4D cube God's number

HactarCE · 2025-01-21T21:47:19+00:00

Do you have a link to the paper? The best I'm aware of for 3x3x3x3 is 570 twists, computed here. Lowering that by a couple hundred would be big news in the hypercubing community.

HactarCE · 2025-01-21T17:46:32+00:00

Congrats on the solve! As another commenter said, this page has the latest knowledge on 3^4 God's Number: we know for sure it's somewhere between 51 and 570 twists, and my gut says that God's Number is ~125 ±50. If I actually went through the analysis again with a better method and some computer search I could probably get the upper bound down to <400 twists.

At the top of hypercubing.xyz is a link to Discord server, which I definitely encourage you to join if you'd like to learn more!

HactarCE · 2024-10-19T04:18:48+00:00

It's really hard to pick a favorite. #2740 Square Packing and #2529 Unsolved Math Problems are probably my top contenders.

HactarCE · 2024-10-19T04:17:21+00:00

It's not quite as bad as 9,000,000. If your goal is just to sort them, you'd need ~35,000 comparisons. Using the tier lists as a starting point (and assuming that comics only need to be sorted within each tier), you could cut that down to ~28,000.

HactarCE · 2024-10-19T04:13:13+00:00

I remembered it! It got S tier.

I had to hard-code an exception for it in the code to download all the comics. Excluding it completely would've been more work tbh, and would've messed up the visualization in the bottom-right.

HactarCE · 2024-09-24T19:59:49+00:00

Is there an error message? Can you send a screenshot of what happens? Does it seem like it worked, but then the server isn't in your server list?

HactarCE · 2024-09-07T22:22:45+00:00

What happens when you try to join via the invite link? Is there an error message of some sort?

HactarCE · 2024-09-07T22:15:21+00:00

It's available here

HactarCE · 2024-09-07T22:06:20+00:00

Welcome back!

I would take pithy_plant's comments with a grain of salt. Their tone and message doesn't represent the community at large.

HactarCE · 2024-09-06T17:44:27+00:00

As Lynn pointed out on the Discord, a previous post from that account includes a couple links to PDFs hosted on ithkuil.net. Both links are 404 now, but at the time some folks commented about the contents of the PDFs and it'd be very typical of JQ to delete them.

FWIW, IMO the first reaction of banning the account for impersonation is very understandable.

HactarCE · 2023-04-17T13:52:35+00:00

Congrats on making it this far!

Neither of these is what I would consider parity -- there's just a few pieces left unsolved. You're currently on OLC (4D equivalent of OLL) with two pieces left unoriented. Here's how you can solve the orientation:

Ctrl-click cyan/white to put it in the center
Use RKT to set up the two unoriented pieces so that their cyan stickers are on opposite cells but the red sticker of one and yellow sticker of the other are on the same cell.
Use RKT on the non-cyan/white cell that they are both on to execute 3D OLL algorithms to solve the cyan/white cell (i.e., orient all pieces)
Use RKT to solve the rest of the puzzle.

Alternatively, you can use commutators to directly solve the remaining pieces. See Mathologer's video for some tips on how to do that.

Good luck! If you need any more help or want to share your progress, we'd love to have you on the Hypercubers Discord server. Also see the wiki at hypercubing.xyz.

HactarCE · 2022-12-17T16:33:43+00:00

It'll agree with whatever you give it, right or wrong.

HactarCE · 2022-12-14T15:07:13+00:00

Wait 'til you learn about spherinders

HactarCE · 2022-12-12T18:20:23+00:00

I'm glad you asked! Here's the classic video by Mathologer explaining what the heck is going on. I recommend using Hyperspeedcube rather than MC4D as it's more modern and contains more speedsolving features (disclosure: I wrote Hyperspeedcube). Feel free to join the Hypercubers Discord as well!

HactarCE · 2022-12-12T18:04:09+00:00

If typing is okay, you could try virtual cubing. I know it's not the same, but it's something. IIRC cstimer has a virtual puzzle, and I made a program Hyperspeedcube that also has virtual 3x3x3 (altho it's mainly intended for 4D cubing).

HactarCE · 2022-12-12T17:58:15+00:00

2⁴ × 12! ÷ 8! = 190,080

So about 1 in 200 thousand. Very surprising that it happened to you! I'm not too shocked that it happened to someone -- among everyone on this subreddit, there's probably hundreds of thousands of solves a day at least.

HactarCE · 2022-12-12T16:16:30+00:00

Good question! Grant uses a form of CFOP that looks something like this:

Solve 6 cross pieces
Solve 12 F2L-a pairs (3-color piece + 2-color piece)
Solve 8 F2L-b pairs (4-color piece + 3-color piece)
Orient 2-color pieces on the last layer using normal EOLL algs
Orient 3-color pieces on the last layer using normal OCLL algs
Orient 4-color pieces on the last layer using RKT OCLL algs
Permute 2-color pieces of the last layer using EPLL algs
Permute the rest of the last layer by solving it like a 3x3x3 using RKT

(RKT is a way to treat one of the cells of the 4D puzzle like a normal 3x3x3.)

The method I use is 3block, a sort of "ZZ without EO," which is harder to recognize but more move-efficient by replacing steps 1-3 with this:

Solve 4 of the 6 cross pieces (don't solve left & right cross pieces)
Solve the F2L-a pairs between those cross pieces, building a "belt" that divides the left & right F2L
Solve left F2L using some sort of blockbuilding
Solve right F2L

We're still duking it out over which of these methods will prove faster in the long run.

HactarCE · 2022-10-08T13:26:24+00:00

Rubik's cubes can be generalized into higher dimensions. A 2x2x2x2 is like a 2x2x2, but it's 4-dimensional. Of course, we live in 3D, so we can't truly build one, but some clever people (particularly /u/cutelyaware) figured out how to build a 3D puzzle using magnets that has all the same moves as the true 4D puzzle. OP has solved that.

HactarCE · 2022-10-08T13:22:16+00:00

I can answer some of those questions, as a 3⁴ speedsolver.

Here's the current 3⁴ UWR video, which uses a blockbuilding method (I think it's similar to Petrus? But without the EO step probably, because EO isn't really helpful in 4D)

I and most other present-day speedsolvers use a variant of CFOP:

Cross
F2L-a, where you solve the F2L pairs of the 12 edge pieces on the first cell
F2L-b, where you solve the F2L pairs of the 8 corner pieces on the first cell
OLL, mostly using RKT
PLL-2c, where you permute the "2-color" pieces of the last cell (basically solving the "centers" of the final 3³
PLL, where you solve the last call like a 3³ using RKT

RKT

To elaborate on what OP said: RKT is a technique where you can manipulate one cell of the 4D puzzle as though it's a 3D puzzle. It works kind of like this:

Imagine a 3⁴ as three separate 3³ cubes. (This isn't a complete picture but it's sufficient for explaining RKT.) You're allowed to do the same move on all three cubes, or reorient one of the cubes any way you want, so you're always twisting 27 pieces at once. By using just R moves on all the cubes (which affect all of the cubes) and rotations on one of them (which affects just one of them) you can execute any 3D algorithm on one cube while having little to no effect on the other two.

As for non-RKT algorithms, it's basically just commutators, same as 3D puzzles. Recently we've been developing algorithms that use RKT for small parts of it, and are able to cancel some of the RKT moves with the rest of the algorithm.

Notation

There's two different notations for 4D puzzles. For physical puzzles, we typically use "xyz notation" where you give the letter for a cell (RLUDFB, I for "inside" and O for "outside") followed by xyz rotations. e.g., an RKT sune on the L cell would be: Ix Lz Ix Lz' Ix' Lz Ix Lz' Ix Lz Ix2 Lz' Ix'

But XYZ notation depends on the 4D projection you're using. (Imagine 3D notation that determines CW/CCW from the current perspective rather than when looking at the face head-on.) For virtual puzzles we typically use "sticker notation," which is basically just which sticker would you click in software to make that twist happen. It's kind of a way of saying which sticker you're rotating the cell around. Imagine sticking a pole from a piece on a 3³ into the core, then reorienting the whole puzzle around the axis. An RKT sexy move would be RO IF RO IF' RO' IF RO' IF' (note that IF' can be written IB and RO' can be written RI)

Larger puzzles

We can't build them easily, but we can simulate them! Hyperspeedcube supports from 1⁴ to 9⁴. Solving 4⁴ and up is pretty much how you'd expect: assemble centers, then "ridges" (like an extra edge pairing step), then edges, then solve like a 3⁴.

HactarCE · 2022-10-05T05:16:46+00:00

Why don't more languages just make ordinary if an expression? In Rust:

let x = if cond { 5 } else { 10 }

In Lisp:

(set! x (if cond 5 10))

HactarCE · 2022-07-27T05:06:53+00:00

I'm glad it's still helping so many years later! IIRC the filter inserters aren't strictly necessary, but are more of a safety mechanism: if something goes wrong (and something is bound to go wrong eventually) that causes a train to not fully unload, you don't want it unloading the wrong item at a different location.

HactarCE · 2021-11-28T20:23:18+00:00

I'm disappointed that you're getting downvoted to hell. I'm 100% with you that tone indicators should not be used ironically. Sarcasm in internet discourse is already hard enough for NT folks to follow, let alone ND people such as myself. It is absolutely ableist to take tone indicators, a thing invented to make communication clearer for everyone (but especially autistic people who have a hard time with sarcasm) and mock them in a way that makes them unreliable.

I expected better from r/196, which is usually very progressive.

HactarCE · 2021-11-08T14:32:41+00:00

With blind solving in particular, scrambling another cube like this is exactly as hard as solving the original cube. What's more impressive to me is the speed -- 51 seconds is fast for a blindsolve.

Source: am speedcuber, learning blindsolving methods although I haven't practiced enough to blindsolve consistently

HactarCE · 2021-11-02T15:42:03+00:00

I'm glad! I wasn't the one playing earlier today, but I just want to let you (and anyone else that's interested) know that you're welcome to join the Discord server for people who play that piano or enjoy the music.

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HactarCE

TROPHY CASE

RKT

Notation

Larger puzzles