Superman’s Christmas present

Tito_H

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May 23, 2024
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Japan
Yesterday, Christmas Eve, Superman visited me at 11:59pm with a huge box. Even he, a strong man, was carrying it with such force.

I had a bad feeling because he had brought me a big and heavy puzzle last time, which I had given up playing.

He said to me, “I brought this for you.”

My bad feeling turned out to be true. I was slightly worried inside, but outwardly I put on a grateful face.

Then, he opened the big box and pulled out a small box with ribbon, and said, “This is my Christmas present for you.”

I was surprised and said to him, “Thank you very much. But why did you bring such a huge box and also look weak?”

He replied, “I had many full big boxes with about 1 billion presents, and have just delivered them to each house in the world, and yours is the last. I am really exhausted.”

Then I understood the reason, but why is he doing that job? I asked him, “Isn't that Santa Claus' job? Why you?”

He replied, “Santa asked me to do this because he saw a Superman movie a while ago, and thought that I could deliver presents in much less time than his sleigh pulled by 9 reindeers.”

Well, well, he was really a multi-purpose man.

Let’s open his present…
Wow! A beautiful LEDs-illuminated 3x3 cube!

Right away I tried to move R U R’, but couldn’t move U. Some of the slices (U, D, F, etc.) could be turned.

Superman explained, “This is a special cube. You can only turn R & L slices and twist the corners.”

I twisted UFR corner clockwise, then the following movements occurred. Of course, these were due to the effect of the LEDs color change, not physical changes.

  • The 3 EPs adjacent to that corner changed their positions to others clockwise. UF->RU->FR->UF.
  • The 3 CPs adjacent to those 3 EPs changed their positions to others clockwise. UFL->RUB->FRB->UFL.
  • The corner which I twisted rotated back counterclockwise to return to the original direction.
For example, I twisted UFR clockwise, and UFL clockwise, then the result was as indicated below.

(Original position)


⇩(after UFR twisted clockwise)



⇩ (and after UFL is twisted clockwise…)



I checked and confirmed that the parities of EP & CP kept maintained. R & L were the same turns as normal cubes. The puzzle was found to be always solvable.

Thank you very much, Santa & Superman!
 
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