Star Battle solving techniques
Every puzzle here is checked before it is published: it has exactly one solution, and the techniques below are enough to reach it without guessing. So when you are stuck, the next step is always one of these.
Start with these
Quick to spot, and most of every board falls to them.
Stars cannot touch
When to look for it. Immediately after placing any star.
No two stars may touch, not even at a corner. So the moment a star goes down, every one of the up to eight cells around it is empty. Crossing them off straight away is what makes the next deduction visible, and skipping it is the most common reason a solvable puzzle feels stuck.
A full line is closed
When to look for it. After placing the last star a row, column, or region was owed.
Every row, column, and region holds exactly its quota of stars, never more. Once that quota is met, every remaining open cell in it is empty. Closing the line off at that moment often collapses a region elsewhere on the board.
Only enough room left
When to look for it. Whenever eliminations have narrowed a row, column, or region down to just enough cells.
A line owing two stars with only two open cells has no choice left to make: both cells are stars. Watch for this straight after a big round of crossing off, since that is what squeezes a line down to its last few cells.
Cells caught between candidates
When to look for it. When a row, column, or region is down to two or three open cells sitting close together.
Suppose a region has only two open cells left and they touch each other. One of them holds a star, though you do not yet know which. Either way, any cell touching both of them ends up beside a star, so it is empty. You get to eliminate without resolving the ambiguity, which is the whole trick.
Cells with no room around them
When to look for it. At the very start of a two-star puzzle, and any time a region owing two or more stars looks cramped. It is usually the first move available on an empty grid.
A region owing two stars has to fit both of them inside itself without them touching. Try a cell and ask whether the rest of the region could still take a second star somewhere far enough away. If it could not, that cell is empty — and you have proved it without deciding anything about where the stars really are. Cells in the middle of a narrow region fail this test constantly, which is why small and thin regions are the right place to start on a two-star board.
A region trapped in a row or column
When to look for it. When every open cell of a region sits in the same row, or in the same column, or spans just two of them.
A region has to place its stars somewhere among its own cells. If those cells all lie in one row, that row is getting a star from this region whether it likes it or not. When that uses up everything the row still owed, every other open cell in the row is empty — including cells belonging to entirely different regions, which is what makes this deduction reach across the board.
A row trapped in a region
When to look for it. When every open cell of a row or column belongs to one region, or to just two.
The mirror image of a region trapped in a row. If a row has open cells in only one region, that region is supplying the row its stars, and once that accounts for everything the region still owed, the rest of the region is empty — including the parts of it sitting in completely different rows.
When you are stuck
Slower, and worth reaching for once the quick ones stop working. Most daily puzzles need at least one of these; Mondays are the likeliest to manage without.
Several regions filling the same rows
When to look for it. When two or three regions are each squeezed into the same small band of rows or columns, and no single one of them is confined on its own.
Take two regions whose open cells all fall within the same two rows. Between them those regions owe some number of stars, and every one of those stars has to land in those two rows. If that is exactly what the two rows still owed, the rows are full up: any open cell in them belonging to a third region is empty. The same argument runs in reverse, with rows squeezed into regions. This is the deduction that most often breaks a hard puzzle open, and the reason to look for it is that no single region looks confined.
Counting across two neighbouring rows
When to look for it. On two-star puzzles, whenever two side-by-side rows or columns are still short of stars and the open cells are bunched together.
Two stars in the same row have to be at least two columns apart. Two stars in rows that touch have to be at least two columns apart as well, or they would meet at a corner. So if you look at a pair of neighbouring rows together, every star in either row claims its own column, and no two of those columns are side by side. Count the columns still open across the pair. If the pair needs five stars, five such columns must exist — and any column that cannot be part of any workable set is empty in both rows. You are counting how many fit, never working out where any particular star goes.
Checking a region case by case
When to look for it. When nothing else is moving, and some region is down to a handful of open cells with only a few sensible ways to fill them.
Pick a region that is nearly boxed in and list the ways its stars could actually sit, remembering they cannot touch each other. If a cell turns up in every single one of those arrangements, it is a star — you have proved it without ever deciding which arrangement is the real one. If a cell turns up in none of them, it is empty. Keep this for regions with a few possibilities rather than a dozen: the point is a short list you can hold in your head, not an exhaustive search. If you find yourself guessing and backtracking, you have left this technique behind and the puzzle does not require it.
Which of these you meet depends on the size of the grid. The pages on 8×8 puzzles and 10×10 puzzles show what share of the boards at that size need each technique.
The hint button on a puzzle shows the cells that justify the next step rather than the cell it is about to fill in. For today’s board, named step by named step, see today’s hints.