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A normal magic hexagon contains the consecutive integers from 1 to 3n 2 − 3n + 1. Normal magic hexagons exist only for n = 1 (which is trivial, as it is composed of only 1 cell) and n = 3. Moreover, the solution of order 3 is essentially unique. [1] Meng gives a less intricate constructive proof. [2]
Mathematically, edge-matching puzzles are two-dimensional. A 3D edge-matching puzzle is such a puzzle that is not flat in Euclidean space, so involves tiling a three-dimensional area such as the surface of a regular polyhedron. As before, polygonal pieces have distinguished edges to require that the edges of adjacent pieces match.
A pentacube puzzle or 3D pentomino puzzle, amounts to filling a 3-dimensional box with the 12 flat pentacubes, i.e. cover it without overlap and without gaps. Since each pentacube has a volume of 5 unit cubes, the box must have a volume of 60 units. Possible sizes are 2×3×10 (12 solutions), 2×5×6 (264 solutions) and 3×4×5 (3940 solutions ...
The Rubik's Cube is a 3D combination puzzle invented in 1974 [2] [3] by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube , [ 4 ] the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in the UK in 1978, [ 5 ] and then by Ideal Toy Corp in 1980 [ 6 ] via businessman Tibor Laczi and Seven ...
The position of this cell is the extreme foreground of the 4th dimension beyond the position of the viewer's screen. 4-cube 3 4 virtual puzzle, rotated in the 4th dimension to show the colour of the hidden cell. 4-cube 3 4 virtual puzzle, rotated in normal 3D space. 4-cube 3 4 virtual puzzle, scrambled. 4-cube 2 4 virtual puzzle, one cubie is ...
Among solutions without holes, the ones with the fewest possible sides are given by a hexagon identified by Scott Kim as a student at Stanford University. [1] It is not known whether five-sided solutions without holes are possible. [2] Kim's solution has 16 vertices, while some of the pentagon solutions have as few as 11 vertices.
A combination puzzle, also known as a sequential move puzzle, is a puzzle which consists of a set of pieces which can be manipulated into different combinations by a group of operations. Many such puzzles are mechanical puzzles of polyhedral shape , consisting of multiple layers of pieces along each axis which can rotate independently of each ...
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