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.
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