrast to the puzzle of Figures 1 and 2, the two arrangements of Figure 3 have different shapes.

It will be noted that the different shapes result in a different number of perimeter pieces in each arrangement. Figure 3b shows that the 6x12 piece puzzle requires thirty-two edge pieces, whereas the 8x9 piece puzzle has only thirty edge pieces. In order to enable the same pieces to be used in each arrangement, it is necessary to "hide" two of the edge pieces within the 8x9 arrangement. This is achieved by abutting the edge pieces as shown at 16 in Figure 3a.

It will be evident that many more edge pieces may be "hidden" in this manner if required. For example, a 64 piece puzzle may be arranged as a 4x16 image and an 8x8 image. This would require eight edge pieces to be hidden within the 8x8 arrangement by abutting four pairs of edge pieces.

It may be desirable for the puzzle maker to "hide" additional edge pieces, even if the perimeters of the two arrangements do not require so doing. This may provide an additional challenge to the user.

There will now be described a method of manufacturing the puzzle. The following description will once again be a simple example of the technique, although it should be appreciated that the technique can be applied to the more complex examples described later.

The method is essentially an iterative process, involving the sequential formation of connectors on adjacent pieces. The first step is to select a first image, to be later placed onto a backing sheet with a shape suitable for that image. The image is then notionally divided into a number of pieces.

In the example shown in Figure 4a, there are 12 pieces in a 4x3 arrangement. Each piece is labelled A_miι where m is the number of rows, and n is the number of columns. The arrangement comprises 2 centre pieces and 10 edge pieces, of which 4 are corner pieces.

The next step is to assign the pieces to a second arrangement, as shown in Figure 4b. The second arrangement in this case has the same 12 pieces, although this time in a 3x4 grid. The pieces are interchanged, such that most are located in different positions in the first and second arrangements. In this example, the edge pieces remain as edge pieces although in different relative locations. However, their orientation is chosen such that the straight edges remain outward, and thus still define the edge of the puzzle. Similarly, the corner pieces of the first arrangement are located in the corners of the second arrangement, with their orientation selected appropriately.

Once each piece is assigned a location in a second arrangement, it is necessary to provide the pieces with connectors, such that engaging means can be formed between adjacent pieces.

Starting with piece A₀o, a connector is formed on the lower edge of the piece. As shown in Figure 4c, the connector in this example is chosen as a rounded protruding connector 41. Thus, adjacent piece Aχo must have a corresponding rounded recess 42 formed on its upper edge. This allows the pieces to temporarily interlock.

Referring to Figure 4d, the rounded recess 42 on the upper edge of piece Aι₀ requires that the adjacent piece Aoi in the second arrangement has a rounded protruding connector 43 on its left-hand edge. Switching back now to Figure 4c, the rounded protruding edge 43 on piece Aoi dictates that piece A₀o has a rounded recess on its right- hand edge .

Once again, the second arrangement requires that piece A₃χ has a rounded protruding connector on its right-hand edge, which consequently requires that A₃₂ (adjacent to A₃ι in Figure 4c) has a rounded recess on its left-hand edge. So the process is continued, with each connector on one piece dictating the shape of a corresponding connector on an adjacent piece in the second arrangement. By switching from one arrangement to the other, the cycle continues until it returns to the originally selected edge of the first piece, A₀o- Figures 4e and 4f show the connectors formed for a completed cycle. As can be seen from Figure 4f, the right-hand edge of piece oi requires that piece A₀o has a rounded protruding connector on its lower edge. This is consistent with the first selected connector 41, as shown in Figure 4c. Furthermore, this approach will always result in the formation of a final connector that is consistent with the first selected connector.

Subsequently, a second cycle is begun by forming a first connector on the lower edge of piece A₀₂. This is shown in Figure 4g as a protruding triangle 45. Switching back and forth from the first and second arrangements determines the shape of the remaining connectors for the edge pieces as shown in Figures 4g and 4h.

Referring to Figure 4i, a protruding square connector 46 is formed on the right-hand edge of piece Aι₀, resulting in a third cycle. Finally, a protruding trapezoidal connector 47 is formed on the right-hand edge of piece A₂o resulting in the fourth and last cycle. The completed arrangements are shown in Figures 4i and 4j .

It should be noted that although the above-described method uses four shapes of connectors, only one or two may be used. The Figures show circular, triangular, square and trapezoidal connectors for the purpose of clarity. However, in practice it is preferred to use connectors of more similar shape. For example, all of the connectors could be rounded, only with subtle differences to prevent too many mismatched pieces being interlocked. A further possibility is to have all the connector shapes the same, with subtle differences in positioning, to make the puzzle more difficult to solve.

The different shaped connectors shown in the Figures may be considered merely as labels for the type of connector used. Each label must match an adjacent label for interconnection to be possible.

Although the connectors are shown as separate, conjoined male and female connectors, they may in fact be of any suitable shape. For example, each connector may comprise a male part and a female part.

Once the form of the connectors has been determined, the first arrangement, shown in Figure 4i, is cut out into its separate pieces. Thereafter, the pieces are reassembled into the second arrangement of Figure 4j . The pieces are now mixed up so that the image formed on the surface of the pieces is not complete. This image corresponds to earlier Figure lb.

The second arrangement is then turned over, so that its (blank) reverse side is visible. A second image of suitable shape is then formed over the assembled pieces on the reverse side.

Thus, the above-described method results in the formation of the puzzle as shown in Figures la, lb, 2a and 2b. The method is applicable to significantly larger puzzles than those in the example shown, for example the puzzle illustrated in Figures 3a and 3b. It can be shown that the method will work for puzzles with any number of pieces.

Furthermore, the puzzles need not be rectangular. Figures 5a and 5b show a circular puzzle in accordance with an embodiment of the invention. The puzzle is divided into 54 pieces formed in a series of concentric rings. Each ring contains 6, 12 or 24 pieces.

Figure 5a shows the pieces arranged in a first, ordered manner, such that the puzzle is solved for an image on the upper surface. The pieces have been interchanged into the arrangement shown in Figure 5b. Due to the nature of this puzzle, each piece must remain in the same concentric ring in both arrangements. However, their relative positions are altered.

Once each piece has been assigned to its position in Figure 5b, the method described above is applied in order to form the connectors, as shown in Figure 5a. Thereafter, the pieces are assembled into the second arrangement (Figure 5b) , and a second image is formed on the reverse of the puzzle.

Figures 6a and 6b show a puzzle in accordance with a second embodiment of the invention. In this case, the two arrangements of the puzzles are of different shapes, the first being octagonal, and the second being substantially rectangular. The puzzles have the same overall area and the same number of pieces. However, the different shape results in the arrangement of Figure 6b having a longer perimeter. Thus, four pairs of edge pieces must be hidden within the arrangement of Figure 6a. There are also four pairs of edge pieces hidden within the arrangement of Figure 6b. Figure 6b has a longer perimeter of horizontal and vertical edges but Figure 6A has the longer diagonal edges . So the horizontal/vertical edges of 6b are hidden in 6a and the diagonal edges of 6a are hidden within 6b.

The Figures show that two shapes of pieces are used in this embodiment: square and triangular. The triangular pieces allow straight edges to be formed around the puzzle.

As before, the above-described method is used in order to determine the shapes of the connectors.

The arrangement shown in Figure 6b comprises a number of edge pieces that have another significant difference from the standard jigsaw. The majority of the edge pieces (i.e. the triangular ones) do not directly interconnect with the adjacent edge pieces. Rather, the pieces come into point contact at the apices of the triangles. This presents an additional degree of challenge to the puzzle solver, because it prevents him/her from starting the solution by first assembling the border of the puzzle, which is a technique used to aid the solving of standard jigsaw puzzles.

Thus far, there have been described a variety of two-way puzzles. However, the present invention provides a flexible technique to allow the production of puzzles with three or more image surfaces as described below. It is possible to create a puzzle with three image surfaces from a number of pieces, with each piece being used in two of the image arrangements. If the three surfaces have N_lA N₂ and N₃ pieces respectively, the total number of pieces T will be T = (Ni + N₂ +N₃)/2. This result occurs if each piece is used in two of the images .

The possible ways in which the images can share pieces must first be calculated. This can be done using the following formula for N_xy, where N_xγ is the number of pieces with surface X on one face and surface Y on the other:

N_XY = (N_x + N_γ - N_z) /2 = T - N_z

Figures 7a to 7f show an example of a three-way puzzle in accordance with the invention.

The puzzle comprises three rectangular image surfaces, being a 3x4 (Figure 7a) , a 4x4 (Figure 7b) , and a 4x5 (Figure 7c). The following table shows the number of each type of piece required for each image surface, where N is the total number of pieces, C is the number of corner pieces, E is the number of edge pieces, and I is the number of internal pieces.

The formula above also applies to corner, edge, and internal pieces, i.e:

C_XY = (Cx + C_γ - C_z)/2 and so the following numbers of each type of piece can be calculated :

Nχ₂ = 4 C₁₂ = 2 E12 = 2 I₁₂ = 0

N₁₃ = 8 C₁3 = 2 E₁₃ = 4 I₁₃ = 2

N₂₃ = 12 C₂₃ = 2 E₂₃ = 6 I₂₃ = 4

By grouping all of the pieces that make up surface one, we can see that the back of surface one comprises 2 corner pieces, 2 edge pieces and 0 internal pieces from surface two, and 2 corner pieces, 4 edge pieces and 2 internal pieces from surface three.

The back of surface two is made up of 2 corner pieces, 2 edge pieces, and 0 internal pieces from surface one, with 2 corner pieces, 6 edge pieces and 4 internal pieces from surface three.

Finally, the back of surface three is made of 2 corner pieces, 4 edge pieces and 2 internal pieces from surface one, as well as 2 corner pieces, 6 edge pieces and 4 internal pieces from surface two.

Figures 7d, 7e and 7f show the rear surfaces of the first second and third arrangements respectively. The pieces are orientated so that the edges and corners are consistent between arrangements.

Note that the discussion above concerns corner, edge and internal pieces only because we are dealing here with rectangular surfaces with square pieces. Other puzzles could have different subsets of pieces and a different number of such subsets. The formulae given above can be applied to each subset.

Once the pieces have been assigned to their positions as shown in Figures 7d to 7f, the connectors are formed according to the method as described with reference to Figure 4. However, for three-way puzzles (and above), there is a further step required in order to ensure that the connectors are formed in consistent cycles.

It will be noted from the above description that the method of forming the connectors involves switching between the two solutions of the puzzle. For a three way puzzle there are, of course, three possible solutions, and in forming a cycle of connectors one switches between all three arrangements. This causes two types of cycles to be formed, referred to herein as "odd" and "even" cycles.

Figure 8 demonstrates the formation of even and odd cycles in a three-way puzzle. Figure 8a is a first arrangement, giving a solution A, with second and third solutions shown by Figures 8b and 8c. Figures 8d to 8f show the reverse sides of the arrangements, as if flipped around a vertical axis at the centre of the page. As shown, the back of solution A is made up of pieces from the B and C solutions. Similarly, the reverse sides of solutions B (Figure 8e) and C (Figure 8f) respectively comprise combinations of pieces from the A and C arrangements.

The cycle formed from piece Aio, shown by triangular connector 81, passes between the arrangements of Figures 8a, 8b and 8f. The cycle completes with a consistent connector from piece B₃₀ to Aio .

This even cycle has a "mirror cycle" that is followed by the reverse of the pieces. The mirror cycle is shown by dotted triangular connectors 82, and the connectors on either side of a single piece are consistent with one another.

An odd cycle is also demonstrated in Figure 8. The connector 83 protruding from piece A₀o is chosen, and in this case is a square, bold connector. The connector determines the shape of the connector on piece Aι₀, which in turn requires that Bι₀ (Figure 8f) has a square connector. Subsequently, B₂o is defined by having a square recess (Figure 8b), as is piece Bι₃, being adjacent to B₂o in Figure 8f . The construction of the cycle continues until closure occurs with the formation of a connector between C₀₂ and A₀₀.

However, upon closer inspection, one can see that the square connectors on the front and rear of a single piece are inconsistent with one another. Thus, in this form, the puzzle could not be manufactured.

This so-called "odd cycle" arises by virtue of the chosen arrangement of pieces; Cio is a piece that forms both part of the cycle, and part of the reverse side of arrangement A (Figure 8d) . Since the puzzle containing an odd cycle is not manufacturable, odd cycles must be avoided.

It can be shown that the odd cycles always form in pairs. That is, there is always an even number of odd cycles. There are three main options for dealing with odd cycles. The first is to abandon the arrangements of pieces, and recommence until an arrangement is found that includes only even cycles.

The second possibility is to use the following simple algorithm: (i) Swap the position of two rear surface pieces chosen at random. The pieces must have the same basic shape. (ii) If this results in an arrangement with more odd cycles, or fewer/longer even cycles, then swap the two pieces back and return to step (i) . (iϋ) If there are still odd cycles then return to step (i) .

This option is likely to be more practical than the first.

Alternatively, by carefully exchanging one or more pieces, the character of the cycles may be altered.

In particular, by swapping two pieces with connectors on different odd cycles, the two odd cycles are combined into a single even cycle. The exchange of two appropriate pieces in this way thus eliminates the inconsistencies between the front and rear surfaces.

An example of the piece exchange process is shown in Figures 9 and 10.

Figure 9 shows the puzzle of Figures 7 and 8 with the connectors being allocated to the pieces. As shown in the Figure, the connectors form four even cycles (depicted by triangular, trapezoidal, and part circular connector shapes) and corresponding mirror cycles (shown by dashed lines) . The odd cycles are depicted by square and circular connector shapes.

The two odd cycles must be eliminated by the exchange of two pieces. The pieces to be swapped can be selected in a variety of ways, but it is important that the swap does not result in a greater number of odd cycles being formed. In this example, piece A₀o (or B₀₃ from the reverse side) is exchanged with piece A₀₃ (or piece B₃₃) . These pieces are selected because they both have connectors formed on the odd cycles that are to be removed.

The interchanging of the two pieces changes the shape of the connectors on those edges that have them. Thus the adjacent pieces are also affected. The cycles of connectors must be reformed, starting from the interchanged pieces. The nature of the new cycles depends on the type of cycle upon which the interchanged connectors lie, and the results are summarised in Figure 17.

In this example, interchanging the corresponding edges corresponding to the right-hand edge of piece A₀o combines the even cycle (shown by the triangular connector) and the odd cycle (shown by the circular connector) into a single odd cycle. Exchanging the bottom two pieces combines two odd cycles to form a single even cycle. The puzzle (shown in Figure 10) is now manufacturable.

The step of exchanging two pieces may be incorporated into a process for forming a puzzle for reasons other than the elimination of odd cycles of connectors. For example, by exchanging two pieces with connectors on the same even cycle, it is possible to split that even cycle into a pair of even cycles. This technique may be utilised in order to provide further variation in the pieces by effectively adding a new cycle and assigning to it a new connector shape. This may be useful if a particularly long cycle has resulted from the connector generation process.

Figures 15a to 15f show the puzzle of Figures 7 to 10 after an even cycle has been converted into two new even cycles. This provides additional variation in piece shapes, and is achieved by the exchange of pieces A₂₂ and C03 •

Various manufacturing techniques may be employed for the production of puzzles in accordance with the invention. For example, it is envisaged that for the purposes of speed and efficiency, a computer program could be used to generate the puzzle arrangements according to the algorithms described.

The computer can generate the arrangements according to instructions input from an operator. Such instructions would include the type of puzzle to be created, the images to be used and the number of pieces.

When the files necessary for the printed images have been generated, the computer could also be used to drive a laser cutter, or to manufacture suitable dies for the die cutting process. For 2-way puzzles two images are required, one for the front surface and one for the back. The front surface image is simply the front picture or pictures. The back surface image is the jumbled up arrangement of pieces resulting from completing the front surface. Hence the cutting process must exactly align to the edges of these pieces.

For 3-way puzzles similar images are required, as shown in Figure 13. However, it should be noted that since the pieces are duplicated for the three-way puzzles, only half the pieces are required.

All the pieces of Figure 13a are required with Figure 13d on the back. However, only half the pieces of 13b are required - those with the C pieces of 13e on the back. The remaining pieces of 13b have A pieces on the back, and are produced with the 13a/13d pieces.

During manufacture, it may be easier to cut out all pieces of 13b but to blank out those pieces that are not required. This may result in some redundant pieces in the puzzle box but the solver can easily discard these pieces if they clearly stand out from the useful ones.

Alternatively, the puzzle may include two sets of pieces so that all images can be produced at once. If only one set of pieces is provided, only one of the three images can be constructed at one time, leaving pieces left over. Allowing all the images to be solved at once may prove to be more satisfying to the solver.

One possible way of cutting the pieces is to use laser cutting. Laser cutters can be driven by computer and simply require a file detailing the necessary cuts. Laser cutters usually have the disadvantage of giving a burnt edge to the pieces, but cutting the pieces out of plastic instead of card eliminates this problem. The laser cutting can be exactly aligned to the printed image so this is not a problem.

For mass production, it may be more practical to use die cutting, as this is much quicker. However, the pieces must be cut from front and back so that examination of the pieces will not show which is the top surface.

It should be noted that although the foregoing description discusses two and three way puzzles, the methods could be applied to higher level puzzles. In particular, the method described with reference to the three-way puzzles, including the step of removing odd cycles of connectors, is a general approach that may be used to construct a puzzle with 2, 3, 4 or more solutions (although in the case of 2-way puzzles, odd cycles will never occur) .

In constructing a four-way puzzle, the ways in which the images share the pieces must be decided. This is achieved using formulae similar to those used for the three-way case described above. For four rectangular image surfaces, with 12, 16, 20, and 24 pieces, the following pieces are required:

The following numbers of each type of piece, shared between surfaces can be calculated:

N₁2 = 3 C12 = 1 E12 = 2 I_i2 = 0

N13 = 4 C13 = 2 Ei3 = 1 I13 = 1

N₁₄ = 5 C₁₄ = 1 E₁₄ = 3 I₁₄ = 1

N₂₃ = 5 C₂₃ = 1 E₂₃ = 3 I₂₃ = 1

₂₄ ⁼ 8 C24 ⁼ 2 E₂4 ⁼ 3 I₂₄ = 3

N34 = 11 C₃₄ = 1 E34 = 6 I34 = 4

The particular arrangement of the pieces is made in accordance with the above sharing rules. As before, when the pieces have been assigned to their positions, connectors are constructed by the method described previously.

Figures 16a to 16h illustrate an example of a four-way puzzle.

Five-way and above puzzles may be constructed using similar techniques.

The remaining Figures demonstrate how the described methods may be used to create multi-way puzzles, the solutions having different shapes. These Figures are examples only, and various other arrangements are possible within the scope of the present invention. Figures 11a to lie show a two-way puzzle wherein the first solution comprises two sub-arrangements (Figures 11a and lib) , and the second solution is a rearrangement of the pieces of the two sub-arrangements into a single dodecagon. As will be noted, the puzzle contains pieces of four different basic shapes.

Figures 12a and 12b show another example of a two-way puzzle. This puzzle has a first rectangular solution and a second hexagonal solution, with pieces based on a hexagonal shape.

Figures 13a to 13f show an example of a three-way puzzle having three rectangular solutions, each of which sharing pieces from the other two. Figure 13d shows the reverse side of Figure 13a, Figure 13e the reverse of Figure 13b and Figure 13f is the reverse of 13c. As shown, the pieces are diagonally cut in this example.

Figures 14a to 14f show a further example of a three-way puzzle, this time the three solutions having different shapes.

All of the above examples, and others, can be constructed using the methods described above.

The present invention provides a method for producing a variety of multi-way puzzles. In doing so, the invention opens up possibilities for a range of puzzles that provide an increased challenge and/or stimulation to a user.

Various modifications may be made within the scope of the invention.

Claims

1. A puzzle comprising: a plurality of pieces each having a first side and a second side, the first and second sides being provided with markings thereon, each piece comprising at least one engaging portion for allowing the piece to temporarily interlock with a corresponding engaging portion on an adjacent piece, the pieces being shaped such that they interlock in a first arrangement defining a first surface upon which the markings form a first image, and interlock in a second arrangement, distinct from the first, defining a second surface upon which the markings form a second image, wherein the pieces are formed in at least three different shapes.

2. The puzzle as claimed in Claim 1 wherein the first and second arrangements comprise the same number of pieces.

3. The puzzle as claimed in Claim 1 or Claim 2 wherein the first and second arrangements comprise exactly the same pieces.

4. The puzzle as claimed in any preceding Claim wherein the second arrangement comprises a plurality of sub- arrangements, each forming a separate image.

5. The puzzle as claimed in any preceding Claim wherein the first arrangement comprises a plurality of sub- arrangements, each forming a separate image.

6. The puzzle as claimed in any preceding Claim wherein the pieces are shaped such that a third subset of the pieces interlock in a third arrangement, distinct from the first and second arrangements, defining a third surface upon which the markings form a third image .

7. The puzzle as claimed in Claim 6 wherein the markings on a single piece form part of any two of the first, second or third images.

8. The puzzle as claimed in Claim 6 or Claim 7 wherein the markings on the first side of a piece form part of one of the images, and the markings on the second side of a piece form part of another of the images.

9. The puzzle as claimed in any of Claims 6 to 8 wherein the pieces are shaped such that a fourth subset of the pieces interlock in a third arrangement, distinct from the first, second and third arrangements, defining a fourth surface upon which the markings form a fourth image .

10. The puzzle as claimed in Claim 9 wherein the pieces are shaped such that there are further subsets of pieces that interlock in further distinct arrangements, defining further surfaces upon which the markings form further images.

11. The puzzle as claimed in any preceding Claim wherein the first and/or second arrangements are in the form of irregular polygons.

12. The puzzle as claimed in any preceding Claim wherein the first and/or second arrangements are in the form of regular polygons.

13. The puzzle as claimed in any preceding Claim wherein the first and/or second arrangements are in a form selected from the group consisting of: circles, triangles, rectangles, hexagons, octagons, dodecagons, and hexadecagons .

14. The puzzle as claimed in any preceding Claim wherein the pieces include a first group of edge pieces forming a perimeter of one of the arrangements, and a second group of edge pieces forming a perimeter of another of the arrangements.

15. The puzzle as claimed in Claim 14 wherein the edge pieces form a smooth edge.

16. The puzzle as claimed in Claim 14 or Claim 15 wherein the first and second groups of edge pieces share some of the pieces.

17. The puzzle as claimed in any of Claims 14 to 16 wherein the first and second groups comprise the same number of edge pieces.

18. The puzzle as claimed in any of Claims 14 to 16 wherein the second group comprises fewer edge pieces than the first group, leaving a surplus of edge pieces.

19. The puzzle as claimed in Claim 18 wherein the surplus of edge pieces is used in the interior of the second arrangement .

20. A method of manufacturing a puzzle comprising the steps of: (i) defining a plurality of pieces, each having a first side and a second side; (ii) assigning each piece to a primary position in a primary arrangement and a secondary position in an secondary arrangement; (iii) allocating a first connector to a first piece, to later form an engaging portion; (iv) sequentially allocating additional connectors on each piece, the shape of the additional connectors being determined by connectors already formed on adjacent pieces in the primary and secondary arrangements.

21. A method as claimed in Claim 20 wherein step (iv) comprises the sub-steps of: (a) allocating a second corresponding connector to a second piece, adjacent to the first piece when in its primary position, to later form an engaging portion for allowing the first and second pieces to temporarily interlock; (b) allocating a third corresponding connector to a third piece, said third piece being adjacent to the second piece when in its secondary position, to later form an engaging portion for allowing the second and third pieces to temporarily interlock in the secondary arrangement; (c) allocating a corresponding connector to a fourth piece, said fourth piece being adjacent to the third piece when in its primary arrangement, to later form an engaging portion for allowing the third and fourth pieces to temporarily interlock in the primary arrangement.

22. A method as claimed in Claim 21 comprising the additional steps of: (v) reiterating sub-steps (a) to (c) for subsequent pieces until a connector is formed with the first piece; (vi) selecting a further piece and repeating steps (iii) to (iv) until all pieces are connected; (vii) forming markings on the first and second sides of the pieces such that the pieces form images when arranged in their primary and secondary positions.

23. The method as claimed in any of Claims 20 to 22 wherein the pieces form at least two images.

24. The method as claimed in any of Claims 20 to 23 wherein the primary and/or secondary arrangements define two or more distinct image surfaces.

25. The method as claimed in any of Claims 20 to 24 including the additional step of: exchanging a pair of pieces and reallocating the connectors, starting from those connectors on the pair of pieces exchanged.

26. The method as claimed in any of Claims 20 to 25 wherein some or all of the steps are carried out by a computer program.

27. The method as claimed in any of Claims 20 to 26 wherein the pieces of the puzzle are cut by laser cutting techniques.

28. The method as claimed in any of Claims 20 to 27 wherein the pieces of the puzzle are cut by die cutting.

29. A method of manufacturing a puzzle comprising the steps of: (i) dividing a first image into a plurality of pieces defining a first arrangement; (ii) assigning each piece to a position in a second arrangement in the shape of a second image; (iii) allocating a first connector to a first piece, to later form an engaging portion; (iv) allocating a second corresponding connector to a second piece adjacent in the first image, to later form an engaging portion for allowing the two pieces to temporarily interlock; (v) allocating a third corresponding connector to a third piece, said third piece being adjacent to the second piece in the second arrangement, to later form an engaging portion for allowing the second and third pieces to temporarily interlock in the second arrangement; (vi) allocating a corresponding connector to a fourth piece adjacent to the third piece in the first arrangement, to later form an engaging portion for allowing the third and fourth pieces to temporarily interlock in the first arrangement; (vii) reiterating the steps (iv) to (vi) for subsequent pieces until a connector is formed with the first piece; (viii) selecting a second piece and repeating steps (iii) to (vii) until all pieces are connected; (ix) forming a second image in a rearranged configuration on the reverse side of the second arrangement.

30. A puzzle comprising: a plurality of pieces each having a first side and a second side, the first and the second sides being provided with markings thereon, each piece comprising at least one engaging portion for allowing the piece to temporarily interlock with a corresponding engaging portion on an adjacent piece, the pieces being shaped such that a first subset of pieces interlock in a first arrangement such that the markings form a first image on a first surface, a second subset of the pieces interlock in a second arrangement, distinct from the first, such that the markings form a second image on a second surface, and a third subset of the pieces interlock in a third arrangement, distinct from the first and second, such that the markings form a third image on a third surface.

31. The puzzle as claimed in Claim 30 wherein the markings on a single piece form part of any two of the first, second or third images.

32. The puzzle as claimed in Claim 30 or Claim 31 wherein the markings on the first side of a piece form part of one of the images, and the markings on the second side of a piece form part of another of the images.

33. The puzzle as claimed in any of Claims 30 to 32 wherein the pieces are shaped such that a fourth subset of the pieces interlock in a fourth arrangement, distinct from the first and second, such that the markings form a fourth image on a fourth surface.

34. The puzzle as claimed in any of Claims 30 to 33 wherein the pieces are shaped such that there are further subsets that interlock in further distinct arrangements, such that the markings form further images on further surfaces.

35. A puzzle comprising: a plurality of pieces each having a first side and a second side, the first and the second sides being provided with markings thereon, each piece comprising at least one engaging portion for allowing the piece to temporarily interlock with a corresponding engaging portion on an adjacent piece, wherein the pieces are adapted to be arranged in three distinct arrangements, each arrangement forming an image .

36. The puzzle as claimed in Claim 35 wherein the markings on a single piece form part of any two of the first, second or third images.

37. The puzzle as claimed in Claim 35 or Claim 36 wherein the markings on the first side of a piece form part of one of the images, and the markings on the second side of a piece form part of another of the images.

38. The puzzle as claimed in any of Claims 35 to 37 wherein the pieces are shaped such that a fourth subset of the pieces interlock in a fourth arrangement, distinct from the first and second, such that the markings form a fourth image on a fourth surface .

39. The puzzle as claimed in Claim 38 wherein the pieces are shaped such that there are further subsets that interlock in further distinct arrangements, such that the markings form further images on further surfaces.

40. The puzzle as claimed in any of Claims 30 to 39 Claim wherein the pieces include a first group of edge pieces forming a perimeter of one of the arrangements, and a second group of edge pieces forming a perimeter of another of the arrangements.

41. The puzzle as claimed in Claim 40 wherein the edge pieces form a smooth edge.

42. The puzzle as claimed in Claim 40 or Claim 41 wherein the first and second groups of edge pieces share some of the pieces.

43. The puzzle as claimed in any of Claims 40 to 42 wherein the first and second groups comprise the same number of edge pieces.

44. The puzzle as claimed in any of Claims 40 to 42 wherein the second group comprises fewer edge pieces than the first group, leaving a surplus of edge pieces .

45. The puzzle as claimed in Claim 44 wherein the surplus of edge pieces is used in the interior of the second arrangement .

46. A puzzle manufactured by the method according to any of Claims 20 to 29.

47. A puzzle comprising a plurality of pieces each piece comprising at least one engaging portion for allowing the piece to temporarily interlock with a corresponding engaging portion on an adjacent piece, the pieces being shaped such that they interlock in a first arrangement to form an image on a first surface, wherein the pieces include a first group of edge pieces forming a border of the first arrangement, and a majority of the edge pieces do not directly interconnect with adjacent edge pieces.

48. The puzzle as claimed in Claim 47 wherein the pieces of the puzzle are adapted to interlock in a second arrangement, distinct from the first, to form a second image on a second side.

49. The puzzle as claimed in any of Claims 30 to 48 wherein the first and/or second arrangements are in the form of irregular polygons .

50. The puzzle as claimed in any of Claims 30 to 48 wherein the first and/or second arrangements may be in the form of regular polygons .

51. The puzzle as claimed in any of Claims 30 to 50 wherein the first and/or second arrangements are in a form selected from the group consisting of: circles, triangles, rectangles, hexagons, octagons, dodecagons, and hexadecagons .