"The Professor" (1986) (Giuseppe Tornatore) is a film that.. just kidding! What you think I'm going full orc and doing movie reviews here?
No no no.
The professor that I am reviewing is a 5x5x5 cube made by ShengShou called the LingLong. It's a white stickered cube and I picked it up because it seemed like a good cube available dirt cheap (less than 2 bitcents) and as such it was my first 5x5x5.
First off, the thing is smooth as fuck. While I imagine there are better speed cubes out there, and of course a stickerless design is always more durable, this thing has greatly impressed me. No pops, no sticks. If you don't have one, why not?
The 5x5x5 being an odd cube has fixed centers, and avoids some parity solving issues which can be annoying on the 4x4x4. It is also not a supercube, which means that chances are it will never return to the same exact position it started. This is because some pieces in a face can swap each other out, so that the cube will be solved but the actual position of the original pieces is now different. Make some markings on a cube to verify this yourself. Neato!
Solving larger puzzles provides new interesting content in a couple of ways, but doesn't get exponentially harder with puzzle size like e.g. juggling does. First of all there is the "hunting" aspect, which is good for getting you to scan areas looking for that one piece you are looking for, and which cause bigger puzzles to take so much more time. Time likely is exponential with puzzle size, but not difficulty. For me, the 5x5x5 seems a great medium.
Then there is the fun of getting the last faces done. Lets back up a bit: the standard route for these things is to get the faces first, then getting the edge pieces matched (not in the right place, but matched together forming complete edges), after which you have something equivalent to an unsolved 3x3x3 and you can proceed to solve it. The first face is easy because you have lots of freedom to move pieces about. Just like with the 3x3x3 however, once you have gotten some pieces where you want them, this takes some freedom away to move other pieces about. The last two faces must be solved simultaneously, every move balanced by a countermove to return the solved faces to where you want them, and it's always a pleasure to see how they wind up falling into place.
The crux and perhaps the most fun bit is getting the last few edges matched. It turns out you will be getting the last three edges matched simultaneously. This is easy to see on the cube but hard to explain. Basically you need to put a piece of one not-yet-solved edge (1) into another not-yet-solved edge (2) to create a solved edge. Then you need to get that solved edge out of the way, replacing it with a not-yet-solved edge (3) before undoing the move which you used to solve the edge - said undoing now not only fixes the faces you have messed up in the procedure but also all edges. The geometry is beautiful here, very often you will see things just fall into place magically as there's nowhere else for the pieces to go after all. In fact this part is nice enough that you might be tempted to not finish the cube after this step, instead messing it up again 🙂
Anyway if you can solve the 3x3x3 you shouldn't need any new algorithms for this cube, until it's time to start shaving tens of seconds off your time that is. It's pure group-theoretical geometrical fun with over 10^74 permutations. Happy cubing!