Kurodoko
Blacken some cells. A numbered cell is always white, and its number is how many white cells it can see — itself, plus the unbroken runs of white in all four directions, each stopping at the first black cell or the edge. No two black cells touch, and all the white cells form one connected group. Click a cell to cycle black → white → blank.
The variable is not the cell
A clue with number k says
1 + up + right + down + left == k, where each term is the
length of an unbroken white run with a hard geometric cap. Four
bounded integers summing to a constant is a shape a solver already
knows what to do with: a direction's run can be no shorter than the
total minus what the other three could contribute at their most
generous, and no longer than the total minus what they must contribute
at their meanest.
Tightening one direction pays out in cells. If the run is at least lo, its first lo cells are white — and that is the part which is safe. The mirror image is not: from "this run is at most hi" it looks obvious that the cell at hi must be black, and it is wrong, because the run can stop short and leave that cell sitting harmlessly beyond the stopping point. That unsound step survived until two brute-force counters disagreed with a third.
Where you measure a rule decides whether it looks useless
Drop the connectivity rule from the strongest fixpoint and the share of cells decided goes from 35% to 34% — on that evidence it is dead weight. It is not. Measure the same rule inside singleton consistency, where its job is to refute an assumption rather than decide a cell outright, and it takes the solver from 8 of 25 boards finished to 25 of 25. Same propagator, same boards, opposite verdict.
Adding a clue never changes the answer
A clue cell is just a white cell carrying a number, and it was white already — so adding a clue cannot change the solution, only remove rivals. That makes generation monotone and termination free: paint a legal board, then keep adding clues until nothing else solves it, and in the worst case every white cell becomes a clue. Then run it backwards and drop every clue that turns out not to be pulling its weight; the sweep removes 17–21% of them.
The previous puzzle in this series, Yajilin, has the opposite character: there a clue cell sits off the loop, so every clue you add changes the solution, and one whole half of the puzzle — the routing — cannot be pinned by clues at all.