[HN Gopher] Can a Rubik's Cube be brute-forced?
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       Can a Rubik's Cube be brute-forced?
        
       Author : lispybanana
       Score  : 31 points
       Date   : 2024-10-28 00:01 UTC (23 hours ago)
        
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       | Terr_ wrote:
       | > The essence of the result is this. Reminiscent of a "meet in
       | the middle" algorithm
       | 
       | Hm, so something akin to a bidirectional path-finding problem,
       | where one can still call it "brute force" because both known
       | positions (start and goal) are each doing a breadth-first search,
       | as opposed to something fancier than picks a direction.
       | 
       | https://en.wikipedia.org/wiki/Bidirectional_search
        
       | dang wrote:
       | Related:
       | 
       |  _Can a Rubik 's Cube be brute-forced?_ -
       | https://news.ycombinator.com/item?id=36645846 - July 2023 (108
       | comments)
       | 
       | (Reposts are fine after a year or so; links to past threads are
       | just to satisfy extra-curious readers)
        
       | pge wrote:
       | This reminds of the time I decided to teach one of my kids about
       | computer programming, and suggested we write a program to solve a
       | rubik's cube as an example (rubik's cubes were popular at her
       | school at the time). Only after we had written a really simple
       | depth-first search did I realize that it would take several
       | lifetimes to run. Great lesson, but not the one I meant to
       | impart!
        
         | Vampiero wrote:
         | In hindsight it should have been fairly obvious that it would
         | immediately explode into a combinatorics problem
        
           | pge wrote:
           | yes, 30 seconds of math would have told me that, but I
           | foolishly jumped in without doing that calculation...
        
             | madcaptenor wrote:
             | Chemists have a saying about this: "A month in the
             | laboratory can save an hour in the library." (The time
             | units can vary, but yes, I did write that correctly.)
        
               | joelwilliamson wrote:
               | A month of programming can save an hour of planning.
        
         | consf wrote:
         | Sometimes the unintended lessons are the most memorable
        
           | lukan wrote:
           | Yes, but usually it is pretty bad for the learning
           | experience, if the teacher stumbles and needs time for
           | himself to figure things out. It _can_ work out to become a
           | deep lesson, if the student is highly motivated and the
           | teacher good at explaining his thought processes - otherwise
           | the student will stand aside and get bored and loose
           | interest, as the problem is way beyond his level to
           | understand.
        
       | krisoft wrote:
       | Of course the true brute-forced algorithm is to pry the cube
       | apart and then assemble it again in the solved state.
        
         | mihaaly wrote:
         | I once rearranged the coloured stickers on the faces. On top of
         | cheating it looked very ugly afterwards. : )
         | 
         | (ps.: after a quick search I see that one can buy replacement
         | stickers for a few bucks on Amazon :D)
        
           | Patrick_Devine wrote:
           | All the good Chinese speed cubes these days are sticker-less,
           | so thankfully no more ugly cubes with grody stickers.
        
       | taeric wrote:
       | Fun to see someone else look at the cube as permutations.
       | https://taeric.github.io/cube-permutations-1.html is one of the
       | more fun visualizations I've made that was looking at this.
       | Reminds me I need to finish it. I can't remember why I haven't
       | gotten further.
        
       | dunham wrote:
       | I had a prof in college describe solving a rubik's cube as group
       | conjugation (e.g. f * g * f^-1).
       | 
       | For example, you find a way to swap two pieces on the top layer
       | and mangle the bottom (f), turn the top (g), and then do the
       | opposite (f^-1), swapping a different pair and un-mangling the
       | bottom. Between complementary swaps, edge flips, and corner
       | rotations, you can build an entire solution with this technique.
       | (My current version of this does the edges first, ignoring any
       | damage to corners and then does corners.)
       | 
       | Somewhat related - many years ago there was a tutorial of the Gap
       | computer algebra system that analyzed the rubik's cube group. I
       | can't find the original, but there is a translation to Julia
       | here: https://oscar-system.github.io/GAP.jl/stable/examples/
        
         | eddd-ddde wrote:
         | Yes! This is also how I learnt to solve Rubik's cubes.
         | 
         | You eventually develop the intuition to solve any move without
         | having to "memorize" anything.
        
       | chris_va wrote:
       | This sounds like bidirectional search + rainbow tables
        
       | wly_cdgr wrote:
       | After 6831 (give or take) hours, I'm pretty sure the answer is
       | "no"
        
       | alexsmirnov wrote:
       | Sure it can. At the peak of Cube popularity, I saw "game set" in
       | store. Included Rubik's Cube and hammer.
        
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