Jump to content
BrainDen.com - Brain Teasers
  • 0
TimeSpaceLightForce

4-axis Rubik's Cubes

Question

4cubes.jpg

Four modified 1x1x1 Rubik's cubes are sticking with each other by magnetics (as shown) forming the 2x2x1 puzzle block.
Starting with all the same colors on the same face to ensure solvability, shuffle by turning any two side by side 
cubes on the axis that connects their centers. Few times will do. 
To solve or play just apply the same rule of turn to rearrange for same colored sides. Maybe a different configuration. 
Note that the 2 cubes cannot rotate on edges or face axis..just on the axis where both centers are.(90 or 180 deg)

If by then only one of the cube is disoriented, how many turns more shall it take to complete the puzzle? 

Share this post


Link to post
Share on other sites

9 answers to this question

Recommended Posts

  • 0
Spoiler

Four.*

Starting with a solved state, label the four cubes as such: (top-down view)
AB
CD

1 - Rotate AC
2 - Rotate CD
3 - Rotate AC (reverse of move 1)
4 - Rotate CD (reverse of move 2)

Cube B is not moved. Cubes A and D are rotated twice, with the second rotation returning the cube to its initial orientation. Cube C is rotated four times, and is the only cube disoriented in the final position. This new position, an example of the position in question, can be returned to the solved state in four moves. QED.

* This does not prove that all such positions can be solved in four moves, though I suspect any that cannot be solved in four moves may be unsolvable. (Open question.)

 

Share this post


Link to post
Share on other sites
  • 0
Spoiler

Let an arrow pointing from front  face to bottom edge be the reference Position 1.Then designate all  other positions ..2-8 (low) ,9-16 (mid) ,17-24 (high).

Any cube (A , B ,C or D) can be rotated to all 24 positions via 2-axes. But not all 24 position is possible for the disoriented cube if it played  from a solved state. 

@Logophobic
Four moves cannot solve all possible positions of the disoriented cube. How many one cube disorientation  can be solved with four ? 

 

 

Share this post


Link to post
Share on other sites
  • 0
Spoiler

The possible position of the disoriented cube that can not be done with 4 moves is one.
Now we search for the least no. of moves to solve that (bad position)..the best answer so far is 8.

For the closing question.. would it be possible from your model:
1 - Rotate AC
2 - Rotate CD
3 - Rotate AC 
4 - Rotate CD 
5 - Rotate AC
6 - Rotate CD (D back in correct position as B)
7 - Rotate AC (A back in correct position as B)?

 

Share this post


Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...

  • Recently Browsing   0 members

    No registered users viewing this page.

×
×
  • Create New...