GB2454538A

GB2454538A - An edge-matching puzzle game with more than one indicia per edge

Info

Publication number: GB2454538A
Application number: GB0722198A
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: GB0722198D0

Abstract

A puzzle game consisting of two or more homogeneous single or multi-facet puzzle pieces, each facet having three or more edges and each edge ascribed with two or more indicia. Each 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 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 or more adjacent puzzle piece(s) 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 in which 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 puzzle game. 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 2454538

A PUZZLE GAME WITH MULTIPLE ENHANCED PUZZLE PIECES

This invention relates to a puzzle game consisting of two or more single or multi-facetted puzzle pieces with two or more indicia 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 located adjacent 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 process (allocation), 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 sot utions or that the allocation of indicia is unique (it is possible for multiple tiles to have the same indicia set). In summary the game although challenging is significantly less demanding than if the game included rotation of the puzzle pieces and guaranteed an unique solution.

The mathematical work of Jorge Rezende has been published in the papers entitled "On the Puzzles with Polyhedra and Nwnbers" and "Puzzles with Polyhedra and Permutation Groups", available via the web site of the Mathematical Group of the University of Lisbon (http:1/gfm.cii. fc. ul. ptfMembersflR.pt PT. html). The publications cover the mathematical methods behind using polygonal plates (tiles), with 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 key feature of the two-highlighted puzzle games is that both utilise puzzle pieces with a single indicia ascribed per edge. This means that when matching indicia, of adjacent puzzle pieces, it is required, at most, to match one puzzle piece to one other.

If the number of indicia per edge were increased to two, for example, a maximum of three puzzle pieces would be involved in the matching. It follows that the maximum number of puzzle pieces that can be matched for a given number of indicia per edge is I + the number of Indicia -although geometric restrictions will limit actual puzzle configurations (ability to actually form puzzle configurations from regular polygons).

The family of puzzle games described by this patent solves the limitations in the two-highlighted puzzle games to produce a set of challenging puzzle games in which the indicia allocation is such there is an unique relative placement' of the puzzle pieces that achieves the required target' configuration. In addition this patent covers puzzle games, with two or more indicia ascribed per edge and with similar sized/shaped puzzle pieces, 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; * 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; * 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 hexahedron brick' shaped puzzle pieces (using only the 4 similar brick' shaped sides of the hexahedron) to form four different two-dimensional Diamond' based puzzles, where a centrally positioned indicia is used to differentiate which facet contributes to which puzzle game. A multi-sided dice could be used to randomly select which of the puzzles (four in this example) the puzzler is to solve; * multi-facet puzzle pieces, which can be combined to form larger regular or irregular polyhedra, e.g. the use 4 hexahedron based puzzle pieces, arranged to form a three-dimensional stack', forming a larger hexahedron.

In all of the above puzzles the objective of the puzzler is to match the edge-ascribed indicia of 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 i possible positional and rotational permutations of the puzzle pieces, guarantees the solution (or target' configuration) requires an unique relative Dlacement 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 (Nr=M=2) grid based puzzle using 4 single-facet square based tiles, with a single indicia ascribed per edge. 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 a single facet N x M (N=M=2) grid based puzzle using 4 single-facet square based tiles, with dual indicia ascribed per edge and the matching of indicia restricted to piece-to-piece. 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 3 shows a single facet diamond' shaped puzzle using 4 single-facet square based tiles, with dual indicia ascribed per edge and the matching of indicia is enhanced so that both piece-to-piece and piece-to-multi-piece matching is required. The allocation of the indicia (to each tile) is such an unique solution exists for the relative position and rotation of the 4 square tiles, whilst minimising the number of different indicia used.

Figure 4 shows a single facet triangular based puzzle using 4 single-facet triangular based tiles, with dual indicia ascribed per edge and the matching of indicia is restricted to piece-to-piece. The allocation of the indicia (to each tile) is such an unique solution exists for the relative position and rotation of the 4 triangular tiles, whilst minimising the number of different indicia used.

Figure 5 shows a single facet star' based puzzle using 7 single-facet triangular based tiles, with dual indicia ascribed per edge and the matching of indicia is enhanced so that both piece-to-piece and piece-to-multi-piece matching is required. The allocation of the indicia (to each tile) is such an unique solution exists for the relative position and rotation of the 7 triangular tiles, whilst minimising the number of different indicia used.

Figure 6 shows a single facet diamond' based puzzle using 4 single-facet brick' shaped tiles, with dual indicia ascribed per edge and the matching of indicia only requires piece-to-multi-piece matching. The allocation of the indicia (to each tile) is such an unique solution exists for the relative position and rotation of the 4 brick' shaped tiles, whilst minimising the number of different indicia used.

Figure 7 shows a single facet diamond' based puzzle using 9 single-facet brick' shaped tiles, with dual indicia ascribed per edge and the matching of indicia only requires piece-to-multi-piece matching. The allocation of the indicia (to each tile) is such an unique solution exists for the relative position and rotation of the 9 brick' shaped tiles, whilst minimising the number of different indicia used.

Figure 8 shows a dual-facet diamond' based puzzle using 9 dual-facet brick' shaped puzzle pieces with dual indicia ascribed per edge and the matching of indicia requires only piece-to-multi-piece matching. The allocation of the indicia (to each puzzle piece) is such an unique solution exists for the relative position and rotation of the 9 brick' shaped puzzle pieces, whilst minimising the number of different indicia used and, importantly, the indicia of adjacent edges on both front and rear facets are required to be matched.

Figure 9 shows a multi-facet stacking' based puzzle using 4 six-facet puzzle pieces (using only the four vertical sides of a each hexahedron) with dual indicia ascribed per edge and the matching of indicia requires piece-to-piece matching. The allocation of the indicia (to each puzzle piece) is such an unique solution exists for the relative position and rotation of the 4 puzzle pieces, whilst minimising the number of different indicia used and, importantly, the indicia of adjacent edges on all four facets (front, left-hand side, rear and right-hand side) are required to be matched.

Figure 10 shows a single facet parallelogram' based puzzle using 6 single-facet brick' shaped tiles, with three indicia ascribed per edge and the matching of indicia only requires piece-to-multi-piece matching. The allocation of the indicia (to each tile) is such an unique solution exists for the relative position and rotation of the 6 brick' shaped tiles, whilst minimising the number of different indicia used.

In figure 1, four single-facet square based puzzle pieces (tiles) form a 2 x 2 (NM=2) grid based puzzle. On each edge of each tile (110, 120, 130 and 140) a numerical indicia (111... 114, 121... 124, 131... 134 and 141... 144) has been allocated, by an IAA, such that there is an unique relative placement (considering possible positional and rotational permutations) of the puzzle pieces to 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. Of particular interest is that the matching of the indicia, on the edges of adjacent puzzle pieces, only involves two puzzle pieces or is piece-to-piece.

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 puzzle pieces that could be positioned in position A', and that each piece could be in any of four rotational positions (equal to the number of edges). If P is the number of puzzle pieces, E the number of edges each puzzle piece has (and hence the number of indicia) and F the number of facets (of each puzzle piece, as F=1 in this case it is ignored) the number of possible permutations for position A is given by P. E. If piece 110 was positioned in position A' (in any rotational state) the puzzler would have to find a 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 pennutations is now given by (r -i). E. If the puzzler continues to find pieces that match for positions C' and D' the puzzler (again ignoring pieces which the indicia do not match) would eventually have to consider (. ( -i). ( -2). (r -3)). (E E E* E) or P!*EpositionaI and rotational permutations to find the target' solution. With P=4, E4 (F= 1) the total number of positional and rotational permutations that the puzzler may have to consider would be 4!*4 = 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 permutation 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. To calculate the number of actual test cases a search-based algorithm 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 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 LAA does produce possible' clues to the solution (especially if numerical indicia are utilised) as the puzzler could guess that the indicia 1' is likely to be used in the top left-hand corner. Applying an interchange (for example 1 -3, 2-' 1, 3-+4 & 4-2) of indicia would remove this dependency -although in practice the number of puzzle pieces has to be higher than 4 to produce useable results.

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 limit the number of occurrences an indicia is (a) used in the whole puzzle (JMJ( PUZZLE), (b) used on a single puzzle piece (I.x_PcE) considering all facets and edges and (c) used on a puzzle piece's facet (I FAcEr). 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 an 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 2 shows an embodiment in which four dual-indicia ascribed per edge square single-facet puzzle pieces (or tiles) form a 2 x 2 (N=M=4) grid-based puzzle (the target' configuration). As with the puzzle shown in Figure 1 the matching of indicia of adjacent puzzle pieces still only involves two puzzle pieces (is piece-to-piece), despite having twice as many indicia per edge.

Figure 3 shows an embodiment, which is of particular interest to this patent, in which four dual-indicia ascribed per edge square single-facet puzzle pieces (or tiles) form a diamond' shaped puzzle (the target' configuration). Analysing the configuration, puzzle pieces 310 and 340 are matched by the four 1' centrally located indicia (dashed oval) using standard' piece-to-piece matching. Puzzle pieces 310, 320 & 340, on the other hand, are matched by the set of four 1' indicia (dashed oval) in a configuration requiring a piece-to-multi-piece matching. Puzzle pieces 310, 330 & 340 also require a piece-to-multi-piece matching, in this case using the indicia pairs 1' and 2' (dashed oval). In both of the piece-to-multi-piece matchings three puzzle pieces are involved -in general the maximum number of puzzle pieces that can be matched for a given indicia/edge configuration is I + I (where I is the number of indicialedge).

Figure 4 shows an embodiment in which four (410.. .440) dual-indicia ascribed per edge triangular single-facet puzzle pieces (or tiles) form a triangular-based puzzle (the target' configuration). As with the puzzle shown in Figure 1 the matching of indicia of adjacent puzzle pieces only involves two puzzle pieces or uses piece-to-piece matching.

Figure 5 shows an embodiment, which is also of particular interest to this patent, in which nine (510... 590) dual-indicia ascribed per edge single-facet triangular shaped puzzle pieces (or tiles) form a star' based puzzle (the target' configuration). Analysmg the configuration, puzzle pieces 520 and 530 are matched by the four I' indicia in a standard piece-to-piece matching. Other piece-to-piece matching also include the set of four I' indicia matching puzzle pieces 530 and 540 and the indicia pairs I' and 2' that match 530 and 570. Puzzle pieces 510, 520 and 540, on the other hand, are matched by the set of four 1' indicia in a configuration requiring a piece-to-multi-piece matching. Puzzle pieces 540, 560 & 570 and the pieces 510, 520 & 550 also require a piece-to-multi-piece matching of indicia. As with the configuration shown in figure 3 a maximum of three puzzle pieces are involved in the piece-to-multi-piece matching.

Figure 6 shows a further embodiment, which is of special interest to this patent, in which four single-facet brick' shaped puzzle pieces (610.. .640) form a diamond' shaped puzzle. The JAA has allocated the indicia so that there is an unique relative position of the puzzle pieces to yield the target'. Unlike the previous dual-indicia ascribed per edge based puzzle pieces the puzzle requires the sole use of the piece-to-multi-piece matching of indicia. Again three puzzle pieces are required in each piece-to-multi-piece matching.

Figure 7 shows a further embodiment in which nine single-facet brick' shaped puzzle pieces (710.. 790) form a larger diamond' shaped puzzle. The IAA has allocated the indicia so that there is an unique relative position of the puzzle pieces to yield the target'. As per Figure 6 the puzzle requires the use of the piece-to-multi-piece matching of indicia.

Figure 8 shows a further embodiment in which nine dual-facet brick' shaped puzzle pieces (810... 890) to form a diamond' shaped puzzle configuration. The target' solution of this puzzle requires that not only the indicia be matched on the front facet of the puzzle pieces but simultaneously also the rear facet. Again only piece-to-multi-piece matching of indicia is utilised, with the enhancement of matching indicia on both facets (front-to-front & rear-to-rear). 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 P! 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 permutations to be considered is now 4!.(4.2) = 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 when considering the requirement to match both front and rear facets of the puzzle pieces.

Figure 9 shows a further embodiment in which four (910... 940) six-facetted brick' shaped puzzle pieces (only the four vertical sides of each hexahedron are utilised) are used to form a stacking' based puzzle. The objective of the puzzle is to match simultaneously the indicia on all four sides of each puzzle piece and position the puzzle piece vertically to form a stack'.

The number of permutations (P=4, E=4, F=4) is given by 4!.(4.4) 1.5728x106, the puzzle has 2 solutions due to rotational symmetry in three-dimensions (top-to-bottom & bottom-to-top). Of significant note is that the IAA, in this case, has determined the indicia set to produce an unique relative placement of the four six-facetted brick' shaped puzzle pieces, when considering the matching of indicia in three-dimensions.

Figure 10 shows an embodiment, which is also of particular interest to this patent, in which six (1010... 1060) triple-indicia ascribed per edge single-facet brick' shaped puzzle pieces (or tiles) form a parallelogram' based puzzle (the target' configuration). Analysing the configuration, puzzle pieces 1020 & 1040 are matched by the four 1' indicia in a standard piece-to-piece matching. Other piece-to-piece matching also include the indicia pairs 1' and 2' matching puzzle pieces 1030 & 1050. Puzzle pieces 1010, 1030 and 1040, on the other hand, are matched by the six 1' indicia in a configuration requiring piece-to-multi-piece matching. Puzzle pieces 1030, 1040 & 1060 and 1010, 1020 and 1040 (ensuring piece 1040 is correctly positioned/orientated) also require a piece-to-multi-piece matching of indicia. As with the configuration shown in figure 3 a maximum of three puzzle pieces are involved in the piece-to-multi-piece matching.

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 two or more indicia, such that when said puzzle pieces are placed in an unique relative positional and rotational configuration, so that adjacent indicia of two or more 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 two or more indicia, such that when said puzzle pieces are placed in an unique relative positional and rotational configuration, so that adjacent indicia on the front and rear viewable facets of two or more different puzzle pieces 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 centrally located indicia and each edge ascribed with a two or more 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 or more 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 as outlined in claims 1 to 3 in which the puzzle game consists of single or multi-facetted puzzle pieces ascribed with two or more indicia per edge and puzzle pieces ascribed with a single indicia per edge.
5. A puzzle game as outlined in claim 2 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.
6. A puzzle game as outlined in claims 1 to 4 in which the indicia inscribed 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.
7. A puzzle game as outlined in claims 1 to 4 in which the total number of puzzle pieces matches or exceeds the number of puzzle pieces required in solving the puzzle (the target').
8. A puzzle game as outlined in claims 1 to 4 in which one or more of the puzzle pieces have a fixed position and orientation.
9. A puzzle game as outlined in claims I to 4 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.
10. 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.
11. 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.