Multisided Value-coded Puzzle Pieces And Supports Therefor

Abstract

A puzzle is provided in which identical planar multiside puzzle pieces carrying a value taken from M possible values at each one of its apices. A support which is preferably a polyhedron is provided and has portions adapted to receive the pieces such that the completed puzzle formed by the pieces arranged on the portions of the polyhedron is substantially that of the polyhedron. According to the preferable rules of the puzzle, the pieces are to be placed on the support in such a manner that in each of the groups of juxtaposed apices, the value carried by each apex is the same as that carried by each of the other apices juxtaposed thereto. Further, the number of puzzle pieces is preferably limited so that all the combinations of M values taken N by N are produced once and only once by the number pieces.

Description

The present invention relates to a puzzle which when complete forms a three-dimensional figure from substantially planar members. The present invention is a further development of the puzzle theory presented in my French Pat. No. 1,582,023.

The present invention extends the theory set forth in that patent to three-dimensional space enclosing figures. It will be appreciated that such a development has the effect of increasing the challenge of the game in that the number of possibilities which must be considered in arranging the pieces is substantially enhanced for a given number of pieces used.

According to said French Patent a given number of polygonal pieces with N apices all having the same dimensional and polygonal shape are provided and are arranged in side-by-side relation in completing a given planar puzzle silhouette. Each such piece is provided at each of its apices with any one of M values and in completing the puzzle according to the rules, apices carrying the same values are arranged juxtaposed to one another. In this respect the puzzle resembles the conventional game of dominoes.

Further according to said French Patent at least one group I of polygonal pieces with N polygonal pieces with N apices all having the same dimensions and the same polygonal shape are provided in which each apex of each pieces carries in a conventional manner a value taken from M possible values arranged following a predetermined convention order, the N values carried by the N apices of the same piece forming a sequence to be read following a predetermined conventional direction of reading and the number of pieces considered being just sufficient for all the combination of M values taken N by N to be produced once and only once by the whole of the sequences carried by the pieces of said group following said direction of reading and respecting the order of said values.

An object of the present invention is a puzzle which employs the same types of pieces as in the said French Patent in combination with means for supporting the pieces in such a way as to form a three-dimensional space-enclosing figure when complete.

An aspect of the present invention consists in a puzzle of the type comprising at least one group of substantially planar multisided pieces, each piece having N apices and substantially identical dimensions and configuration, each apex of each piece carrying a value taken from M possible values arranged in a predetermined order, in combination with support means adapted to receive at least some of the pieces in side-by-side relationship so that the pieces form a space-enclosing three-dimensional figure when the puzzle is completed.

Preferably, the number of pieces of said group are limited so that all the combinations of M values taken N by N are produced once and only once by the pieces of the group.

Preferably, the means for supporting the pieces is a regular polyhedron support, for example, a regular tetrahedron, a cube, an irregular polyhedron support such as truncated tetrahedron with a reentrant portion, or other space-enclosing figure in which one or more of the sides is not adapted to receive pieces.

Preferably, the pieces are temporarily secured to the support by securing means such as by forming the pieces at least partially of a magnetic material and the corresponding portions on the support of a ferromagnetic material, or vice versa. In such case the pieces may be easily reversible to provide mirror-image pieces.

According to one modification, two or more supports may be secured together by any suitable means in order to provide a combined support structure, for example, supporting a first regular tetrahedron support on the face of a second regular tetrahedron whose edges are three times those of the first regular tetrahedron.

Various other features and characteristics of the invention will be brought in the description of the embodiments which follows.

The invention will now be described with respect to the accompanying drawings which show by way of example various embodiments according to the invention, wherein:

FIG. 1 shows a perspective view of a regular tetrahedron support with triangular faces with puzzle pieces superposed thereon;

FIG. 2 shows a perspective view of a cube support with puzzle pieces superposed on its faces;

FIG. 3 shows a perspective view of a regular tetrahedron in which each of its triangular faces is again divided into four triangular portions.

FIG. 4A shows an equilateral triangular puzzle piece for use with the support shown in FIG. 3;

FIG. 4B shows the reverse side of the puzzle piece shown in FIG. 4A;

FIG. 5 shows the tetrahedron support of FIG. 3 with pieces such as shown in FIG. 4 superposed on particular portions thereof;

FIG. 6 shows a perspective view of a tetrahedron support with a reentrant apex;

FIG. 7 is a sectional view taken along the line VII--VII in FIG. 6 with puzzle pieces superposed thereon;

FIG. 8A shows a perspective view of a tetrahedron support such as shown in FIG. 3;

FIG. 8B shows a perspective view of a tetrahedron support such as shown in FIG. 1;

FIG. 8C shows a perspective view of a combined support in which the support shown in FIG. 8B is supported on one of the faces of the support of FIG. 8A;

FIG. 9 shows a plan view of an alternative embodiment of a puzzle piece in position in a portion of the support of FIG. 3;

FIG. 10 shows a perspective view of a cube support with the faces thereof divided into four squares and a puzzle piece superposed on one of the portions thereof;

FIG. 11 shows a section taken along the line XI--XI in FIG. 10 illustrating the piece being put into position;

FIG. 12 shows a perspective view of an alternative embodiment of the support for use with square puzzle pieces; and

FIG. 13 shows a perspective view of a regular icosahedron support with a piece superposed on one of its triangular sides.

For the sake of clarity, the following convention will be adopted: the whole of the numerical values shown at the apices of a piece will be represented by the sequence of the three indicia of its three apices, starting with the smallest numerical value and reading the other values in the counterclockwise direction (which defines the order of these values and their reading direction). The piece shown diagrammatically in FIG. 4A is thus (1,3,2).

The number and distribution of the values shown at the apices of the pieces, and the number of these pieces, are established as follows: the table is prepared of the various possible combinations of numerical values which can be marked on the apices in order to define only the required number of pieces, so that all the combinations may be presented the same number of times, for example once. The following table is given as an example: ---------------------------------------------------------------------------

000 (100) (200) (300) 001 (101 (201) (301 002 (102) (202) (302 003 (103 (203 (303) (010 (110) (210) (310) 011 111 (211) (311) 012 112 (212 (312) 013 113 (213) (313) (020) (120) (220) (320) (021)+ (121) (221) (321) 022 122 222 (322) 023 123 223 (323) (030) (130) (230) (330) (031)+ (131) (231) (331) (032)+)+ (132)+ (232) (332) 033 133 233 333 __________________________________________________________________________

In the above table there have been shown all the possible combinations of four different values (M = 4 represented by "zero," "one" "two" and "three" and taken in combinations of three by three. It is noted that any other indicia may be used, for example four different colors, four different designs, letters.

By reading the above table from the top to the bottom for the first left-hand column, and then for the second column, and so on, there have been put in brackets the combinations already shown, taking into account the reading order of the equilateral triangle. Thus, the sequence (0,1,0) would correspond to a piece which already exists under the sequential denomination (0,0,1) since by simply rotating through 120.degree., the same triangular piece corresponds to these two sequences. It will be derived from this table that only 20 pieces will be required to have available pieces which are all different by four values zero, one, two and three carried at the apices; these 20 pieces constitute a group A of the puzzle pieces.

The said table also shows the existence of four pieces in which the three numerical values are also shown on another piece, but in a different order, and such that no rotation provides an equivalent; thus, the sequential distribution (0,2,1) groups together three values already shown in the distribution (0,1,2), but the two pieces cannot be superimposed. The same thing is true for any triangle the apices of which carry three values different from each other, namely in group A, the triangles (0,1,2), (0,1,3), (0,2,3) and (1,2,3,). The 20 triangles of group A can then be completed by four triangles corresponding respectively to the sequences (0,2,1), (0,3,1), (0,3,2) and (1,3,2), these four additional pieces called mirror-image pieces, constitute a group B according to the invention; they are indicated in the said table by the + sign.

By way of example, FIG. 4A shows the piece (1,3,2) of group A and FIG. 2B the piece (1,2,3 which is the mirror image of the preceding piece and belongs to group B and is formed by simply turning over the piece if it is reversible.

Of the 24 triangular pieces forming the pieces thus defined form a combined group A-B in which the following features are noted.

There are four puzzle pieces called "triples" in that they each carry the same value at each one of the apices.

Twelve puzzle pieces called "doubles" in that they have the same value in two of their three apices; and

Eight pieces called "singles" in that all the three values at their apices are different. These eight single pieces can be included in two categories those of Group A and those of Group B which are the so-called mirror-image or reverse sides in the case of reversible pieces.

The playing of the game according to the invention briefly explained in the preamble of the present application may necessitate elaborate reasoning, more developed than those of the conventional game of dominoes, and facilitated by the logic of distribution of the present puzzle of the sequences of values carried by the pieces.

FIG. 1 shows the most elementary puzzle support according to the present application, i.e., a regular tetrahedron in which each of the faces is adapted to be covered by a single puzzle piece formed as an equilateral triangle, thus in total four pieces. The rules of the game require that all juxtaposed apices must bear the same value. Accordingly, at each corner of the tetrahedron the apices of three pieces are juxtaposed and each of these apices must bear the same value. A sample solution is indicated by the pieces 3, 3b, 3c in FIG. 1, the fourth piece 3d is not shown, i.e. piece 3a has the value sequence (0,2,3), piece 3b has the value sequence (1,3,2), the piece 3c has the value sequence (0,3,1 and piece 3d has the value sequence (0,3,1). There are, of course, other solutions. Certain pieces however cannot be used if the puzzle is going to be solved and completed. In particular, any of the triples, since all the other pieces would have to be either triples of the same value, but there exists only one triple of each value, or three identical doubles but again there are no identical doubles in the group of 24. It is however possible for example to solve the puzzle using two nonidentical doubles. It can also be logically deduced that the solution of such a puzzle is also not possible with a single double or three doubles; it is however, as seen above with regard to the sample solution possible with four singles.

The puzzle of FIGS. 3-5 is developed into a more challenging problem by the division of each of the faces of the tetrahedron into four equilateral triangular portions thereby requiring a total of 16 pieces to complete the puzzle. FIG. 3 shows a tetrahedron support 20 in which the sides 22 and 24 which are visible in FIG. 3 are divided into equilateral triangles 22a-d and 24a-d respectively. Each of these portions being adapted to receive and support a single puzzle piece of substantially the same shape and dimensions. Further, in the embodiment shown in FIG. 3 the entire tetrahedron is formed of sheet stainless steel. In such a case there need not be further differentiation between adjacent portions, such as 22a and 22b. This is not the case with other means for supporting the pieces as will be discussed infra.

FIG. 4A shows a puzzle piece suitable for use with the tetrahedron support of FIGS. 3 in that it has the same dimensions as that of the portions 22a-d and 24a-d. Further, the puzzle piece 23 is formed as a plate of magnetized material, preferably, ferrite in a rubber or plastics material binder. Similar plates in which all or a part thereof is magnetized can be used, for example comprising one or more magnets secured to a nonmagnetic puzzle piece.

The value indicia at the apices of the triangle are provided by dots or apertures preferably extending through the piece 23. The values may however be indicated in any desired manner by symbols, colors, numbers, letters or the like capable of providing distinguishable values at the apices. The piece 23 carries the values (1,3,2) according to the convention for reading the values set forth hereinabove.

FIG. 4b shows the reverse side 23' of the piece 23 shown in FIG. 4A. When the piece is turned to its reverse side 23' the value of the piece is changed to (1,2,3) according to the convention for reading the values. Further, the reverse side 23' is thus the equivalent of a mirror-image piece. Accordingly, with the use of reversible pieces, mirror-image pieces could be eliminated. Note also in this regard that no extra pieces are effected by the reversibility of the pieces since the reverse side of every piece is either identical to the front side of a piece or its mirror image. Also, the use of apertures for indicating the values is particularly useful where the reversibility is desired.

FIG. 5 illustrates the placing of the pieces 23 on the various portions of the faces 22 and 24 of the tetrahedron support 20 shown in FIG. 3. A first piece 23' as shown in FIG. 4B is positioned on portion 24c. A second piece 23b having the values (0,0,1) is positioned on the portion 24d in such a way that its apex carrying the value 1 is in position juxtaposed to the apex of the piece 23' carrying the value 1. A third piece 23c having the values (0,2,1) is then put into position on the portion 22c so that its apex carrying the value 1 is juxtaposed to the apices of pieces 23' and 23b and so its apex carrying the value 2 is in position juxtaposed to the value 2 of the piece 23'. It should be noted that the third piece 23c might have been positioned in portion 22d in such a case its value 0 would be juxtaposed to the value 0 of the piece 23b and value 1 of the piece 23c would be juxtaposed to the apex carrying the value 1.

FIG. 6 shows a modification of the tetrahedron support shown in FIG. 3 in that a pyramidal portion defined by the triangular portions 22d and 24d the portion 26d not shown in FIG. 3 is severed from the rest of the tetrahedron 20 and inverted therein forming a reentrant pyramidal portion of the same dimensions as the severed pyramidal portion. This same process could be carried out with respect to each of the apices of the tetrahedron 20 to form an entirely inverted structure. It should be noted that there are no substantial consequences in the solution of the puzzle with the support of FIG. 6 over that of the support of FIG. 3.

A section view of the tetrahedron of FIG. 6 with a reentrant portion is shown in FIG. 7. In this figure the structure of the support 20 is clearly illustrated and includes an interior layer 21 formed of a sheet of cardboard, pasteboard or nonmagnetic plastics material. A portions 28 of ferrite in a rubber of plastics material binder is secured to the cardboard support preferably by glueing or any other suitable mean. The puzzle pieces 23 for use with this puzzle support 20 will be formed of a magnetic material such as stainless steel. The inverse such as shown in FIGS. 1, 2, 3 and 5 is always possible in which case the pieces are formed of ferrite in a binder and the support formed of stainless steel preferably without the undersupport of cardboard as it will not be necessary.

A further modification of the tetrahedron support is illustrated in FIGS. 8A-C. FIG. 8A shows a tetrahedron support such as illustrated in FIG. 3. FIG. 8B shows a tetrahedron support as illustrated in FIG. 1. FIG. 8C shows a combined structure resulting from the securing of the tetrahedron 1 on one of the faces of the tetrahedron support 20. In this case the result of the puzzle is different than that of the tetrahedron support shown either in FIGS. 3-5 or 6 and 7 in that the combined puzzle support of FIG. 8 requires the use of 18 pieces and not 16 to cover its surfaces. Accordingly the point 27 on the combined structure will be the point at which the apices of seven rather than six triangles will have to carry the same value. Other solid figures may also be combined with the basic tetrahedron support structure to further challenge the players. Note that the combining of the support structure could be left to the player, the sole requirement being that all the pieces required by such a combined structure must be identical.

A further series of supports are possible by combining two pyramidal structures of the same shape and dimensions. For example two identical tetrahedrons of the type shown in FIG. 1 could be combined to form a hexahedron with equilateral triangular faces. Further, instead of the tetrahedron support of FIG. 1 a pyramid with a square base and equilateral triangular side faces were provided and connected to an identical pyramid along the square bases an octahedron support could be formed in which each of the eight faces adapted to receive a puzzle piece is formed as an equilateral triangle.

FIG. 13 shows a icosahedron support 60 in which the 20 sides are formed as equilateral triangles 62. An equilateral triangular piece 63 is placed in position on one of the sides 62 as shown in FIG. 13. The apices of the pieces are grouped in groups of five at each of the apices 66 of the icosahedron 60. The solution of this puzzle requires four triples, 12 doubles and four singles of which two are of group A and two are of Group B or mirror-image pieces.

Such an embodiment in view of its many sides and corresponding number of pieces required is suitable for playing with more than one person. In such a case the players could be required to place puzzle pieces on the support in consecutive order. In such a case each player could be given the same number of puzzle pieces to be held on a rack provided for this purpose to the conceal each players pieces from these of his opponents. The object of such a competitive puzzle could be for example the placement of one's pieces on the support before one's opponent keeping in mind the rules of the puzzle set forth hereinabove and respecting a certain consecutive playing order.

In the case of more than one player, identical supports could be provided for each player, and each player could pick pieces from a given number of pieces equal to or greater than the total number of pieces necessary for the puzzles of all of the players which may involve one or more groups as discussed hereinabove. For example, with two players each with a puzzle support such as shown in FIG. 1, each player could pick four pieces from the group of 24 pieces attempting to complete the puzzle therewith before his opponent and if a solution is not found with these pieces each player can exchange a piece for one of the remaining pieces and so on.

FIG. 9 shows a further modification of the puzzle pieces. According to this modification, a quadrilateral piece is provided which has two opposed 90.degree. angles and opposed 60.degree. and 120.degree. angles. Each such piece is one-third of the equilateral triangular piece 23 shown for example in FIG. 4A. Instead of the equilateral triangular pieces used in all of the embodiments of FIGS. 1 and 3-8, the quadrilateral pieces can be used. In such a case three times as many pieces will be necessary to complete the puzzle corresponding to any of the supports and many more combinations will have to be computed to solve the puzzle. Again in this embodiment, all the permutations and combinations can be calculated by the values on the four corners of the piece in order to deduce the group of 16 different pieces by their values.

In contrast to all the previous embodiments wherein the regular tetrahedron has been the basic element of the puzzle support, FIG. 2 shows a cube support 10. Accordingly, the pieces 13 are square and have a total of four indicia values corresponding to each corner. The cube 10 requires six such pieces to complete the puzzle and at each corner of the cube 10 meet the corners of three square pieces 13. The pieces 13a-c are put in place on the support 10, the values at each of the corners being the same. The cube 10 could be secured to a base in which case there would be only five available portions adapted to receive the pieces 13. Accordingly, the mental calculations for solving the puzzle are interesting in that at the upper corners the corresponding corners of three pieces will be juxtaposed while at the lower corners, at which the puzzle support engages the base, the corresponding corners of two pieces will be juxtaposed.

FIG. 10 shows a cube 40 such as shown in FIG. 2 wherein each of the square sides such as 42, 44, 46, of the cube is divided into four portions 42a-d, 44a-d, 46a-e which are themselves square. The three sides not seen in FIG. 10 are similarly divided into such portions thereby forming 24 portions on the surface of the cube for receiving corresponding square puzzle pieces 43, one of which being shown in position on portion 42a. It is noted relative to this puzzle support 40 the apices of three pieces 43 are juxtaposed at each corner of the cube and the apices four pieces 23 are juxtaposed at all the other points of juxtaposition.

FIG. 11 illustrates the putting into position of a piece 43 on the portion 42a of the cube support 40. In all of the previous embodiments the combination of magnetized pieces and magnetic portions or vice versa has been employed as means for supporting the pieces on the support. Other suitable means are of course possible, for example, that which is shown in FIG. 11. A projection 45 is preferably provided at the center of each piece and is formed or deformable plastics material and dimensioned to be e received in the cooperating recess 45a in the portion 42a. The piece 43 is secured simply by exerting a force in the direction indicated by the arrow in FIG. 11. In order to aid the removal of the piece means to grip the piece may be provided on the top of side surface thereof. Other suitable means of securing the pieces to the portions may also be provided.

FIG. 12 shows a three-dimensional space-enclosing support 50 formed of cubic elements and adapted to receive square puzzle pieces 53 on its square portions 52. The support 50 includes 25 portions 52. The entire support 50 is mounted on a base 51 which thereby eliminates from play all of the bottom faces of the lower row of cubic elements. A single cubic element 55 is surmounted on the central cubic element of the bottom row of elements. This cubic element 55 is analogous to the base supported modification of FIG. 2 discussed hereinabove. In this puzzle support 50 there are certain points such as at 56 at which three apices meet, other points such as 57 where two apices meet, other apices such as 58 where four apices meet and finally other apices such as 59 where five apices meet. Accordingly, the problems of permutations and combinations required to solve this puzzle is relatively complicated. This support can be easily modified at the will of the players by replacing the single cubic element 56 by a different structure formed of square portions 52.

A further possible modification of this support 50 can be effected by providing rectangular portions having nonequal sides such as for example with the ratio 2 to 1. Pieces similar to the portions thus modified would of course have to be provided.

Indeed there are many other possible varieties of supports which have not been illustrated but which fall within the scope of the invention. Particular attention is drawn to the possibility of forming a structure which has no "positive" portions composed entirely of so-called reentrant portions such as illustrated in FIGS. 6 and 7 with regard to one of the apices of the tetrahedron, this process could be employed at each of the apices thereof effecting a structure formed solely of ribs forming reentrant portions. This works particularly well with a 24 sided figure using again equilateral triangular pieces and portions.

A ferromagnetic compound in the form of a paint could be used in place of the magnetized material indicated hereinbefore. Such a paint is suitable for covering a nonmagnetic surface of cardboard, wood or plastics material to form either the pieces or the support.

The puzzle according to the present invention has uses as a teaching tool especially in the field of chemistry. In particular it is noted that amino acids present in proteins are of 20 or 24 in number associated with ribosomes in the form of regular icosahedrons such as described with regard to the embodiment of FIG. 13. Accordingly, such a puzzle could be used for demonstrative purposes with regard to the above.

The present invention is not intended to be limited to the embodiments and modifications shown and described herein but includes all equivalents, and variations falling within the scope of the appended claims.

Claims

I claim:

1. A puzzle of the type comprising at least one group of substantially identical and planar multisided puzzle pieces wherein each apex of each piece carries a value taken from M possible values, in combination with a support means adapted to receive at least some of said pieces in side-by-side relation so that when all the pieces adapted to be received by said support means are in place thereon, said pieces form a three-dimensional space-enclosing figure.

2. A puzzle as claimed in claim 1, wherein the support means for supporting at least some of the pieces of said group in side-by-side relation is such that the three-dimensional space-enclosing figure is a polyhedron.

3. A puzzle as claimed in claim 2, wherein the pieces are formed as regular polygon and the polyhedron as a regular polyhedron.

4. A puzzle as claimed in claim 2, wherein the pieces are formed as regular polygon and the polyhedron as an irregular polyhedron.

5. A puzzle as claimed in claim 4, wherein the irregular polyhedron has at least one reentrant apex adapted to receive puzzle pieces thereon.

6. A puzzle as claimed in claim 3, wherein the support means is a three-dimensional space-enclosing figure of substantially the same dimensions and shape as the three-dimensional space-enclosing figure formed by the pieces.

7. A puzzle as claimed in claim 6, wherein the support means is a body having portions of the same shape and dimensions as the pieces and adapted to receive the pieces thereon.

8. A puzzle as claimed in claim 7, wherein the pieces and the portions include cooperating means for securing the pieces in position on the portions of the support means.

9. A puzzle as claimed in claim 8, wherein the cooperating means comprise forming at least part of each portion and each piece of magnetic material.

10. A puzzle as claimed in claim 9, wherein the magnetic material for one of the pieces and the portions is ferrite in a binder.

11. A puzzle as claimed in claim 8, wherein the cooperating means comprise recesses and cooperating projecting portions adapted to be received matingly therein.

12. A puzzle as claimed in claim 1, wherein the support means comprises at least two polyhedrons adapted to be secured to one another thus forming a combined support.

13. A puzzle as claimed in claim 1, wherein the puzzle pieces have a value sequence comprising the values of each of its apices taken in a predetermined reading order and wherein the pieces are reversible thus effecting a certain number of additional pieces by their reversal owing to the predetermined reading order.

14. A puzzle as claimed in claim 1, wherein there are more than one identical support means and the number of pieces is sufficient for completing the puzzles of all the supports.

15. A puzzle of the type comprising at least one group of substantially identical and planar N-sided puzzle pieces wherein each apex of each piece carries a value taken from M possible values, the number of the pieces of said group being such that all the combinations of M values taken N by N are produced once and only once by the pieces of said group, in combination with a support means adapted to receive at least some of said pieces in side-by-side relation so that when all the pieces adapted to be received by said support means are in place thereon said pieces form a three-dimensional space-enclosing figure.

16. A puzzle as claimed in claim 12, further comprising at least one additional group of substantially identical and planar N'-sided puzzle pieces and each carrying a value taken from M' possible values, the number of pieces of said additional group being such that all the combinations of M' values taken N' by N' are produced once and only once by the pieces of said additional group.