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- Jul 4, 2012
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I have been trying to find a puzzle with the largest number of permutations without being massive, like a petaminx. The most "efficient" way to get a large number of permutations. One of the things I have been looking at is types of turning. There are skewb puzzles, face-turning puzzles, corner turning puzzles, and edge turning puzzles. From here, I used process of elimination. The skewb doesn't have a whole lot of permutations (so it seems), so I cut that one out. Same thing with the dino cube.
Here is where I have some questions. I was going to compare the curvy copter cube (edge turning) to the rubik's cube (face turning) because it appears to be the 3x3 equivalent of the helicopter cube. However, the curvy copter cube jumbles while the rubik's cube does not. So, to fix this problem, I decided to only allow 180 degree moves on the curvy copter. This way, it wouldn't be able to go into other "orbits" or jumble. However, I cannot find the number of permutations using this guideline. Can anyone help me with this?
Okay, so after that, I had more questions. What about sliding puzzles? If you were to have a sliding puzzle that was the equivalent size to a 2x2 Rubik's cube, which would have more permutations? This concept has been demonstrated by Oskar's sliding cube, shown here:
http://www.youtube.com/watch?v=S9HH2FlOmv0
And, if it did have more permutations, then why? Is it because you can move each piece individually, not dependent on which face or edge it is on?
Which brings me to a new question I had, which is what about these:
http://www.twistypuzzles.com/forum/viewtopic.php?f=15&t=15126
In this video:
http://www.youtube.com/watch?feature=player_embedded&v=COtfw9-UvJY
the creator demonstrates how you can flip one piece at a time. Does this mean that this puzzle can switch "orbits?" (or "universes?")
Do these flexagon puzzles have more permutations than other puzzles?
Thank you if you've read this whole post, I'm looking forwards to what discussion may come of it.
Here is where I have some questions. I was going to compare the curvy copter cube (edge turning) to the rubik's cube (face turning) because it appears to be the 3x3 equivalent of the helicopter cube. However, the curvy copter cube jumbles while the rubik's cube does not. So, to fix this problem, I decided to only allow 180 degree moves on the curvy copter. This way, it wouldn't be able to go into other "orbits" or jumble. However, I cannot find the number of permutations using this guideline. Can anyone help me with this?
Okay, so after that, I had more questions. What about sliding puzzles? If you were to have a sliding puzzle that was the equivalent size to a 2x2 Rubik's cube, which would have more permutations? This concept has been demonstrated by Oskar's sliding cube, shown here:
http://www.youtube.com/watch?v=S9HH2FlOmv0
And, if it did have more permutations, then why? Is it because you can move each piece individually, not dependent on which face or edge it is on?
Which brings me to a new question I had, which is what about these:
http://www.twistypuzzles.com/forum/viewtopic.php?f=15&t=15126
In this video:
http://www.youtube.com/watch?feature=player_embedded&v=COtfw9-UvJY
the creator demonstrates how you can flip one piece at a time. Does this mean that this puzzle can switch "orbits?" (or "universes?")
Do these flexagon puzzles have more permutations than other puzzles?
Thank you if you've read this whole post, I'm looking forwards to what discussion may come of it.