by jcalx on 10/31/24, 9:56 PM
You can solve a (legally scrambled) Rubik's Cube with no knowledge of its initial state, as long as someone stops you when you've done it.
You also need several billion years to do this, so it's not recommended for beginner solvers.
by throwaway81523 on 11/4/24, 1:34 AM
This is neat, though it's from 2012 or maybe earlier.
I wonder if there is a single not-too-long rotation sequence that generates the whole cube group. That is, a sequence XYZ that you can perform repeatedly and have that bring you through every cube state. If not, maybe there is some other very simple algorithm that traverses all the states, instead of a zip file that uncompresses to 200MB.
by _kb on 11/4/24, 8:18 AM
Bit of a meta note: grown adult here who never got into cubing earlier in life. Recently picked one up as some non-screen entertainment for some long haul flights and train travel. Highly recommend.
by Retr0id on 11/4/24, 1:21 AM
For anyone wondering what an illegal cube scramble looks like, you can rotate one of the corners or edge pieces in-place, on the more forgiving cube designs. This renders the cube unsolvable (via regular legal moves) until you revert the illegal move(s).
by sixfiveotwo on 11/4/24, 8:53 AM
My intuition when reading the first lines of this article was that, just like when searching exhaustively for the correct combination on a padlock, one would cycle through each subgroup, where each of them would represent a digit on the lock. On the lock, one would do 9 steps (not 10, as this would loop the lock to a previously seen combination) on the least significant digit, then propagate the carry to the next digits. But it seems that this more complicated than that, as the steps at which subgroups connect (the carry) are not always the same?
by n00b101 on 11/4/24, 5:46 PM
FYI, it would take approximately 99.3 billion years to complete the Hamiltonian circuit of the Rubik's cube’s quarter-turn metric Cayley graph using the GAN 12 Maglev UV Coated 3x3 Rubik's cube.