Rubik's Magic

Rubik's Magic

Rubik's Magic, like Rubik's Cube, is a mechanical puzzle invented by the Hungarian sculptor and professor of architecture Ernő Rubik and first manufactured by Matchbox in the mid-1980s.

The puzzle consists of 8 black square tiles (changed to red squares with goldish rings in 1997) arranged in a 2 × 4 rectangle; diagonal grooves on the tiles hold wires that connect them, allowing them to be folded onto each other and unfolded again in two perpendicular directions (assuming that no other connections restrict the movement) in a manner similar to a Jacob's Ladder toy. The front side of the puzzle shows, in the initial state, three separate, rainbow-coloured rings; the back side consists of a scrambled picture of three interconnected rings. The goal of the game is to fold the puzzle into a heart-like shape and unscramble the picture on the back side, thus interconnecting the rings.

Rubik's Magic (solved)

Numerous ways to accomplish this exist, and experienced players can transform the puzzle from its initial into the solved state in less than 2 seconds.[1] Other challenges for Rubik's Magic include reproducing given shapes (which are often three-dimensional), sometimes with certain tiles required to be in certain positions and/or orientations.

In 1987, Rubik's Magic: Master Edition was published by Matchbox; it consisted of 12 silver tiles arranged in a 2 × 6 rectangle, showing 5 interlinked rings that had to be unlinked by transforming the puzzle into a shape reminiscent of a W. Around the same time, Matchbox also produced Rubik's Magic Create the Cube,[2] a "Level Two" version of Rubik's Magic, in which the puzzle is solved when folded into a cube with a base of two tiles, and the tile colors match at the corners of the cube.[3] It did not have as wide a release, and is rare to find.

In 1996, the original version of Rubik's Magic was re-released by Oddzon, this time with yellow rings on a red background; other versions (for example, a variant of the original with silver tiles instead of black ones) were also produced, and there also was a strategy game based on Rubik's Magic. An unlicensed 2 × 8 version was also produced, with spheres printed on its tiles instead of rings. Custom versions as large as 2 × 12 have been built using kits available from Oddzon.

Professor Rubik holds both a Hungarian patent (HU 1211/85, issued March 19, 1985) and a US patent (US 4,685,680, issued August 11, 1987) on the mechanism of Rubik's Magic.

Details

It can be seen that the total number of 2 × 4 rectangles that can possibly be created using Rubik's Magic is only thirty-two; these can be created from eight distinct chains. The easiest way to classify chains is by the means of the middle tile of the puzzle's finished form (the only tile that has segments of all three rings) and the tile next to it featuring a yellow/orange ring segment (the indicator tile).

Every chain either has the middle tile on the outside (O) or the inside (I) of the chain; if it is arranged so that the indicator tile is to the right of the middle tile, then the position of the ring segment on the indicator tile can either be the upper left (UL), upper right (UR), lower left (LL) or lower right (LR) corner. The position and orientation of the remaining tiles is then determined by the middle and indicator tiles, and eight distinct chains (OUL to ILR) is obtained, although the naming convention is not standardized.

Similarly, the 2 × 4 rectangle forms of them can be categorized. Each of these forms has exactly one chain associated with it, and each chain yields four different rectangle forms, depending on the position of the edge where it is folded with regard to the middle tile. By concatenating one of the numbers 0, 1, 2 or 3 to the chain's name, depending on whether the number of tiles to the right of the middle tile before the folding edge, a categorization of the rectangle forms is obtained. The starting position, for example, is rectangle form OUR2. The cube now is rainbow and has silver rings. A game rule for this is one is you can match the silver rings and color squares, which can make it more complicated. A similar classification can also be obtained for the heart-shaped forms of the puzzle, of which 64 exist.

Analysis

One important question when analyzing Rubik's Magic concerns its state space: What is the set of configurations that can be reached from the initial state? This question is harder to answer than for Rubik's Cube, because the set of operations on Rubik's Magic does not form a mathematical group. The basic operation (move) consists of transferring a hinge between two tiles T1 and T2, from one pair of edges (E11 of T1 and E21 on T2) to another pair E12 and E22. Here, edges E11 and E12 are adjacent on tile T1, and so are edges E21 and E22 on tile T2 but in opposite order. See the figure below for an example, where E11 is the East edge of the yellow tile, E21 is the West edge of the red tile, and both E21 and E22 are the North edges.

A basic move, transferring a hinge between two tiles to another pair of edges

In order to carry out such a move, the hinge being moved cannot cross another hinge. Thus, the two hinges on a tile can take up one of five relative positions (see figure below). The positions are encoded as a number in the range from -2 to +2, called the wrap. The difference between wrap -2 and wrap +2 is the order of the neighboring tiles (which one is on top). The total wrap of a configuration is calculated as the alternating sum of the wraps of the individual tiles in the chain. The total wrap is invariant under a move. Thus, one can calculate the number of theoretically possible shapes of the chain (disregarding the patterns on the individual tiles) as 1351.[4]

All possible relative positions of the two hinges on a single tile; the number below the tile is the amount of wrap

Furthermore, the other tiles in the chain will have to move through space appropriately to allow the folding and unfolding needed to carry out a move. This limits the practically reachable number of configurations further. That number also depends on how much stretching of the wires you tolerate.

Records

The world record for a single solve of the Magic is 0.69 seconds, set by Yuxuan Wang of China at Beijing Spring 2011. Yuxuan Wang also holds the record for an average of five solves - 0.76 seconds set at the Beijing Summer Open 2011 competition.[5] Since 2013 Magic is no longer an official event on competitions. The current unofficial world record single solve was set by Zach Emery with a time of 0.49 seconds, which can be found online.

See also

References

  1. ↑ Official World Rankings
  2. ↑ Rubik's Create The Cube at TwistyPuzzles.com, retrieved May 2, 2007
  3. ↑ Rubik's Magic: Create the Cube at Jaap's Puzzle Page, retrieved May 2, 2007
  4. ↑ Verhoeff, Tom (1987). "Magic and Is Nho Magic" (PDF). Cubism For Fun (15): 24–31. Retrieved 2014-08-27.
  5. ↑ World Cube Association Official Results - Rubik's Magic

External links

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