ab wrote:Have any puzzle compilers explored this?
Yes, many... More than you can imagine... Not only some cage sums can be omitted, even some of the cages themselves can be omitted...
Many players of Killer Sudoku puzzles on the web gather at
this forum... In there you'll see about half of the puzzles compiled there have many "blank regions" (what we call "Zero Killer Sudoku" puzzles)...
Even in this particular place you can see some of these puzzles:
Mikejapan's Killer AlbumsJean-Christophe's (Non)Consecutive Zero Killer XRichard S's Double Killer - 007(There are extra rules in some of them...)
As early as 2005, Ms Miyuki Misawa, the "mother of Killer Sudoku", already posted puzzles with blank regions, and even puzzles with no cage sums, only inequality signs between cages...
http://www7a.biglobe.ne.jp/~sumnumberplace/22326860/http://www7a.biglobe.ne.jp/~sumnumberplace/79790008/