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An example of a 3 × 3 × 3 magic cube. In this example, no slice is a magic square. In this case, the cube is classed as a simple magic cube.. In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an n × n × n pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four ...
A geometric magic square, often abbreviated to geomagic square, is a generalization of magic squares invented by Lee Sallows in 2001. [1] A traditional magic square is a square array of numbers (almost always positive integers ) whose sum taken in any row, any column, or in either diagonal is the same target number .
An example is the 4-dimensional 3×3×3×3 ... treated as a number magic square puzzle on each of the six faces ... puzzle implemented as computer games.
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Three-dimensional tic-tac-toe on a 3×3×3 board. In this game, the first player has an easy win by playing in the centre if two people are playing. One can play on a board of 4x4 squares, winning in several ways. Winning can include: four in a straight line, four in a diagonal line, four in a diamond, or four to make a square.
Five-dimensional 2 5 puzzle partial cutaway demonstrating that even with the minimum size in 5-D the puzzle is far from trivial. The 4-D nature of the stickers is clearly visible in this screen shot. The Rubik's Cube is the original and best known of the three-dimensional sequential move puzzles.
His interest in magic squares led to higher dimensions: magic cubes, tesseracts, etc. He developed a new diagram for the four-dimensional tesseract. This was published in 1962 when he showed constructions of four-, five-, and six-dimensional magic hypercubes of order three. [1] He later was the first to publish diagrams of all 58 magic ...
A magic hyperbeam (n-dimensional magic rectangle) is a variation on a magic hypercube where the orders along each direction may be different. As such a magic hyperbeam generalises the two dimensional magic rectangle and the three dimensional magic beam, a series that mimics the series magic square, magic cube and magic hypercube.