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A solved Rubik's Revenge cube. The Rubik's Revenge (also known as the 4×4×4 Rubik's Cube) is a 4×4×4 version of the Rubik's Cube.It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the Sebestény Cube until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube. [1]
Whenever Maker picks an element of a pair, Breaker picks the other element of the same pair. At the end, Breaker has an element in each pair; by condition 2, he has an element in each winning-set. An example of such pairing-strategy for 5-by-5 tic-tac-toe is shown above. [1]: 2–3 show other examples for 4x4 and 6x6 tic-tac-toe.
C-C_pairing.pdf (352 × 387 pixels, file size: 8 KB, MIME type: application/pdf) This is a file from the Wikimedia Commons . Information from its description page there is shown below.
Petersen's theorem can also be applied to show that every maximal planar graph can be decomposed into a set of edge-disjoint paths of length three. In this case, the dual graph is cubic and bridgeless, so by Petersen's theorem it has a matching, which corresponds in the original graph to a pairing of adjacent triangle faces. Each pair of ...
The pair of swapped places corresponds to the direction of the edge. (In the example image the vertices (3, 2, 1, 4) and (2, 3, 1, 4) are connected by a blue edge and differ by swapping 2 and 3 on the first two places. The values 2 and 3 differ by 1. All blue edges correspond to swaps of coordinates on the first two places.)
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