Hi Twisty Puzzles designers,
Here is a challenge: design a good Nightmare 3x3x3.
You may know the Nightmare Cube
by Adam Cowan and Noah. This is a 2x2x2, based on a bandaged 3x3x3 inside. The bandaging was chosen such that
1) When solved, all 2x2x2 turns are possible.
2) The internal middle 3x3x3 layer can never move freely.
The first point enhances the surprise: it turns like a normal 2x2x2 at start. The second point assures that the puzzle never locks up internally.
One approach to design a Nightmare 3x3x3 would be to bandage an internal 5x5x5, and extend the central centers, middle edges and corners to the outside 3x3x3. However, you might find a better approach. Here are some criteria what may constitute a good Nightmare 3x3x3 design (assuming a 5x5x5 core).
a) When solved, all 3x3x3 turns are possible.
b) The internal 5x5x5 layers no.2 and no.4 can never move freely.
c) The bandaging is non-trivial. It should be a true Nightmare puzzle.
d) The bandaging is minimalistic, no more bandaging that essentially needed.
e) The bandaging is elegant. E.g. as many different pieces as possible, or as many the identical pieces as possible, or a subtle broken symmetry, or [fill in your own criterion].
Here is a graphic representation of a 5x5x5, with circles indicating the 3x3x3. You may use it to sketch your proposed bandaging.
Nightmare 3x3x3 - view 1.jpg [ 37.05 KiB | Viewed 671 times ]
Here is a filled-in example. I shall leave it to you to verify which of the above criteria it violates. But your entry may look similar to this (and hopefully better).
Nightmare 3x3x3 - view 2.jpg [ 40.88 KiB | Viewed 671 times ]
An entry, posted in this thread, only qualifies if it includes evidence (e.g. analyses or arguments) that it satisfies the criteria. Criteria a), b) and c) are essential. Criteria d) and e) are qualitative, but should be as good as you can design them.
If there is an entry that I like enough, then I will make a prototype of it, crediting the winning designer.
I shall be looking forward to your designs and analyses!