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Subject: "Cube Sequence Difficulty"     Previous Topic | Next Topic
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Predrag Savic
guest
Jun-01-07, 08:30 AM (EST)
 
"Cube Sequence Difficulty"
 
   Hi:


Please,consider the following problems:

https://www.mathlinks.ro/Forum/viewtopic.php?t=105712
And
https://www.mathlinks.ro/Forum/viewtopic.php?t=70759

Apparently,the problems belong to the same class of "recreational math and logic" problems.


I would like to to hear your opinion if computer assistance is required to completely solve them, and how many colored squares should be there on the final cubes?

Perhaps,the transition code logic has something to do with Rubik's cube solving algorithms, but I'm not quite sure.

I haven't seen such codes before,but I find them intriguing and interesting. I'm very curious becouse of the "solution-uniqueness" claim in the text.

Do you know how to attack these problems? Please,help if you can .
I hope you will find the problems interesting as I do. I'm a college freshman at University of Zagreb,interested in math, computers and natural sciences.


Best regards,
Predrag Savic


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Predrag Savic
guest
Jun-18-07, 12:39 PM (EST)
 
1. "RE: Cube Sequence Difficulty"
In response to message #0
 
   At first glance I thought that numbers 0,1,2,3 in the
code indicate spatial rotations by corresponding
0,90,180,270 degrees.
Perhaps I'm wrong but looks like it's not the case.

Then I tried putting 3×3×3 cubes into a one big 6×6×6 cube
and then to analyze the codes.Nothing that made clear sense
I noticed.

One more crazy idea is to try to relate it with hypercubes...
Opinions?
I wish I knew total number of coloured squares on the last
cube in the sequence.That could help to work the puzzle out
"backwards".
Anybody knows anaything about origin of these problems?


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amel
guest
Sep-14-07, 06:54 AM (EST)
 
2. "RE: Cube Sequence Difficulty"
In response to message #1
 
   I think that in first task, number in code after sign - presents differences in number of colored fields between two adjacent cubes. so in the last cube the total number of coloured squares would be 1.


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Pierre Charland
Member since Dec-22-05
Sep-26-07, 08:06 AM (EST)
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3. "RE: Cube Sequence Difficulty"
In response to message #0
 
   The pattern code is based on:
rows A,B,C on top face,
rows D,E.F on left face,
rows G,H,I on right face.

Still to find transition codes.

see attached image.

AlphaChapMtl

Attachments
https://www.cut-the-knot.org/htdocs/dcforum/User_files/46fa57aa7834e52b.jpg

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Pierre Charland
Member since Dec-22-05
Sep-26-07, 08:34 AM (EST)
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4. "RE: Cube Sequence Difficulty"
In response to message #3
 
   Transition seems to be absolute difference in # red cells on faces Top,Left,Right.

So 103 means:
# red cells in Top face has changed by 1
# red cells in Left face has changed by 0
# red cells in Right face has changed by 1

However, if this is the case, then a given transition code does not lead to a single configuration, unless an extra rule is at play her.

AlphaChapMtl


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itineracy
guest
Oct-13-08, 07:19 AM (EST)
 
5. "RE: Cube Sequence Difficulty"
In response to message #0
 
   Hi Predrag,

I think the solution for "70759" would be A3F1
I'll be happy to provide you with the rationale of that, but will not do so on this public forum... If my solution is the correct one, that would spoil the fun somewhat, me reckons...


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