Rubik's Tetris simulator

[Tito_H]

Original condition:

• 6 Tetris pieces appear once
• Tetris colors do not change
• Center pieces are preserved

⇩
There is only one pattern in this condition.

Revised condition:

• 6 Tetris pieces appear once
• Tetris colors do not change
• Center pieces are NOT preserved

⇩
I will try to check how many patterns there are in this condition.

 

[bcube]

Same piece arrangement but different color order => another valid solution for the physical cube I guess.

 

[Tito_H]

Your cube can be created by placing the Magenta Center on top, rotating the original center color arrangement 180 degrees along the Y axis, and simultaneously matching the color of the Tetris pieces to that center color (without rotating the cube itself).

Therefore, if you rotate the center color by 90, 180, or 270 degrees on the X, Y, or Z axis and match the color of each Tetris piece to its center, you can create a "different-color clone," so I think there are a total of 9 "different-color clones."

If the Black color should be kept as a Center alone (not converted to the Tetris piece), only Y rotation (90, 180, 270 degrees) is valid. In this case, there are only 3 "different-color clones."

 

[bcube]

If the Black color should be kept as a Center alone (not converted to the Tetris piece), only Y rotation (90, 180, 270 degrees) is valid. In this case, there are only 3 "different-color clones."

Agreed. The physical cube seems to be manufactured in this specific pattern. Since we currently know 2 different piece arrangements, we currently know 2x(1+3)=8 valid solutions for the physical cube.

 

[Tito_H]

<Mission>
To get the number of possible Tetris cube patterns

<Tetris pieces & colors>

1. J piece Blue
2. L piece Orange
3. S piece Green
4. Z piece Red
5. T piece Magenta
6. O piece Yellow

<Other pieces>

1. Center piece Black
2. Edge piece White

<Conditions>

• 6 Tetris pieces (+ Black center & White edge) appear once
• Colors of Tetris and other pieces do not change
• Center colors are Orange, Green, Red, Magenta, Yellow, and Black (neither Blue or White)
• Positions of the Center colors are not pre-established

<Method>

• Brute force
• Place the Blue J piece on the back of the U side of the cube, and then place the Tetris colors 2 to 6 on the U→F→R→B→L→D sides in that order.

<Result>
It was found that there are 19 patterns, as shown in the simulation below.

1.


2.


3.


4.


5.


6.


7.


8.


9.


10.


11.


12.


13.


14.


15.


16.


17.


18.


19.


<Observation>
The number of corners that a Tetris piece occupies is as follows:

- S, Z, O pieces: 1 corner
- T piece: 0 or 2 corners
- L, J pieces: 1 or 2 corners

They can contain a minimum of 5 corners (1+1+1+0+1+1 = 5) and a maximum of 9 corners (1+1+1+2+2+2 = 9). Because the cube has 8 corners, it is necessary to arrange the T, L and J pieces so that T contains 2 corners, L and J contains 1 corner and 2 corners (1+1+1+2+1+2 = 8).

In this mission, the conditions require that the Blue J piece must have 2 corners and the Orange L piece must have 1 corner, but if we change the conditions and allow the Blue to be the center color, we can make the former have 1 corner and the latter have 2 corners (since both pieces are symmetrical), which would add 19 new possible patterns.

 

[JazzerThighs]

<Mission>
To get the number of possible Tetris cube patterns

<Tetris pieces & colors>

1. J piece Blue
2. L piece Orange
3. S piece Green
4. Z piece Red
5. T piece Magenta
6. O piece Yellow

<Other pieces>

1. Center piece Black
2. Edge piece White

<Conditions>

• 6 Tetris pieces (+ Black center & White edge) appear once
• Colors of Tetris and other pieces do not change
• Center colors are Orange, Green, Red, Magenta, Yellow, and Black (neither Blue or White)
• Positions of the Center colors are not pre-established

<Method>

• Brute force
• Place the Blue J piece on the back of the U side of the cube, and then place the Tetris colors 2 to 6 on the U→F→R→B→L→D sides in that order.

<Result>
It was found that there are 19 patterns, as shown in the simulation below.

<Observation>
The number of corners that a Tetris piece occupies is as follows:

- S, Z, O pieces: 1 corner
- T piece: 0 or 2 corners
- L, J pieces: 1 or 2 corners

They can contain a minimum of 5 corners (1+1+1+0+1+1 = 5) and a maximum of 9 corners (1+1+1+2+2+2 = 9). Because the cube has 8 corners, it is necessary to arrange the T, L and J pieces so that T contains 2 corners, L and J contains 1 corner and 2 corners (1+1+1+2+1+2 = 8).

In this mission, the conditions require that the Blue J piece must have 2 corners and the Orange L piece must have 1 corner, but if we change the conditions and allow the Blue to be the center color, we can make the former have 1 corner and the latter have 2 corners (since both pieces are symmetrical), which would add 19 new possible patterns.

I made a new pre-generated list of tetronimo packings that are demonstrated in this codepen app.

I have in it packing of pieces that contain as many as 6 of one piece, and also the ones with one of each tetronimo, and everything in between; even packings that involve the pieces to occupy the center. There's settings to only see the more pleasing subsets, as well.

Disclaimer: This was created with AI, but it does the job.

https://codepen.io/editor/JaredPTheGuyWithHats/pen/01a126b8-5fe6-7078-b3b8-7c15db4a6e3d

 

[Tito_H]

I made a new pre-generated list of tetronimo packings that are demonstrated in this codepen app.

I have in it packing of pieces that contain as many as 6 of one piece, and also the ones with one of each tetronimo, and everything in between; even packings that involve the pieces to occupy the center. There's settings to only see the more pleasing subsets, as well.

Disclaimer: This was created with AI, but it does the job.

https://codepen.io/editor/JaredPTheGuyWithHats/pen/01a126b8-5fe6-7078-b3b8-7c15db4a6e3d

Thanks for your interest on this issue.
I am too old to understand what I can do with that codepen app. Also, I think my iPhone7 is too old to use that app