It occurs to me to ask another question about Killer Sudoku puzzles: is it possible to design puzzles that omit sums for some portions of the diagram, or have cages that overlap--& for the puzzles still to be soluble & unique? It occurs to me that if the standard setup (requiring every cell to belong to exactly one cage, no more no less) were varied then this might make for an interesting, elegantly sparser variation, which would also be in some ways closer to the "original" sudoku (where many cells are left blank with no initial hints at all). It would also make the 45-sum rule trickier to apply, which might give some extra zest/difficulty to puzzles....

Anyway, I know there are some puzzles where you could leave out a few of the caged sums & they'd still be soluble (I say this because I've occasionally worked from partially illegible puzzles--there were a few days where the Times' puzzle online was really hard to decipher), but I wonder how many could be omitted before it became impossible to solve.