2
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Solution guide: http://rubiks.com/uploads/general_content/Rubiks_cube_3x3_solution-en.pdf

I can get to this point pretty reliably now, but when I try the method shown I'm just as likely to go from one or no corners to two yellow corners as I am to go back again the next round. I don't mess up the solved rows of the cube; things just seem to shuffle at random at this step. I get the feeling I might not be fully understanding what it means to re-orient the cube.

For example:

State 1:
  Y B Y
G O Y B R
R Y Y Y O
Y G Y O Y
  R G B

Which produced State 2:
  Y O R
O B Y G Y
B Y Y Y R
Y R Y Y O
  B G G

Rotated 90° clockwise (to match state 2 as per the guide) and produced State 3:
  R O O
G Y Y Y G
B Y Y Y G
O Y Y Y R
  B R B

...which coincidentally solves it this time. Guess it sensed my crying out for help.

I guess what it boils down to is I'm not sure what to do when I get two corners up, as I haven't gotten particularly good at predicting where pieces will end up at this stage in the puzzle as of yet. Any advice to be offered on that point?

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Hmm, what I find lacking in the guide is the positioning of the yellow faces on the side. (which I rely on in the previous step to be more likely to end up with the 'fish' pattern on top).

You may want to look at the instruction for the several 'cases' for the different top patterns to be able to fix it. It relies on the same 8-step move as described in the guide your reference, but shows them visually:

Link to Ryan Heise's page on cube solving

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  • $\begingroup$ Ah! So proper orientation in this case means with a block the same color as the fish along its front, and then basing the pattern on where his nose is pointing. Thanks! $\endgroup$ – Kaji Aug 29 '14 at 13:32
  • $\begingroup$ Yup. Also, in the page before that (where you go from a single center square, to a line, to a small 'L'-shape, having a yellow one in the top row of the front face is probably also relevant. Hence my generalisation of those positions lacking in the link you gave. $\endgroup$ – Tim Couwelier Aug 29 '14 at 14:50

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