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Hey guys,
Here is my next entry for the shortest competition, using the same starting
state as Remi. It totaled 298 moves, and I hope it will really give Remi
and others a run for their money!
In thinking about the theoretical bounds of this method, I thought averaging
2^(C-1) moves for each piece type might be doable (2 moves for 2C faces, 4
moves for 3C edges, and 8 moves for 4C corners). This would put one at
304. But I thought it'd be sweeter to cross the 300 barrier, which would
also reduce the record length by over 10%. I barely made it, and had to
backup and retry the last 3 sequences to squeeze away an extra preliminary
move (I was a little disappointed earlier today as I thought 300 was going
to be it this time).
There was nothing fundamentally new in my approach. I thought about trying
to do some coding to help, but that quickly felt like it would be a bigger
project than I cared to tackle, plus I knew there would be a good argument
that any resulting solution shouldn't count. So I started as before, though
I tried to take more of a zen approach this time vs. an OCD one. I just
really took my time and let each sequence seep into my brain as a mini
puzzle, playing with different preliminary move combinations and
brainstorming ideas to accomplished multiple goals at once. This often paid
off, as the extra time allowed me to find previously unseen shortcuts. I
tried to not spend a lot of time at once on the puzzle (less successful near
the end), and to not work on it if it was feeling laborious. I mostly only
worked out one or two sequences a night, hanging out with my wife as she
watched TV.
Given the ups and downs, I figure my luck was run of the mill, so this is
surely beatable, especially if someone happens to have more things "just
work out" for them. Some things did work out well for me, but some
roadblocks were frustrating.
The Good:
- Some preliminary move sets ended up really nice and short, which felt
lucky.
- It came about that I needed to do an even number of corner sequences (if
it had been odd, I would have had to finish with a 16-move corner sequence
instead of the 8-move sequence that must be done in pairs).
The Bad:
- I ended up with 1 twirled edge piece after placing the rest.
- I was again haunted by the single flipped piece towards the end, though I
was able to take steps to lower the cost of this. aside: I had initially
thought this might be something that statistically happens 50% of the time,
but now I think it may happen 75% of the time, since for a single unsolved
piece, there is 1 possible correct orientation and 3 possible flipped ones.
- I never got lucky enough to find an unintended solved piece, (which had
happened with the first corner in my 334 length solution).
- I seemed to have an unnaturally high number of correctly placed, but
incorrectly oriented corners along the way.
I didn't best Remi's effort on the face pieces, and was still only able to
pull off 48 twists for them. The point where the edges were complete was
blurred because I left the single twirled edge unsolved until near the very
end, and also because I was able to place 2 corners during my last edge
sequence (I used the unsolved edge to my advantage after realizing it gave
me some control in avoiding the dreaded single unsolved corner). But
anyway, my last edge sequence was done at move 184.
That's about it I guess, without going overboard into detail...
Take Care,
Roice
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Hey guys,
Here is my next entry for the shortest competition, using the same starting state as Remi. It totaled 298 moves, and I hope it will really give Remi and others a run for their money!
In thinking about the theoretical bounds of this method, I thought averaging 2^(C-1) moves for each piece type might be doable (2 moves for 2C faces, 4 moves for 3C edges, and 8 moves for 4C corners). This would put one at 304. But I thought it'd be sweeter to cross the 300 barrier, which would also reduce the record length by over 10%. I barely made it, and had to backup and retry the last 3 sequences to squeeze away an extra preliminary move (I was a little disappointed earlier today as I thought 300 was going to be it this time).
There was nothing fundamentally new in my approach. I thought about trying to do some coding to help, but that quickly felt like it would be a bigger project than I cared to tackle, plus I knew there would be a good argument that any resulting solution shouldn't count. So I started as before, though I tried to take more of a zen approach this time vs. an OCD one. I just really took my time and let each sequence seep into my brain as a mini puzzle, playing with different preliminary move combinations and brainstorming ideas to accomplished multiple goals at once. This often paid off, as the extra time allowed me to find previously unseen shortcuts. I tried to not spend a lot of time at once on the puzzle (less successful near the end), and to not work on it if it was feeling laborious. I mostly only worked out one or two sequences a night, hanging out with my wife as she watched TV.
Given the ups and downs, I figure my luck was run of the mill, so this is surely beatable, especially if someone happens to have more things "just work out" for them. Some things did work out well for me, but some roadblocks were frustrating.
The Good:
- Some preliminary move sets ended up really nice and short, which felt lucky.
- It came about that I needed to do an even number of corner sequences (if it had been odd, I would have had to finish with a 16-move corner sequence instead of the 8-move sequence that must be done in pairs).
The Bad:
- I ended up with 1 twirled edge piece after placing the rest.
- I was again haunted by the single flipped piece towards the end, though I was able to take steps to lower the cost of this. aside: I had initially thought this might be something that statistically happens 50% of the time, but now I think it may happen 75% of the time, since for a single unsolved piece, there is 1 possible correct orientation and 3 possible flipped ones.
- I never got lucky enough to find an unintended solved piece, (which had happened with the first corner in my 334 length solution).
- I seemed to have an unnaturally high number of correctly placed, but incorrectly oriented corners along the way.
Take Care,
Roice
What can I say Roice? On one hand I knew that you would never rest while
someone else held the record for shortest 3^4, but on the other hand it
really does seem like we're pushing up against some sort of hard limit
for this method. I never expected to see sub-500 twist solutions, and
now with sub-300 solutions, well, I guess I'll just stop trying to
predict these things. I stand completely in awe of all you guys.
Congratulations, Roice.
-Melinda
Roice Nelson wrote:
>
> Hey guys,
>
> Here is my next entry for the shortest competition, using the same
> starting state as Remi. It totaled 298 moves, and I hope it will
> really give Remi and others a run for their money!
>
> In thinking about the theoretical bounds of this method, I thought
> averaging 2^(C-1) moves for each piece type might be doable (2 moves
> for 2C faces, 4 moves for 3C edges, and 8 moves for 4C corners). This
> would put one at 304. But I thought it'd be sweeter to cross the 300
> barrier, which would also reduce the record length by over 10%. I
> barely made it, and had to backup and retry the last 3 sequences
> to squeeze away an extra preliminary move (I was a little disappointed
> earlier today as I thought 300 was going to be it this time).
>
> There was nothing fundamentally new in my approach. I thought about
> trying to do some coding to help, but that quickly felt like it would
> be a bigger project than I cared to tackle, plus I knew there would be
> a good argument that any resulting solution shouldn't count. So I
> started as before, though I tried to take more of a zen approach this
> time vs. an OCD one. I just really took my time and let each sequence
> seep into my brain as a mini puzzle, playing with different
> preliminary move combinations and brainstorming ideas to accomplished
> multiple goals at once. This often paid off, as the extra time
> allowed me to find previously unseen shortcuts. I tried to not spend
> a lot of time at once on the puzzle (less successful near the end),
> and to not work on it if it was feeling laborious. I mostly only
> worked out one or two sequences a night, hanging out with my wife as
> she watched TV.
>
> Given the ups and downs, I figure my luck was run of the mill, so this
> is surely beatable, especially if someone happens to have more things
> "just work out" for them. Some things did work out well for me, but
> some roadblocks were frustrating.
>
> The Good:
>
> - Some preliminary move sets ended up really nice and short, which
> felt lucky.
> - It came about that I needed to do an even number of corner sequences
> (if it had been odd, I would have had to finish with a 16-move corner
> sequence instead of the 8-move sequence that must be done in pairs).
>
> The Bad:
>
> - I ended up with 1 twirled edge piece after placing the rest.
> - I was again haunted by the single flipped piece towards the end,
> though I was able to take steps to lower the cost of this. aside: I
> had initially thought this might be something that statistically
> happens 50% of the time, but now I think it may happen 75% of the
> time, since for a single unsolved piece, there is 1 possible correct
> orientation and 3 possible flipped ones.
> - I never got lucky enough to find an unintended solved piece, (which
> had happened with the first corner in my 334 length solution).
> - I seemed to have an unnaturally high number of correctly placed, but
> incorrectly oriented corners along the way.
>
> I didn't best Remi's effort on the face pieces, and was still only
> able to pull off 48 twists for them. The point where the edges were
> complete was blurred because I left the single twirled edge unsolved
> until near the very end, and also because I was able to place 2
> corners during my last edge sequence (I used the unsolved edge to
> my advantage after realizing it gave me some control in avoiding the
> dreaded single unsolved corner). But anyway, my last edge sequence
> was done at move 184.
>
> That's about it I guess, without going overboard into detail...
>
> Take Care,
>
> Roice
>