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Three-dimensional logical cube

A three-dimensional logical cube has 6 faces in the same configuration of Rubik's Cube (trademark). A three-dimensional logical cube has an N×N array of cells on each face. Each cell on a three-dimensional logical cube has a numerical value, solid and hollow dots, solid dots, or shapes, on it. A 2×2×2 cube has four numbers from 1 to 4 on its face; a 2×2×2 cube has two solid dots and two hollow dots with the same color on its face (2×2×2 alternate embodiment); a 2×2×2 cube has 1 dot to 4 dots on its cell (2×2×2 alternate embodiment); a 2×2×2 cube have same kind of shape on its face (2×2×2 alternate embodiment); a 3×3×3 cube has nine combination numbers between 1 to 12 on its face; a 3×3×3 cube has nine numbers from 1 to 9 on its face (3×3×3 alternate embodiment); a 3×3×3 cube has either a blank cell or a dot on its face (3×3×3 alternate embodiment); a 3×3×3 cube have same kind of shape on its face (3×3×3 alternate embodiment); a 4×4×4 cube has sixteen numbers from 1 to 16 on its face; and a 5×5×5 cube has twenty-five numbers from 1 to 25 on its face; The present three-dimensional logical cube when successfully solved, for numerical cell cubes, all six faces, and nine rows (six rows for 3×3×3 cubes) of adjacent cells located on four adjacent faces (two adjacent faces for 2×2×2 cube and three adjacent faces for 3×3×3 alternate embodiment) will have difference numerical numbers on its cell (no two numbers are alike); for shape cube, all six faces will have same shape for each cell on the same face; for solid and hollow dot cube, any faces will have the two solid dots and two hollow dots on its for all six faces; for solid only dot cube (3×3×3), any two opposite faces will have total of seven dots for all six faces; and solid only dot (2×2×2), each cell on the same face has 1 dot, 2 dots, 3 dots and 4 dots for all six faces, and four adjacent cells located around two faces will have 1 dot, 2 dots, 3 dots and 4 dots on its cell. The present three-dimensional logical cube is more challenging than the Rubik's Cube (trademark) with 2×2×2 the simplest logical cube to 3×3×3 challenge, 4×4×4 more challenge, and 5×5×5 which is the most challenge logical cube to solve.
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