# 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:

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