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 Post subject: Jumbling Puzzle Order
PostPosted: Mon Jul 12, 2010 12:29 am 
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Many jumbling puzzles act extremly different from eachother. I propose giving all jumbling puzzles a number. This number would be how many times the puzzle has been unbandaged from its most bandaged state. The smaller the number, the more bandaged the puzzle would act. The larger the number, the more open and unbandaged the puzzle would feel until at infinity the puzzle becomes fudged and non jumbling.

Any thoughts about this idea?

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 Post subject: Re: Jumbling Puzzle Order
PostPosted: Mon Jul 12, 2010 1:10 am 
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It sounds like a good idea, but I can't think a good way to properly measure it. Counting the number of bandages doesn't seem right because you can't always agree on on what the most basic bandage jumbling version is. Also, I would say that the helicopter cube and helicopter dodecahedron should be have the same "jumble distance" but if you just count bandages, the cube would seem way less unbandaged.


Somehow this reminds me of fractal dimension. I don't immediately know how it would/could connect to jumble distance, but it's a cool concept none the less.

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 Post subject: Re: Jumbling Puzzle Order
PostPosted: Mon Jul 12, 2010 12:57 pm 
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I agree the hard part would be finding the puzzle with a jumble order of 0. From there however, it would be easy to find the jumble order of the unbandaged puzzle. Take the puzzle with a jumble order of zero and color all cuts red. With yellow cuts, unbandage it so that all red cuts are unbandaged. This would produce the puzzle with a jumble order of 1. Continue this until all cuts exist that are on the puzzle needing to be classified. If a puzzle has a jumble order of 7 but has less cuts then the unbandaged 7 times version, it could be considered bandaged from the jumble order 7 puzzle.

I might have designed a puzzle with a jumble order of zero a while ago. From the solved state, any rotation was possible. After any rotation however, only one more rotation could be made before it being forced back into the solved state.

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 Post subject: Re: Jumbling Puzzle Order
PostPosted: Mon Jul 12, 2010 6:39 pm 
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Hmmm. I've had this same idea and it does seem like a viable thing to consider about a jumbling puzzle.

I also agree, for a jumble puzzle that would be labelled with a 0, every move (every cut) should be available in the natural, solved state. An example of this would be More Madness by Oskar. I think there is a clear definition of what 0 should be for jumbling puzzles: If and only if every cut lines up with a face of the core and the planes that line up with every face of the core extend through the whole puzzle in its initial, natural state (i.e. every move is available and there are no additional cuts except those needed for these moves in the natural state)

However, it gets very tricky after that as you can come up with your next iteration of cuts in many different ways. It seems to me that many of Oskar's other jumbling puzzles: Meteor Madness, Asteroid Attack, Fairly Twisted, Jumblix, etc. should be labelled as 1 since some cuts are not immediately accesible.

Also, I really don't like your term "order" as that already has a pretty universal meaning that does not relate to the number of "unbandagings". Since you are taking the initiative to organize jumbling puzzles, I'll let you come up with a name for this particular aspect. But please, not order.

Good Luck!
Matt Galla

PS when Oskar says he "fudged" to make a puzzle work it means that the angles/geometry on the inside of the puzzle TECHNICALLY do/does not support the puzzle. An example would be a square where every angle is actually about 89 degrees and the edges are slightly rounded, but still using that piece in a sliding square puzzle like th 15 puzzle. It is a mathematical approximation of a physical structure requirement that in the two cases Oskar has used the term (Illegal Cube/Jumblix) is necessary because it is impossible to come up with a perfect mech. You seem to relate the term fudging to carrying out to infinity. When concerning the topic of infinity it usually preserves the properties of the iterations to get there. A jumbling puzzle that is unbandaged 70,000 times over again, while incredibly nasty-looking and certainly impossible to allow a stable construction, is by no means fudged. Just wanted to make sure that was clear.


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 Post subject: Re: Jumbling Puzzle Order
PostPosted: Mon Jul 12, 2010 6:55 pm 
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With fudging, I was thinking about the illegal cube. With a jumbling (not order) of infinity, any puzzle would not jumble. The puzzle would also have pieces that would not exist any more while others still would. In the case of the illegal cube, it produces a puzzle that mechanically can exist.

From the puzzle with the jumble (not order) of zero, only those cuts would be used to unbandaged the puzzle to a jumble (not order) of 1.

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