Abstract: A cube packing comprises two truncated pyramids configured for a packing mode and a stand mode. In the packing mode, each pyramid touches three faces. In the stand mode, a first pyramid lays on a substantially horizontal surface, a second pyramid rests on the first pyramid and a large cube resides in the second pyramid while having a vertex pointing upwards. The large cube consists of eight small cubes, which in turn consist of a first group of eight pieces and a second group of 16 pieces. Each small cube includes one piece of the first group and two pieces of the second group. The eight pieces of the first group include at least three pieces different from each other at least by color, and may include at least three pieces different from each other at least by shape. In addition, the 16 pieces of the second group include at least three pieces different from each other at least by shape, and may include at least three pieces different from each other at least by color.

Abstract: A cube packing comprises two truncated pyramids configured for a packing mode and a stand mode. In the packing mode, each pyramid touches three faces. In the stand mode, a first pyramid lays on a substantially horizontal surface, a second pyramid rests on the first pyramid and a large cube resides in the second pyramid while having a vertex pointing upwards. The large cube consists of eight small cubes, which in turn consist of a first group of eight pieces and a second group of 16 pieces. Each small cube includes one piece of the first group and two pieces of the second group. The eight pieces of the first group include at least three pieces different from each other at least by color, and may include at least three pieces different from each other at least by shape. In addition, the 16 pieces of the second group include at least three pieces different from each other at least by shape, and may include at least three pieces different from each other at least by color.

Abstract: The invention provides a puzzle game comprising a background defining a graph (40, 80, 1 10), having nodes (44, 46, 82, 84) connected by lines, or a diagram having sites or nodes, and elements (51-59, 102, 104, 106) having a plurality of indices disposed thereon. The background is metallic or non-metallic board, and the game might be implemented on an electronic game apparatus or on a computer system. The elements are removably disposable on the graph nodes. The indices are of one of up to three distinct types. An arrangement of the elements disposed on the graph nodes defines a magic graph so that patterns of the magic graph are characterized by having a first relationship and a second relationship. The graph may be a triangle, a hexagram, a heptagram, a tri-trapezoid shape, or other shape which is substantially symmetric under a rotation. The indices might be numbers, colors, domino-like groups of dots, symbols, or a geometric structure.

Abstract: It is provided a game system which includes 36 indexed elements, and a pattern structure having six hexagonal patterns arranged in a cycle such that each pattern has two neighboring patterns. Each element has an index of six different indexes. Two or more indexed elements are associated with each index. Each pattern has two sites shared with each of the two neighboring patterns, and one non-shared site. The system includes a cube for selecting a sub-set of 24 indexed elements. In a number version, the different indexes constitute a single arithmetic series. In a two-party game version, 12 pattern sites are associated with a first site index and 12 pattern sites are associated with a second index, six of the sites having the first site index and six of the sites having the second site index are shared sites, and the other sites are non-shared sites. A computerized two party game includes means for prohibiting a player from disposing an indexed element on a pattern site already having that indexed element.

Abstract: A puzzle game includes a first and a second group of several pieces each. Several assemblies of pieces may be selected of the two groups. Three pieces of the first group are different from each other by the piece shape. Each of the pieces of the second group of pieces are different in shape from each of the pieces of the first group. Each of the assemblies forms an object, which objects are externally the same. Each of the different assemblies includes at least one piece of the first group and at least one piece of the second group. The formed objects are two or three dimensional objects. Preferably, each of the formed objects consists of identical cells. For example, the first and second groups consist of respectively three and six pieces. Each of three assemblies includes one piece and two pieces of the respective first and second groups.

Abstract: It is disclosed an educational arithmetic game set having a board game. The board game includes four neighboring rectangles around a central rectangle, twelve corner nodes on corners of the four neighboring rectangles, and twelve indexed elements for disposing on the twelve corner nodes. Each rectangle having four nodes, whereas two nodes are shared by the each rectangle and a neighboring rectangle, and two nodes are associated with only the each rectangle. The twelve indexed elements consisting of a four groups of two to four identical elements, each element in a group is indexed by a number in the range 1-4. The twelve indexed elements may be disposed on the twelve corner nodes, such that a sum of numbers associated with the four elements disposed on respective four nodes of each rectangle is the same sum for each rectangle. Each group of two to four identical elements may have a unique color not shared with other group of two to four identical elements. The board game may be included in a computer game.

Abstract: A puzzle game includes a first and a second group of several pieces each. Several assemblies of pieces may be selected of the two groups. Three pieces of the first group are different from each other by the piece shape. Each of the pieces of the second group of pieces are different in shape from each of the pieces of the first group. Each of the assemblies forms an object, which objects are externally the same. Each of the different assemblies includes at least one piece of the first group and at least one piece of the second group. The formed objects are two or three dimensional objects. Preferably, each of the formed objects consists of identical cells. For example, the first and second groups consist of respectively three and six pieces. Each of three assemblies includes one piece and two pieces of the respective first and second groups.

Abstract: It is provided a game system which includes 36 indexed elements, and a pattern structure having six hexagonal patterns arranged in a cycle such that each pattern has two neighboring patterns. Each element has an index of six different indexes. Two or more indexed elements are associated with each index. Each pattern has two sites shared with each of the two neighboring patterns, and one non-shared site. The system includes a cube for selecting a sub-set of 24 indexed elements. In a number version, the different indexes constitute a single arithmetic series. In a two-party game version, 12 pattern sites are associated with a first site index and 12 pattern sites are associated with a second index, six of the sites having the first site index and six of the sites having the second site index are shared sites, and the other sites are non-shared sites. A computerized two party game includes means for prohibiting a player from disposing an indexed element on a pattern site already having that indexed element.

Abstract: It is disclosed a board game including patterned graph boards, sets of grouped index elements, and disparate successful arrangements. Each patterned graph board has graph patterns associated with several nodes of the same number for all the graph patterns. Two nodes of a given graph pattern are shared by two graph patterns. Each set of grouped index elements includes three or more groups, each having two or more identical index elements of certain numerical value unique to the each group. The disparate successful arrangements are successful arrangements that differ from each other by an arrangement result value, or by being a Latin arrangement, and by being associated with certain patterned graph board. The successful arrangement has an arrangement result value, the same for all graph patterns of a given patterned graph board under a given pattern operation.

Abstract: The invention provides a puzzle game comprising a background defining a graph (40, 80, 110), having nodes (44, 46, 82, 84) connected by lines, or a diagram having sites or nodes, and elements (51-59, 102, 104, 106) having a plurality of indices disposed thereon. The background is metallic or non-metallic board, and the game might be implemented on an electronic game apparatus or on a computer system. The elements are removably disposable on the graph nodes. The indices are of one of up to three distinct types. An arrangement of the elements disposed on the graph nodes defines a magic graph so that patterns of the magic graph are characterized by having a first relationship and a second relationship. The graph may be a triangle, a hexagram, a heptagram, a tri-trapezoid shape, or other shape which is substantially symmetric under a rotation. The indices might be numbers, colors, domino-like groups of dots, symbols, or a geometric structure.