Can someone explain what stored cuts are? I see that term thrown around in the descriptions of some of the more exotic custom puzzles but can't find a proper definition anywhere. Also, how is it related [if at all] to difficulty and the concept of jumbling?

This is a very good question, and I would also like to know more about stored cuts, as well as other types of cuts (Conical, Planar, Spherical, etc.
The only thing I can think of is that I believe the Square-2 has stored cuts, and that it is considered by some to be fully unbandaged because of this.

-Doug

Here is my definition of a stored cut:

For something to be considered a stored cut, it must satisfy 2 conditions:

1: The move must not be available when the puzzle is in its "solved state", save partial turns (i.e. ghost cube)
2: Some combination of moves must exist where the move can be reached.

I think my Coumpound Crystal puzzle sum the idea up quite nicely. For a further explination about "reaching" the cuts, I made a Youtube Video

For some other examples, look at Oskar's crazy Comet, Uncanny cube, and Asteroid Attack.

As far as the relationship with jumbling goes, All I can say is that I cannot think of any (not-unbandaged) jumbling puzzle that has stored cuts. I may be wrong here, but every time a jumbling puzzle has had unbandaging applied to it, the resulting added cuts end up being stored cuts; I cannot think of a counterexample. Earlier in my post I link to Oskar's Asteroid attack, which may seem like a counterexample to what I said, but it is actually an unbandaged jumbling puzzle.

Like every other discussion that relates to jumbling, it seems that asking a single questions plants a seed that eventually grows and branches out into a tree full of questions.

I plan on coming back later and fleshing out this post (I'm in the middle of class now ) Hopefully someone will add on to what I've said, because I have only brushed on the topic.

Another example:
http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=3278
Not every gap between two pieces can be "used" for a move but with some additional setup-moves every two adjacent pieces can be seperateds from each other.

When I read the original post this morning I thought the exact same thing. The trouble with a statement like this is that we have some puzzles that really blur the lines.

One that comes to mind is the Split Jing's Pyraminx:


It has stored cuts and those cuts are what enable the jumbling. I think this really comes down to definitional matters. The "natural" base puzzle is the Jing's Pyraminx which doesn't jumble and doesn't have stored cuts and isn't bandaged or unbandaged. If you "unbandage" it by adding the stored cuts, it turns into a jumbling puzzle.

So it was a doctrinaire puzzle that was unbandaged, not a jumbling puzzle that was unbandaged. Sorta a gray area for your statement.


Edit: wordsmithing pass.

I think it's better that we leave out the Square-1 and Square-2 from this discussion. The middle layer is "bandaged" on both in that it only has one cut so to reach most cuts you need to turn the top or bottom layer to align it with the middle layer.

If you can imagine a 2-layer Square-1 or Square-2 (missing the middle layer) then neither has any stored cuts.

As I think about it more... I think it's best that we leave out all bandaged puzzles from this discussion. Most bandaged puzzles will have cuts that are stored in one state but not in another.

Would it be correct to say that, in the solved position, stored cuts represent an incomplete circle [arc] on the Jaap's sphere? And that after some number of moves, they match with other arcs, whether they be other stored cuts or arcs of proper circles, to complete a new circle? This would imply that when one stored cut is "activated," some other cut would be stored.

My brain hurts

Well the Golden Cube and Ghost Cube both have stored cuts in their solved state but not in their scrambled states. Again this comes down to definitional matters. I'd say their solved state is not the natural solved state for their geometry.


That's the whole point of this hobby and forum