Interesting point to compare it to Two-away or Consecutive Sudoku – all these “relationship X between two squares” puzzles (and there are lots of other variants) work on similar lines of course. The secret (as a creator) is to find the sweet-spot where the extra information rewards rather than creates extra work – in this puzzle it obviously went too far towards the latter.

The only other implication of the 4/5 break-down I was inferring is simply that in all the ones I solved myself I found that I ended up with lots of pairs, triples and quads, but much more clearly signalled than in a regular puzzle.

I don’t see how you could say “It eliminates lots of possibilities from squares relatively quickly, so you’re left with more deductive logic and less pencil-mark housekeeping.” … I had to eventually use a loop technique to crack it. Of course I probably missed something as usual … but it was very frustrating. Makes me not look forward to the one in Issue 4.

I was also frustrated with 2-away consecutive sudokus as well. In those the adjacent numbers paired up into EVEN/EVEN or ODD/ODD (rather than ODD/EVEN), but at least you knew the range of numbers given one of the digits.

So going on from what you have told us:

1. The only way for the sum to be odd is if one of the numbers next to the O is odd and the other is even.

2. There are 5 odd numbers and 4 even numbers per row/column/region. (As usual)

….is there something else I am missing that might help me solve these?