# 5x5x5 Rubik's cube

It might be surprising that the 5x5x5 Rubik's cube (also called the Professor's cube) is not more difficult than the 4x4x4 Rubik's cube. Due to its enormous number of combinations, which equals 282 870 942 277 741 856 536 180 333 107 150 328 293 127 731 985 672 134 721 536 000 000 000 000 000, it's just more time-consuming.

• 5x5x5 Rubik's cube - grouping of 4 centers
• 5x5x5 Rubik's cube - grouping of 2 remaining centers
• 5x5x5 Rubik's cube - pairing-up of pieces within composite edges
• 5x5x5 Rubik's cube - reduction to the 3x3x3 cube
• world record videos

## 5x5x5 Rubik's cube - grouping of 4 centers

Group 4 out of six centers so that the remaining 2 centers would be adjacent to each other. Inner 3x3 pieces on each cube face are understood as a center here. Solving order on a simulator: white, yellow, green and orange center.

## 5x5x5 Rubik's cube - grouping of 2 remaining centers

Group 2 remaining centers using commutators. For X-centers (see a terminology on Fig. 1 on a page about the number of combinations for the NxNxN Rubik's cube) it can be used r'urUr'u'rU' sequence, and for +centers, it can be used MuM'UMu'M'U' sequence (see a notation), where the lowercase letters have the same meaning as the uppercase letters, however, the inner layers are being rotated instead of outer ones.

## 5x5x5 Rubik's cube - pairing-up of pieces within composite edges

Commutators also come in useful to pair-up the pieces within composite edges. For this purpose, a simulator mainly uses r'U'R2Ur and rU'R2Ur' sequences (the sequence should end with R2' by commutator definition, nevertheless, in this case it is not necessary to execute that move - the more correct term than a commutator is a conjugation then). From algorithm executions it is evident that the first move is pairing-up a wing edge with a central edge, by the second, third and fourth move we will exchange already paired-up wing edge for some non-paired-up one, by the last move we will group the centers again.

Besides the situations shown on a simulator (including a grouping of wing edges with central edges in case of only two (red-blue and red-green) remaining composite edges - see moves 93-110), also a so-called OLL parity can occur on the puzzle - when it seems that we need to orient only two wing edges within one composite edge. We will limit ourselves here to the solution of only this configuration because everything important (such as how to avoid a so-called OLL parity at the end of a solve in 100% of cases, or what's the cause of this phenomenon) can be found in a parity problem article which also includes the Cage method.

Except for nothing-saying algorithm like r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2, we can also solve a so-called OLL parity intuitively. Scramble and re-group the center pieces in a way so that the number of executed moves with inner layers (while the M, E and S moves are not permitted for a considered model (of fixed centers)) would be odd - see the last simulator. Although non-paired-up pieces within composite edges will be created by that (after the ninth move), after their subsequent grouping and reduction of a puzzle to the 3x3x3 cube we won't further encounter a so-called OLL parity. You don't necessarily have to pair-up wing edges with central edges in the order which is used by the simulator to solve these pieces - however, if you find this way interesting, see its explanation in the first video in a previously linked article about a parity problem.

## 5x5x5 Rubik's cube - reduction to the 3x3x3 cube

Now the 3x3x3 Rubik's cube solution tutorial can be used, see the picture below.

## World record videos

As a football has FIFA and athletics has IAAF, also the 5x5x5 Rubik's cube has some sort of board that organizes the competitions worldwide. It is WCA - World Cube Association. Thus it can be officially competed in a solving of the 5x5x5 Rubik's cube. It is competed in two formats: single fastest solve of the puzzle and average solve. As an average, five consecutive times of one round are taken, the best and the worst time is not considered and from the remaining three times an arithmetic mean is calculated.

 event: 5x5x5 single solve name: Max Park (USA) result: 37.28 s scramble: available upon request solution: available upon request cube brand: QiYi MoFangGe WuShuang M solving methods: reduction, then CFOP personal opinion on used methods: see below competition: SacCubing IV; 27. 5. 2018; USA

 event: 5x5x5 average solve name: Feliks Zemdegs (Australia) result: 43.21 s scrambles: available upon request solutions: available upon request cube brand: QiYi MoFangGe WuShuang M solving method: reduction, then CFOP + ZBLL personal opinion on used method: see below competition: Melbourne Cube Days; 18-19. 11. 2017; Australia

A 5x5x5 Rubik's cube is being solved while blindfolded as well. You can see world record videos in the blindfolded solving section.

If you find a so-called speedcubing interesting, check out an article about where to buy a Rubik's cube, what cube is the best and how to solve it faster.

Personal opinion on methods used in the world records

5x5x5 Rubik's cube:

While several methods used by speedcubers can be found for a solving of smaller cubes (2x2x2 - 4x4x4), for a 5x5x5 cube there is completely dominating reduction with subsequent 3x3x3 cube method - mostly CFOP and also ZBLL in case of top cubers. Alternatively, another variant of solving of last layer can be used, such as COLL + EPLL, for example. In my opinion, methods based on edges-and-corners-first solving and then centers solving (when viewed as a 3x3x3 cube) are not as profitable as in comparison to e.g. a 4x4x4 cube. Only a tiny amount of world class cubers use other solving method.

After grouping of centers is finished, pieces within composite edge are being paired-up, while usually both wing edges are being paired-up with central edge at once in a way that allows to keep the centers seemingly scrambled. This process is done 8x, then re-grouping of centers is done, and last 4 composite edges are being resolved so that the centers are no longer scrambled.

The page was graphically improved by Michael Feather and Conrad Rider.