1x1x1 Cube

1x1x1 Alternative names: 1x1 Shape: Cube Internal Mechanism: 1x1x1 Inventor: None Year: Produced by:

The 1x1x1 Cube (also referred to as the 1x1x1 or 1x1) is a 'twistable puzzle' consisting of a single solitary cube or cubie.

The 1x1x1 cube has six different coloured uniform faces. Although often considered a joke (with numerous "solution guides" on YouTube), it does nevertheless exist. Some people make their own for fun, but in the 2010s it has also become available to purchase in many online cube stores. It is sometimes bought by cubers to complete the traditional standard cubes collection, so that they don't start at the 2x2x2 Cube.

Mathematics

Although relatively trivial, the mathematics of the 1x1x1 cube puzzle have been studied, usually in relation to the larger cubes as the simplest case available (ignoring the even simpler 0x0x0 Cube). God's Number is easily determined for the 1x1x1 cube, and God's Algorithm (the optimal solution to produce a required state) is easy to compute.

• Ignoring cube rotations, i.e. whole cube rotations are considered to be equivalent (as with the standard Rubik's Cube) then there is only one state, nothing can ever move, and the puzzle is always solved.

• If orientation of the cube is important, e.g. that one particular colour must be on top, then there are 6 distinct states of the cube. God's number is 1 in HTM and 2 in QTM.

• If one considers whole cube rotations to be distinct, then there are a total of 24 distinct states. God's number in this situation is is 2 in HTM and 3 in QTM.

Discussions:

• God's Algorithm for the 1x1x1 Rubik's Cube, Jerry Bryan, Cube Lovers, 14 November 1995
• Hamiltonian Circuit for a 1x1x1 cube, Discussion in 'Puzzle Theory' started by ortwin, February 7, 2016, Speedsolving Forums

See also

• Boob Cube

Regular cubic twisty puzzles
0x0x0	1x1x1	2x2x2 Pocket Cube	3x3x3 Rubik's Cube	4x4x4 Rubik's Revenge
5x5x5 Professor's Cube	6x6x6 V-Cube 6	7x7x7 V-Cube 7	8x8x8 V-Cube 8	9x9x9
10x10x10	11x11x11	12x12x12 SengSo 12x12	13x13x13 MoYu 13x13	14x14x14 SengSo 14x14
15x15x15 MoYu 15x15	16x16x16 SengSo	17x17x17 Over The Top	18x18x18	19x19x19 SengSo
20x20x20	21x21x21 MoYu	22x22x22	23x23x23 YJ	24x24x24
25x25x25	26x26x26	27x27x27	28x28x28	29x29x29
30x30x30	31x31x31	32x32x32	33x33x33	34x34x34
Key:	Mass-produced	Exists, not manufactured	Work in progress	Not existent