CFOP Superman’s clairvoyance (Hidden faces hunting)

[Tito_H]

Today Superman came to see me, and presented a quiz, to check if my ability of seeing though had been improved.

He said, "Cross and the first F2L (dBL) have been completed. Now, let's determine whether it is possible to theoretically estimate the colors of all the hidden faces of the pieces of the following cube. If you can't guess, can you explain why?"

Oh no! I've had a slight headache since the beginning of the year...Can you help me?

(Position: Yellow top, Orange front)

 

[bcube]

Now, let's determine whether it is possible to theoretically estimate the colors of all the hidden faces of the pieces of the following cube. If you can't guess, can you explain why?

All corners except for both yellow-blank-blank ones -> all edges -> remaining 2 yellow-blank-blank corners.

 

[Tito_H]

Thanks for your help, bcube.

Based on your thought process, I started deciphering as follows:
1. (Obvious) UFL is white-green-orange, UBR is white-blue-orange, and DFR is yellow-red-green.

2. Yellow is visible in four corners. White faces appear in UFL and UBR. Since F2L is complete, DBL is white-red-green. Therefore, UBL is a white-blue-red corner.

3. The red-green EP and red-white EP have already been used in Cross and F2L, and the red-blue EP is in UR. Therefore, UL is red-yellow.

4. For EPs containing yellow, yellow-orange and yellow-blue are visible. From 3 above, UL is yellow-red. Therefore, UB is yellow-green.

5. The green-white EP and green-red EP have already been used in Cross and F2L. From 4 above, UB is green-yellow. Therefore, BR is green-orange.

6. Orange-yellow is visible. Orange-white is used in F2L. From 5 above, BR is orange-green. Therefore, FL is orange-blue.

7. Only DFL and DBR remain unsolved.

The 7 above is a little tricky part, since both corners show only a yellow face…

 

[Tito_H]

7. Only DFL and DBR remain unsolved.

The 7 above is a little tricky part, since both corners show only a yellow face…

Well, as for the No. 7 (DFL and DBR which remain unsolved), I deciphered as follows:

There are 5 EP exchanges (odd parity). If DFL is yellow-blue-orange and DBR is yellow-blue-red, there will be 5 (odd) CP exchanges. If DFL is yellow-blue-red and DBR is yellow-blue-orange, there will be 6 (par) CP exchanges. Therefore, DFL is yellow-blue-orange and DBR is yellow-blue-red.



Test passed!