Snake Cube ​

Game ​

A snake cube is a sequence of 27 small cubes connected by an elastic that goes through each cube.
The elastic goes either straight through the cube, from one face to the opposite, or turns inside the cube and goes from one face to an adjacent one.

The aim of the game is to fold the snake cube into a 3x3x3 cube, if a solution exists. In technical terms such a solution is an undirected Hamiltonian path in the 3x3x3 grid graph.

Sample snake cube solution

Definitions ​

The following definition help clarify this document:

• cubelet: One small cube, among the 27 that make up a snake cube.

• turn cubelet: A cubelet linked to previous/next cubelet by adjacent faces.

• straight cubelet: A cubelet linked to previous/next cubelet by opposite faces.

• end cubelet: A cubelet linked to only one other cubelet, positioned at an end.

• snake cube: A chain of 27 cubelets, irrespective of its position in space, flat or folded.

• snake: A synonym of snake cube.

• sequence: The representation of a snake cube as a list of 27 "0" or "1".
  EXAMPLE: the sequence for the snake cube above is "001010110111010111101010100".

  Code	Description
  1	turn cubelet
  0	straight cubelet or end cubelet

• path:: A path in 3D space coordinate {x, y, z} each an element of P=[0, 1, 2], representing a snake cube in folded position.
  EXAMPLE: the sample snake cube solution path is :

  json

  // [x, y, z]
  // axis direction: x -> right, y-> reader, z-> down
  [
    [[1,16,23],[18,17,22],[19,20,21]],
    [[2,15,24],[5,6,7],[10,9,8]],
    [[3,14,25],[4,13,26],[11,12,27]]]
  ]
  

• direction:: The representation of a path as a list of 26 steps in 3D from start position.
  EXAMPLE: the sample snake cube solution direction is : [1,1,2,-1,3,3,2,-3,-3,1,3,-2,-2,-1,-1,2,-3,2,3,3,-2,-2,1,1,2,2]

  Code	Axis	Direction
  +1	x	positive
  -1	x	negative
  +2	y	positive
  -2	y	negative
  +3	z	positive
  -3	z	negative

• start position:: The coordinates of the first element of a path.
  EXAMPLE: the sample snake cube solution start position is : [0,0,0]

• solution:: A way to fold a snake cube. It can be represented as follows. Both unambiguously define a way to fold a snake cube:

  • A path
  • A start position and a direction.

• palindrome:: A snake which sequence is the same as its reverse.