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.
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