GB2454536A

GB2454536A - A puzzle game having edge-matching puzzle pieces

Info

Publication number: GB2454536A
Application number: GB0722195A
Authority: GB
Inventors: Nigel Robert Wood
Original assignee: Individual
Current assignee: Individual
Priority date: 2007-11-12
Filing date: 2007-11-12
Publication date: 2009-05-13
Also published as: GB0722195D0

Abstract

A puzzle game consists of two or more homogeneous single or multi-facet puzzle pieces, each facet having three or more edges and each edge ascribed with a single indicia. The indicia are allocated such that when all, or a sub-set, of the puzzle pieces are placed in an unique relative two or three-dimensional positional and rotational configuration, so that indicia of two adjacent puzzle piece match in either two or three-dimensions, a required two or three-dimensional configuration/pattern ('target') is obtained. In an embodiment of the puzzle game, two or more multi-facet puzzle pieces are used to form two or more two-dimensional configurations/patterns ('targets'), the puzzle pieces have centrally located inscribed indicia on each facet to indicate which facet contributes to which configuration/pattern. The indicia can be an alphanumeric character, a solid or broken colour, a pattern consisting of two or more colours, raised dots, one or more shapes/symbols or combinations of these. The puzzle pieces may have attachments allowing them to be joined. The pieces may also have passive or electronic identification to allow the location of the pieces within the completed puzzle to be determined. The puzzle may be implemented electronically via a computer program or the like.

Description

1 2454536

A PUZZLE GAME WITH MULTIPLE PUZZLE PIECES

This invention relates to a single player puzzle game consisting of two or more single or multi-facetted puzzle pieces, of the same size and shape, with a single iridicia ascribed per edge.

Many people, young and old, enjoy the mental stimulation and achievement satisfaction solving a puzzle game brings, whether this be a traditional puzzle game such as Towers of Hanoi', Solitaire or a Jigsaw puzzle; or one of the newer puzzle games such as Rubik's Cube or Sudoku. All of these puzzle games have one common factor that a single player (or puzzler) traditionally plays them.

As means of introducing the key aspects covered by this invention consider Microsoft Corporation's computer-based puzzle game Tetravex and the mathematical work of Jorge Rezende, University of Lisbon, Portugal.

The computer-based puzzle game Tetravex, devised by Scott Ferguson of Microsoft Corporation, was distributed as part of the Entertainment Pack' for the company's Windows95 Operating System. Various clones have been produced since for other Operating Systems, for example Linux. The puzzle game involves the visual representation of an N x M grid of single-facet square tiles, with numerical indicia ascribed to each of the four edges (of each tile). From notes on the game, and that of its clones, allocation of the paired indicia of adjacent (touching) edges of different tiles relies solely on a random allocation process, with edges of tiles forming the outer boundaries of the grid also being allocated random indicia. At the beginning of the game the solution' is shown until the player starts the game -the position of the tiles is then randomly shuffled. The objective of the game is to restore the position of the tiles to reproduce the starting configuration (the solution') by the game player (puzzler) selecting and swapping tiles. The game is restrictive in that only the position of the tiles can be varied -no rotation is possible. Although a solution is implicitly guaranteed, through the allocation of the indicia, there are no checks made to remove the possibility of multiple solutions or that the allocation of indicia is unique (it is possible for multiple tiles to have the same indicia set).

In summary the puzzle game, although challenging, is significantly less demanding than if: I) the puzzle game included rotation of the puzzle pieces; ii) the allocation of the indicia was controlled and guaranteed an unique solution.

The mathematical work of Jorge Rezende has been published in the papers entitled "On the Puzzles with Polyhedra and Numbers" and "Puzzles with Polyhedra and Permutation Groups", available via the web site of the Mathematical Group of the University of Lisbon (httix//gfm.cii.fc. ul. nt1MembersIIR.tPT.html). The publications cover the mathematical methods behind using polygonal plates (tiles), with a single numerical indicia ascribed to each edge, to form the surface of regular polyhedron. Although the analysis is very detailed and covers a method (effectively a search based routine) that determines how many solutions a particular indicia set can produce, i.e. how many different ways the tiles can be arranged to form the surface of the polyhedron by matching adjacent indicia of different tiles, there is no discussion on limiting the allocation of the indicia to ensure an unique solution.

The family of puzzle games described by this patent solves the limitations outlined above in the two references to produce a set of challenging puzzle games in which the indicia allocation is such that there is an unique relative placement' of the puzzle pieces that achieves the required target' configuration. In particular this patent covers puzzle games having puzzle pieces of the same size and shape and a single indicia ascribed per edge, utilising: single-facet puzzle pieces (single-facet tiles) to form two-dimensional puzzle game configurations, e.g. N x M grids, regular and irregular polygons, or the surface of regular and irregular polyhedra; * dual-facet puzzle pieces (dual-facet tiles) to form dual-sided puzzle games, e.g. dual-sided N x M grids, regular and irregular polygons, or the surface of regular and irregular polyhedra; * multi-facet puzzle pieces to form multiple puzzles where each puzzle piece facet contributes to one two-dimensional puzzle, e.g. the use of 9 six-sided hexahedron (cube) based puzzle pieces to form six different 3 x 3 (N x M) two-dimensional grid based puzzles, where a centrally positioned indicia is used to differentiate which facet contributes to which puzzle game. A multi-sided dice (six-sided in this example) could be used to randomly select which of the puzzles (six in this example) the puzzler is to solve; multi-facet puzzle pieces, which can be combined to form larger regular and irregular polyhedra, e.g. the use of 8 hexahedron (cube) based puzzle pieces, arranged in a three-dimensional grid (2 x 2 x 2), to form a larger hexahedron (or cube).

In all of the above puzzles the objective for the puzzler is to match the single edge ascribed indicia of two adjacent puzzle pieces, in either two or three dimensions, to form the required target' configuration. The key aspect of this invention is the allocation of the indicia which controlled by an Indicia Allocation Algorithm (IAA), that takes into account li possible positional and rotational pennutations of the puzzle pieces, guarantees the solution (or target' configuration) requires an unique relative Diacement of the puzzle pieces. It should be noted that in many cases the target' configuration may have many rotational symmetrical configurations and, hence, several actual' solutions may exists, e.g. an N x M grid (with N=M) would have 4 actual solutions and an N x M grid (if N!= M) would have 2 actual solutions, due to rotational symmetry of the grid.

Embodiments of the invention will now be described, by way of example only, with reference to the accompanying diagrams, in which: Figure 1 shows a single facet N x M (N=M=2) grid based puzzle using 4 single-facet square based tiles. The allocation of the indicia (to each tile) is such an unique solution exists for the relative position and rotation of the 4 tiles, whilst minimising the number of different indicia used.

Figure 2 shows the result of applying an indicia interchange (swap) on the indicia set of the puzzle shown in figure 1.

Figure 3 shows a single facet N x M (N=M=4) grid based puzzle using 16 single-facet square based tiles. The allocation of the indicia (to each tile) is such an unique solution exists for the relative position and rotation of the 16 tiles, whilst minimising the number of different indicia used Figure 4 shows a single facet triangle based puzzle using 9 single-facet triangular based tiles.

The allocation of the indicia (to each tile) is such an unique solution exists for the relative position and rotation of the 9 tiles, whilst minimising the number of different indicia used.

Figure 5 shows a single facet based puzzle using 7 single-facet hexagonal based tiles. The allocation of the indicia (to each tile) is such an unique solution exists for the relative position and rotation of the 7 tiles, whilst minimising the number of different indicia used.

Figure 6 shows a single facet based puzzle using 8 single-facet equilateral triangle based tiles to form the surface of an octahedron (8 facets or sides). The allocation of the indicia (to each tile) is such an unique solution exists for the relative position and rotation of the 8 tiles, whilst minimising the number of different indicia used.

Figure 7 shows a dual-facet N x M (N=M=3) grid based puzzle using 9 dual-facet square based puzzle pieces. The allocation of the indicia (to each puzzle piece) is such an unique solution exists for the relative position and rotation of the 9 tiles, whilst minimising the number of different indicia used and the indicia of adjacent edges both front and rear facets are required to be matched.

Figure 8 shows a multi-facet based puzzle using 8 six-facet (hexahedron or cube) based puzzle pieces to form a larger (2 x 2 x 2) cube. The allocation of the indicia (to each puzzle piece) is such an unique solution exists for the position and rotation of the 8 puzzle pieces, whilst minimismg the number of different indicia used, and the indicia of adjacent edges require matching in three-dimensions.

In figure 1, four single-facet square based puzzle pieces (tiles) form a 2 x 2 (N=M=2) grid based puzzle (target' configuration). On each edge of each tile (110, 120, 130 and 140) a numerical indicia (11 1... 114, 121... 124, 131... 134 and 141... 144) has been allocated by an IAA. The IAA determines the indicia required such that when adjacent indicia are matched there is an unique relative placement (considering jj possible positional and rotational permutations) of the puzzle pieces that form the target' configuration (a 2x2 grid). In addition the IAA has minimised the number of different indicia used, maximising the puzzle's difficulty. The numerical indicia 1' (112, 113, 122, 124 and 131) is used 5 times, 2' (111, 123, 132, 141 and 144) is also used 5 times, 3' (114, 121, 133 and 134) is used 4 times and finally 4' (142 and 143) is used 2 times. The encircled indicia highlight the indicia required to be matched (total of 8) to form the target' configuration.

With reference to figure 1, allocate A' to the top left-hand corner position, B' to the top right-hand corner position, C' to the lower left-hand corner position and D' to the lower right-hand corner position. When the puzzler commences to solve the puzzle the puzzler has 4 possible (all) puzzle pieces that could be positioned in position A', and that each puzzle piece could be in any of four rotational positions (equal to the number of edges). Let P equal the number of puzzle pieces, E the number of edges each puzzle piece has (and hence the number of indicia, as there is only one indicia ascribed per edge) and F the number of facets (of each puzzle piece, as F=l in this case it is ignored). The number of possible permutations (puzzle piece and the piece's rotation) for position A is given by P* E. If piece 110 were positioned in position A' (in any rotational state) the puzzler would have to find a puzzle piece that would fit in position B' which has the same indicia on its left-hand edge (matching the indicia on the right-hand edge of piece A'). Ignoring pieces that do not have indicia that match, the number of permutations is now given by (P -1). E. If the puzzler continues to find pieces that match for positions C' and D' the puzzler (again ignoring pieces for which the indicia do not match) would eventually have to consider (P.fr-l).(P-2).fr-3)).(I.i.i.E) or P!*E17positional and rotational permutations to find the target' solution. With P=4, E=4 and F=1 (in this example) the total number of positional and rotational pennutations that the puzzler may have to consider would be 4!.44= 6144. It should be noted that as the N x M (N=M) grid has 4 symmetrical rotational states out of the 6144 possible permutations 4 permutations would yield a solution.

The pennutation equation, defined above, only provides a relative indication of a particular puzzle configuration's difficulty, as the actual number of test scenarios (position and rotation of the puzzle pieces), that the puzzler may have to consider, is dependent upon the actual indicia set utilised (and hence piece-to-piece matching). To calculate the number of actual test cases a search-based algorithm would have to be utilised.

For the puzzle in figure 1 the search algorithm (or puzzler) would have to find the solution as follows: for position A' there are 16 scenarios (P.E), i.e. each puzzle piece in each rotational state. For each of the position A' scenarios determine the unique puzzle piece in position B' that would match (right-hand edge indicia of piece in position A' matching the left-hand edge indicia of piece in position B') -there are a total of 44 cases. For each of these 44 cases find the unique puzzle piece (remembering that each puzzle piece can only be utilised once) that fits in position C' matching the piece (it's indicia) in position A'-this results in 63 valid cases. Finally find the unique puzzle piece for position D' that matches both of the pieces (their indicia) in positions B' and C'. Out of the 63 cases only 4 will result in a valid position D' match, these 4 being the 4 rotational solutions to the puzzle.

As shown in figure 1, the IAA does produce possible' clues to the solution (especially if numerical indicia are utilised) as the puzzler could guess (or commence with) the indicia 1' is likely to be used in the top left-hand corner. Applying an indicia interchange (for example 1-3, 2-1, 3-4 & 4-.2) would remove this dependency, as shown in figure 2-although due to the low number of puzzle pieces (in this test case) the actual benefit of this shuffle is not as beneficial as it could be for puzzles with a larger number of puzzle pieces.

The IAA utilised is flexible in that by using a combination of constraints and indicia interchanges it is possible to produce different puzzle configurations with differing degrees of difficulty. The constraints utilised limit the number of occurrences an indicia is (a) used in the whole puzzle (Ix_puzzij), (b) used on a single puzzle piece (I?x_PzEcE) considering all facets and edges and (c) used on a puzzle piece's facet (IMAX_FACET). For puzzle pieces with only one facet (F=l) constraints (b) and (c) are equal. It should be noted that by just applying an indicia interchange to a valid' (achieves a particular target') indicia set, consisting of I' different indicia, I' factorial (I!) different puzzle targets' could be derived -for the puzzle in figure 1, with 4 different Indicia, this could be 24(4!).

If the indicia where non-alpha numerical characters the target' solution would be better hidden, as it removes any link to numerical sequences. For this reason it is considered that an actual puzzle implementation would use colours, shapes, shading patterns or combination of these three. The key is to have sufficient different patterns to enable unambiguous discrimination between different indicia and to avoid any possibility of the indicia providing any clue to the correct orientation of the puzzle piece in the target'. It should also be noted that raised dots could be utilised to aid blind or partially sighted puzzlers.

Figure 3 shows an embodiment in which sixteen (310... 385) single-facet square puzzle pieces form a 4 x 4 (N=M=4) grid-based puzzle (the target' configuration). Using the pennutation equation above the number of scenarios to be considered would be 161.416 or 8.986x1022, highlighting that as P increases the difliculty level of the puzzle increases significantly. The IAA has been applied with the set of constraints MAx_PuzzI 10, MAX_PIECE = 2 and M4JC FACET = 2 and with the indicia interchange of 1-4, 2-'6, 3-�8, 4-'l, 5-3, 6-.7, 7-5 and 8-i2 (which is I of the 40,320 [8 factorial] possible indicia interchange scenarios). As with figure 1 the encircled indicia are required to be matched -a total of 48 indicia out of the total of 64.

Figure 4 shows a further embodiment in which nine single-facet triangular puzzle pieces (410... 490) form a triangular shaped puzzle of height (1-1) = 3. Using the permutation equation (P9, E=3, F=l) the number of permutations is given by 9!*3= 7.142x109. As the puzzle has a rotational symmetry of 3 there are 3 solutions to the puzzle.

Figure 5 shows a further embodiment in which seven single-facet hexagonal puzzle pieces (510... 570) form a flower' shaped puzzle. Using the permutation equation (P7, E=6, F1) the number of permutations is given by 7!*6 = 1.41x109, the puzzle having 6 solutions due to rotational symmetry.

Figure 6 shows a further embodiment in which eight single-facet equilateral triangle based puzzle pieces (610... 680) form the surface (or plan) of an octahedron (as per the work of Jorge Rezende). The number of permutations (P=8, E=3 & F1) is given by 8!*3 = 2.64x108, the puzzle has 24 (8 x 3) solutions due to rotational symmetry. The IAA has allocated the indicia so that there is an unique relative position of the puzzle pieces that yields the target' solution -extending the work of Jorge Rezende. Note that the dotted lines indicate the indicia that match to form the surface of the polyhedra (an octahedron).

Figure 7 shows a further embodiment in which nine dual-facet square puzzle pieces (710... 790, 750 is centrally located) form a dual-facetted 3 x 3 (N=M=3) grid. The target' solution of this puzzle requires that not only the indicia be matched on the front facet of each puzzle piece but also the rear facet. In a typical implementation the puzzle pieces could, for example, be held vertically in a frame allowing the puzzler to easily view both facets of each puzzle piece. With the puzzle using multi-facet puzzle pieces the permutation equation is no longer valid. The modified permutation equation (including F) is given by Pt. F' E, which can be simplified to P!.(E.F. If, for example, P=4, E=4 and F=2 (dual-facet) the number of pennutations to be considered is now 4t.(4.2)4 = 98,304 (compared with 6,144 for the same single-facet configuration). Again using constraints and indicia interchange different indicia sets can be produced with varying degrees of difficulty -even whilst considering the requirement to match both front and rear facets of the puzzle pieces.

Figure 8 shows a further embodiment in which eight six-facetted hexahedron (cube) shaped puzzle pieces (810... 880, note 850 is hidden) form a larger hexahedron (cube) shaped puzzle, when configured in a 2 x 2 x 2 (X, Y and Z) arrangement. The number of permutations (P8, E4, F=6) is given by 8!.(6*4? = 4.438x1015, the puzzle has 24 (6 x 4) solutions due to rotational symmetry in three-dimensions. Of significant note is that the IAA has determined the indicia set to produce an unique relative placement of the eight cube shaped puzzle pieces, when considering the matching of indicia in three-dimensions -only considering the indicia that are visible on the outer side (facet) of the target' cube (hexahedron).

Claims

A puzzle game consisting of two or more moveable regular polygon based puzzle pieces (tiles), with a single symmetric facet having three or more edges and each edge ascribed with a single indicia, such that when said puzzle pieces are placed in an unique relative positional and rotational configuration, so that adjacent indicia of two different puzzle pieces match, a required two-dimensional configuration/pattern (the target') is achieved.
2. A puzzle game consisting of two or more moveable polyhedra based puzzle pieces, with two or more symmetric facets having three or more edges and each edge ascribed with a single indicia, such that when said puzzle pieces are placed in an unique relative positional and rotational configuration, so that adjacent indicia of two different puzzle pieces of their front and rear viewable fcets match, a required configuration/pattern (the target') is achieved.
3. A puzzle game consisting of two or more moveable polyhedra based puzzle pieces, with two or more symmetric facets having three or more edges, with each facet ascribed with a centmlly located indicia and each edge ascribed with a single indicia, such that when said puzzle pieces are placed, using only the facets of puzzle piece's with a matching centrally located indicia, in an unique relative positional and rotational configuration, so that adjacent indicia of two different puzzle pieces match, two or more different configurations/patterns (targets') can be achieved, the selection of which target' is required is chosen by means of a random process.
4. A puzzle game consisting of two or more moveable regular polygon based puzzle pieces, with one or more symmetric facets having three or more edges and each edge ascribed with a single indicia, such that when said puzzle pieces are placed in an unique relative positional and rotational configuration, so that adjacent indicia of two different puzzle pieces match, a required surface of a regular or irregular polyhedra (the target') is achieved.
5. A puzzle game consisting of two or more moveable regular polyhedra based puzzle pieces, with multiple symmetric facets having three or more edges and each edge ascribed with a single indicia, such that when said puzzle pieces are placed in an unique relative positional and rotational configuration, so that adjacent indicia of two different puzzle pieces match in three-dimensions, a required three-dimensional regular or irregular polyhedra (the target') is achieved.
6. A puzzle game as outlined in claims 2 and 5 in that there is a means of support or inter-connection of the puzzle pieces allowing said puzzle pieces to be positioned vertically, aiding the viewing of the viewable front and rear facets of each puzzle piece.
7. A puzzle game as outlined in claims 1 to 5 in which the indicia ascribed on each puzzle piece's edge and any indicia ascribed in a centrally located position on a puzzle piece's facet are implemented as an alphanumeric character, a solid or broken colour, a pattern consisting of two or more colours, a pattern of raised dots suitable for blind or partially sighted puzzlers, a pattern consisting of one or more shapes or symbols or combinations of the aforementioned.
8. A puzzle game as outlined in claims 1 to 5 in which the total number of puzzle pieces matches or exceeds the number of puzzle pieces required in solving the puzzle (the target').
9. A puzzle game as outlined in claims 1 to 5 in which one or more of the puzzle pieces have a fixed position and orientation.
10. A puzzle game as outlined in claims 1 to 5 in which one or more moveable puzzle pieces, identified with a centrally ascribed indicia on one or more facets, has to be positioned in a specified position and/or orientation.
11. A puzzle game, as outlined in the preceding claims, in which by the addition of a passive or electronic means, to each of the puzzle piece facets, allows the unique identification of a particular puzzle piece, it's position in the puzzle and it's orientation so that feedback to the puzzler can be provided, indicating that the puzzle has been solved or to supply continuous or upon request hints to the puzzler.
12. A puzzle game, as outlined in the preceding claims, in which the puzzle game is implemented in software and/or fixed or programmable logic so that the puzzle game can be played either on a personnel computer, a games console, a hand-held dedicated gaming device or a mobile communications device.