1x1 Indiana Jones' Special Dice cube

[Tito_H]

One day, Indy came to visit me. I said, "Indy, it's been a while. Have you been on any adventures lately?"

He replied, "I'm getting older, so I can't travel the world as often as I used to, but I've been to a few countries. I recently found a place that seems to have a lot of gold buried there. But there's one problem. When I went to that place (the cave), I found a large iron door like a bank vault, with something like a Rubik's Cube embedded in the lock. Apparently, if I could solve it (= change the number to the specified number) in five moves, the iron door would open."

He then showed me a video of the cube and explained it to me as follows.

- It was a 1x1x1 cube like the one below.



- The faces are touchscreens, and when you lightly swipe your finger, the cube appears to rotate 90 degrees on the X, Y, and Z axes. It doesn't physically rotate; instead, the light indicators on each face change, creating the illusion of rotation.

- When the cube rotates 90 degrees, the numbers displayed on the 4 faces you moved change. Upon closer observation, the original numbers on each face become (the original number + the newly added number). However, if the number exceeds 6, it is replaced with the remainder (mod 6).

For example, if you rotate the cube from the initial arrangement of numbers x → y → z with Yellow top and Blue front, the numbers on each face will change as shown below.

(Initial arrangement)


⇩When rotated in x direction...


⇩and when rotated in y direction additionally...


⇩and when rotated in z direction additionally...


Then, how do you rotate the cube (x, y, or z) to change the initial dice arrangement to the specified arrangement with 5 rotations (in the QTM base)?
(Cube orientation: Yellow top, Blue front)

<Initial dice arrangement>

⇩
<Specified dice arrangement>


Since the numbers change with (mod 6), there is probably no fixed solution, so why not think about it while you kill time or practice playing the cube?

I hope you open the iron door of the cave and get your hands on a mountain of gold!

 

[Tito_H]

Later, I received a package from Indy with a letter inside. The letter said, "I finally managed to solve the mystery of that dice cube." He then added, "By the way, I'll tell you how I solved it."

The contents of his answer were as follows:

(Initial arrangement)

1
4 2 3 5
6



⇩x rotation

3
4 2 3 6
5



⇩y rotation

3
6 5 3 4
5



⇩z rotation

3
5 5 6 4
2



⇩x rotation

2
5 1 5 1
6


⇩z rotation

1
5 1 1 1
5



It was x → y → z → x → z!
All I had to do was add x → z to the x → y → z I gave as an example.

I think Indy opened the iron door to the cave and got a lot of treasure. The package contained an old Dice cube that had been stuck to the iron door as a Christmas present for me.

Thank you, Indy!