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The Four Color Cube only features stickers in four different colors. In the initial state the colors are arranged in such a way that no two adjacent stickers share the same color. This sticker arrangement follows the 'four color theorem', also known as 'four color map theorem'. In mathematics it states that, no more than four colors are required to color the regions of a map, so that no two adjacent regions have the same color.

The layout of the Four Color Cube was created in 2015 by Evgeniy Grigoriev. The color scheme was created in 2015 by Walter Randelshofer.

The intuitive statement of the 'four color theorem', i.e. «that given any separation of a plane into contiguous regions, called a map, the regions can be colored using at most four colors so that no two adjacent regions have the same color», needs to be interpreted appropriately to be correct.

First, all corners, points that belong to (technically, are in the closure of) three or more countries, must be ignored. In addition, bizarre maps (using regions of finite area but infinite perimeter) can require more than four colors. Second, for the purpose of the theorem, every 'country' has to be a connected region, or contiguous. In the real world, this is not true (e.g. the Upper and Lower Peninsula of Michigan, Nakhchivan as part of Azerbaijan, and Kaliningrad as part of Russia are not contiguous). Because all the territory of a particular country must be the same color, four colors may not be sufficient.

This problem is sometimes also called 'Guthrie's problem' after F. Guthrie, who first conjectured the theorem in 1852. The conjecture was then communicated to de Morgan and thence into the general community. In 1878, Cayley wrote the first paper on the conjecture.

The four color theorem was proven in 1976 by Kenneth Appel and Wolfgang Haken. It was the first major theorem to be proved using a computer.

3 Chessboards

**Algorithm** Walter Randelshofer 2015

U · F B' · R · F B · U' R' D' L U' · L R · D' B R' · F2 B · R (19 ltm, 19 ftm, 20* qtm)

**Algorithm** Walter Randelshofer 2015

U · L R' · B2 U2 B D · L2 R2 · U D' · L D F2 D' L' U' (17 ltm, 17* ftm, 22 qtm)

**Algorithm** Walter Randelshofer 2015

CF CR · R MF L2 D2 L U MF2 MD L D F2 D' L' U' (14* ltm, 17* ftm, 22 qtm)

**Note**

Creates a solid face on the top, 2 H's on the front and on the back and 3 Chessboards on the remaining faces.

2 Fish

1 K

1 Chessboard

**Algorithm** Walter Randelshofer 2015

L F U R B' · R2 L · F' L' F L B · U' D · B' R' F2 R (18 ltm, 18* ftm,20* qtm)

**Algorithm** Walter Randelshofer 2015

CF' CR · MF R MF' U2 MR D F' B2 D MF' D' F' MR2 U R' (15* ltm, 20 ftm,24 qtm)

**Note**

Creates as much single colored faces as possible: While the face on top has a single color, the right face is solid except
for 1 edge, the faces on the front and on the back are solid except for 2 edges, the left face is solid except for 3 faces and the face on
the bottom is solid except for 4 edges.

(6 Dots)

**Algorithm**

MR MF' MR' MF (4* ltm, 8* ftm, 8* qtm)

**Algorithm**

MD' MR' MD MR (4* ltm, 8* ftm, 8* qtm)

**Algorithm**

(MR · CD')4 (4* ltm, 8* ftm, 8* qtm)

**Note**

On the Four Color Cube, the 6 Dots pattern creates a Gift-wrapped Cube.

(4 Small Edge Triangles)

**Algorithm** Michael Reid

R L · F' D · F B' · U D' · F' D B U' · F B' · U D' · B U' · R L (20 ltm, 20 ftm, 20* qtm)

**Algorithm** Tomas G. Rokicki 2003

R' D' · R L' · U' · F B' · L' F' U' F' R' B' L' U' R' · U D' · R' U' (20 ltm, 20 ftm, 20* qtm)

**Algorithm** Tomas G. Rokicki 2003

U' · F' B' · U' · R L · U' · F2 B2 · R2 L2 · D' · F B · D' · R' L' · D' (18 ltm, 18* ftm, 22 qtm)

**Algorithm** Michael Reid

L' · U' D' · L' · F B · L' · U2 D2 · F2 B2 · R' · U D · R' · F' B' · R' (18 ltm, 18* ftm, 22 qtm)

**Algorithm** Herbert Kociemba 2010

CD2 MF2 · D2 MR2 U' B' MR MD' B R' MF' MD R U' (13* ltm, 19 ftm, 24 qtm)

**Note**

On the Four Color Cube, the 4 Small Edge Triangles pattern creates 6 H's With Dots.

(4 Small Edge Triangles With 6 Dots)

**Algorithm** Walter Randelshofer 2015

U D · R' B · U' D · F' B · U' L D R' · F' B · R' L · B U' · R L (20 ltm, 20 ftm, 20* qtm)

**Algorithm** Walter Randelshofer 2015

U2 F U R B L' U2 · F B · L2 U2 · F' B' · D' F U L B (18 ltm, 18* ftm, 22 qtm)

**Algorithm** Walter Randelshofer 2015

CF' CR · MF2 D2 MR2 U' F' MR' MD' F R' MD MF' R U' (13* ltm, 19 ftm, 24 qtm)

**Note**

On the Four Color Cube, the 4 Small Edge Triangles With 6 Dots pattern creates 6 H's.

(Irregular Pattern)

**Algorithm** Walter Randelshofer 2015

F' R' · U D' · L' R · U B' · L R' · B' F · R U' (14 ltm, 14* ftm, 14* qtm)

**Algorithm** Ralph Jones 2015

CR CD' · U' F' MR' MD' F R' MD MF' R U' (10* ltm, 14* ftm, 14* qtm)

**Note**

On the Four Color Cube, this irregular pattern creates 6 H's. Compared to the 6 H's (4 Small Edge Triangles With 6 Dots) it requires less moves in all metrics.

(2 Small Edge Triangles)

**Algorithm** Ronald Flettermann

D' R U2 B' U2 R' · U' D · B D2 R D2 B' U (14 ltm, 14* ftm, 18* qtm)

**Algorithm** Tomas G. Rokicki 2003

U L' D2 F D2 L · U' D · F' U2 L' U2 F D' (14 ltm, 14* ftm, 18* qtm)

**Algorithm** Mirek Goljan 1982

MR U2 R2 F' MD L' MD2 L MD F R2 U2 MR' (13 ltm, 18 ftm, 24 qtm)

**Algorithm** Herbert Kociemba 2010

MD R' U2 B L' MD2 L MD2 B' U2 R MD' (12* ltm, 16 ftm, 22 qtm)

**Note**

On the Four Color Cube, the 2 Small Edge Triangles pattern creates The Color-Labyrinth of Minos.