Rung 1 — Trivial marks
The foundation is relentless bookkeeping. Every star you place eliminates its eight neighbors — mark them. Every row, column, or region that reaches its star count is finished — sweep the rest of it with X's. And when a unit has exactly as many open cells as stars still owed, those cells are all stars.
On this site the auto-X assist performs the first two automatically. Purists can toggle it off, but either way the habit matters: on paper, the strongest solvers are the busiest markers.
Rung 2 — The 2×2 rule
Because stars can't touch, any 2×2 block of cells holds at most one star. That innocuous fact does surprising work: if a region needing two stars fits inside two 2×2 blocks, each block holds exactly one — and any cell that would break that budget is eliminated.
Watch especially for cramped regions: a four-cell square region needing two stars is impossible, and a region whose remaining cells fit in a single 2×2 can supply at most one star. Budget arguments like these are usually the first non-obvious eliminations on a medium board.
Rung 3 — Confinement (1×N arguments)
When all of a region's remaining cells sit in a single row, that region's stars must come from that row — so if the counts match, every other cell in the row is an X. The same works in reverse: if a row's remaining open cells all belong to one region, the row's stars are also the region's, and the region's cells outside the row empty out.
Confinement is the defining medium-difficulty technique, and it chains: one confinement's eliminations often cramp a neighboring region into its own confinement. When a board suddenly cascades, this is usually why.
Rung 4 — Exclusion
Exclusion asks of a single cell: if a star sat here, could every row, column, and region still reach its count? Placing a hypothetical star wipes out its eight neighbors — and if that wipe-out would strand some region with too few usable cells, the hypothetical is impossible and the cell is an X.
You don't need deep look-ahead; one placement plus one feasibility check is enough. Scan cells that crowd small regions — corners and choke points between two regions are the classic victims.
Rung 5 — Under- and overcounting
The expert rung. Take a band of rows — say the top three of a two-star board: they must hold exactly six stars. Now count the regions that live entirely inside the band. If those regions' quotas already supply all six stars, then every region that merely pokes into the band contributes nothing there — all its cells in the band are X's. Run the same argument with columns, and in reverse: when the regions touching a band can only just cover its quota, each of them must place all its stars inside.
Counting arguments crack the positions where nothing local works. Hard boards here are built to require them — and nothing beyond them. There is always a next deduction; bifurcation is never needed.