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Rubik's puzzle

A Rubik's Snake (also Rubik's Twist, Rubik's Transformable Snake, Rubik’s Snake Puzzle) is a toy with 24 wedges that are right isosceles triangular prisms. The wedges are connected by spring bolts, so that they can be twisted, but not separated. By being twisted, the Rubik's Snake can be made to resemble a wide variety of objects, animals, or geometric shapes. Its "ball" shape in its packaging is a non uniform concave rhombicuboctahedron. The snake was invented by Ernő Rubik, better known as the inventor of the Rubik's Cube. Rubik's Snake was released during 1981 at the height of the Rubik's Cube craze. According to Ernő Rubik: "The snake is not a problem to be solved; it offers infinite possibilities of combination. It is a tool to test out ideas of shape in space. Speaking theoretically, the number of the snake's combinations is limited. But speaking practically, that number is limitless, and a lifetime is not sufficient to realize all of its possibilities." Other manufacturers have produced versions with more pieces than the original.

The 24 prisms are aligned in row with an alternating orientation (normal and upside down). Each prism can adopt 4 different positions, each with an offset of 90°. Usually the prisms have alternating colors.

The position of the 23 turning areas can also be written directly after each other. Here the positions 0, 1, 2 and 3 are always based on the degrees of twist between the right hand prisms relative to the left hand prism, when viewed from the right of the axis of rotation. However, this notation is impractical for human readers, because it is difficult to determine the order of the twists.

Rather than numbers, Albert Fiore uses letters to refer to the direction the second (rightward) section is turned in relation to the first (leftward) section: D, L, U, and R. These are listed consecutively rather than numbered, so that a completely straight figure rather than being presumed as a starting point is notated DDDDDDDDDDDDDDDDDDDDDDD.

The number of different shapes of the Rubik's Snake is at most 423 = 70,368,744,177,664 (⁠ ⁠≈⁠ ⁠7×1013 or 70trillion), i. e. 23 turning areas with 4 positions each. The real number of different shapes is lower, since some configurations are spatially impossible (because they would require multiple prisms to occupy the same region of space). Peter Aylett computed by an exhaustive search that 13,446,591,920,995 (≈ 1.3×1013 or 13 Trillion) positions are possible when prohibiting prism collisions, or passing through a collision to reach another position; or 6,721,828,475,867 (≈ 6.7×1012) when mirror images (defined as the same sequence of turns, but from the other end of the snake) are counted as the one position, and likewise for rotational symmetries in loops (where the sequence of turns in a loop is cycled).