That was fun. Took a while for me to figure out the pidgeonholing of numbers on the first and second rows. (the lower left corner I got immediately though).

I've gotten fairly into burr design lately (some of my designs just went up on Ishino's site). It turns out that burrs are themed as well, although novel themes are hard to come up with. It makes some sense that kenken would lend itself well to theming, because the now totally out of fashion type of puzzles where longhand operations had the digits replaced by letters were a big thing in their day, with lots of novel and interesting puzzles designed by hand.

I've hardly designed any burrs without the auto-solver. I'm a wuss that way.

I can appreciate the value of an auto-solver when constructing - I got a taste of it when I was writing some of Mutant Sudoku with Wei-Hwa and for some variations it was very helpful to confirm/construct designs that I could not do exclusively by hand.

I think it varies by puzzle-type. KenKen is incredibly easy to construct (at least for me, as I'm very good at packing latin squares in my head already from sudoku, and removing that box constraint is a huge assist). I somehow doubt Burr puzzles are as easy to construct; if you have tools to assist the process, you might as well use them.

Sudoku-type puzzles are certainly a lot easier to do in your head than burrs - I don't think I've ever heard of someone doing a burr without manipulating it. The sequential movements make it too hard to backtrack and remember all the positions.

The ethos of cyborg design is quite different. At least the way I do it, there's a themed puzzle - basically like a mutant sudoku, and you pick out the best one or two instances of that puzzle as worthy of showing to other people. The problem is that auto-generated instances are way, way too difficult, so you compensate by making the puzzle so impossibly small that even the hardest auto-generated instances are reasonably approachable simply by dint of smallness. I frequently also pick out specific instances for aesthetic criteria, such as having a unique solution or having two pairs of pieces instead of four different ones.

The dance of making it as hard as possible and then undermining yourself by making it so small and simple it isn't so difficult any more is an interesting one. Some simple-looking instances aren't really in the realm of human solvability, they're more exercises in industrial engineering.

Today's Beatles tribute:

Obviously all regions use subtraction or division. The 2-cell regions must be subtraction, as division would require two of the same number in the same cell. Three cell regions can be 4-2-1, 3-1-1, 4/2/2, or N/N/1, but the straight one can only be 4-2-1. The four cell region must be division, and had better be 4/2/2/1 if we want any hope of uniqueness (N/N/1/1 is also possible).

So we get the lower left corner is 3 immediately. Above it is 2 or 4. 3/3/1/1 is not possible for the 4-cell region, so there is no way to put a 3 in it. Thus, the horizontal region in row 3 must begin with a 3, and the horizontal region in row 1 contains a 3.

The bent 3-cell region must also contain a 3 in row 2. This leaves only 3-1-1 and 3/3/1 as possibilities, and the latter conflicts with an existing 3. So it is 3-1-1.

Then the remaining 1s and 3 can be placed. Row 2 must contain 2 and 4, and the 2 must come first to make the 4-cell result work out. Everything else can be filled by elimination.

1234
2413
4321
3142

While the "internets" provide debate that this could be a Beatles tribute, I thought (and still think) One is a Three Dog Night song. The rest of your analysis is spot on.

Ah well, since I wrote it at dark-o-clock this morning, I'm glad the only mistake I made was in the cultural reference.