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Re: Corner Perm.

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  • Grant Tregay
    ... In case you cared to know for sure, you re correct. I had written this into a program a bit ago and this is from the output - # of edge orientation states
    Message 1 of 11 , Apr 5, 2004
      --- Ron van Bruchem wrote:
      > ... Another thing is this: without looking at the cross, just orient
      > all edges. This is much easier than for blindfold because you can
      > do F to flip 4 edges. I think the maximum depth for edge
      > orientation is 7 moves...

      In case you cared to know for sure, you're correct. I had written
      this into a program a bit ago and this is from the output - # of edge
      orientation states at each depth:
      depth 0: 1 0.05%(solved)
      depth 1: 2 0.10%
      depth 2: 21 1.03%
      depth 3: 178 8.69%
      depth 4: 592 28.91%
      depth 5: 914 44.63%
      depth 6: 327 15.97%
      depth 7: 13 0.63%
      Total : 2048

      After that, corners can be oriented in at most 7 more moves, though
      I'm sure us human solvers won't always see the optimal solution when
      it's 5-7 moves away.

      - Grant
    • Stefan Pochmann
      ... Can you tell us what these 13 states are? ... though ... when ... Hmm, maybe a simple greedy algorithm could work... but I haven t tried it yet, this is
      Message 2 of 11 , Apr 6, 2004
        > depth 7: 13 0.63%

        Can you tell us what these 13 states are?

        > After that, corners can be oriented in at most 7 more moves,
        though
        > I'm sure us human solvers won't always see the optimal solution
        when
        > it's 5-7 moves away.

        Hmm, maybe a simple greedy algorithm could work... but I haven't
        tried it yet, this is just an idea that came to my mind as a
        response to your statement...

        Cheers!
        Stefan
      • Stefan Pochmann
        How fast can you execute this? Some time ago I found that you can get the same using a double Sune , i.e. (L U L U L U2 L) (R U R U R U2 R ) This will
        Message 3 of 11 , Apr 6, 2004
          How fast can you execute this? Some time ago I found that you can
          get the same using a "double Sune", i.e.

          (L' U' L U' L' U2 L) (R U R' U R U2 R')

          This will twist the UFR and URB, so rotate the cube to achieve
          exactly what your alg does. Due to the nature of the above alg you
          can easily mirror it just by doing the second part first, i.e. try

          1. (L' U' L U' L' U2 L) (R U R' U R U2 R')
          2. z'
          3. (R U R' U R U2 R') (L' U' L U' L' U2 L)
          4. z

          Cheers!
          Stefan


          --- In blindfoldsolving-rubiks-cube@yahoogroups.com, "Michael
          Atkinson" <unipsycho6@y...> wrote:
          > One algorithm that I often use is from Richard Carr's document:
          >
          > R'D'LDRD'L'DUL'UR2U'LUR2U2
          >
          > You hold it so there's a corner with orientation 2 in position
          UFR,
          > and a corner with orientation 1 directly below that. It's my main
          > corner orientation algorithm.
        • Brent Morgan
          I agree, all these algs are fast... but I think, ... the fastest way is just looking and planning ahead w/ nonstop, as ron says: just simply looking ahead
          Message 4 of 11 , Apr 6, 2004

            I agree, all these algs are fast...  but I think, ...  the fastest way is just looking and planning ahead w/ nonstop, as ron says: "just simply looking ahead makes a huge difference"
            -bm
            Stefan Pochmann <pochmann@...> wrote:
            How fast can you execute this? Some time ago I found that you can
            get the same using a "double Sune", i.e.

            (L' U' L U' L' U2 L) (R U R' U R U2 R')

            This will twist the UFR and URB, so rotate the cube to achieve
            exactly what your alg does. Due to the nature of the above alg you
            can easily mirror it just by doing the second part first, i.e. try

            1. (L' U' L U' L' U2 L) (R U R' U R U2 R')
            2. z'
            3. (R U R' U R U2 R') (L' U' L U' L' U2 L)
            4. z

            Cheers!
            Stefan


            --- In blindfoldsolving-rubiks-cube@yahoogroups.com, "Michael
            Atkinson" <unipsycho6@y...> wrote:
            > One algorithm that I often use is from Richard Carr's document:
            >
            > R'D'LDRD'L'DUL'UR2U'LUR2U2
            >
            > You hold it so there's a corner with orientation 2 in position
            UFR,
            > and a corner with orientation 1 directly below that. It's my main
            > corner orientation algorithm.




            :)
            --Brent


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          • Grant Tregay
            ... Hmm... I sent a response to this yesterday, and it doesn t appear to have gone through - I ll repost. Not surprisingly, the 13 states are superflip along
            Message 5 of 11 , Apr 8, 2004
              --- Stefan Pochmann wrote:
              > > depth 7: 13 0.63%
              >
              > Can you tell us what these 13 states are?

              Hmm... I sent a response to this yesterday, and it doesn't appear to
              have gone through - I'll repost.

              Not surprisingly, the 13 states are superflip along with 12 states
              with 10 edges flipped. Here's a summary:
              1) Superflip (all edges flipped)
              2-5) UF or DF and BL or BR
              6-9) UB or DB and FL or FR
              10-13) Two edges across F or B from each other (e.g. FR and FL or UB
              and DB)

              Here's a list of the edges flipped (and not flipped) in each of the
              13 states:
              1) UF UB UR UL DF DB DR DL FR FL BR BL (All Flipped)
              2) UF UB UR UL DF DR DL FR FL BR (Not DB BL)
              3) UF UB UR UL DF DR DL FR FL BL (Not DB BR)
              4) UF UB UR UL DB DR DL FR BR BL (Not DF FL)
              5) UF UB UR UL DB DR DL FL BR BL (Not DF FR)
              6) UF UR UL DF DB DR DL FR FL BR (Not UB BL)
              7) UF UR UL DF DB DR DL FR FL BL (Not UB BR)
              8) UB UR UL DF DB DR DL FR BR BL (Not UF FL)
              9) UB UR UL DF DB DR DL FL BR BL (Not UF FR)
              10) UF UB UR UL DF DB DR DL FR FL (Not BR BL)
              11) UF UB UR UL DF DB DR DL BR BL (Not FR FL)
              12) UF UR UL DF DR DL FR FL BR BL (Not UB DB)
              13) UB UR UL DB DR DL FR FL BR BL (Not UF DF)

              - Grant
            • Grant Tregay
              ... I didn t say that right; the summaries of 2-13 indicate which edges are not flipped in each state. - Grant
              Message 6 of 11 , Apr 8, 2004
                --- Grant Tregay wrote:
                > Here's a summary:
                > 1) Superflip (all edges flipped)
                > 2-5) UF or DF and BL or BR
                > 6-9) UB or DB and FL or FR
                > 10-13) Two edges across F or B from each other (e.g. FR and FL or
                > UB and DB)

                I didn't say that right; the summaries of 2-13 indicate which edges
                are not flipped in each state.

                - Grant
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