Star Battle · the complete method
You never have to guess. Every star in every puzzle in this book can be found by reasoning alone — starting with one star to a row, then two, and ending with the seven deductions that between them finish any grid we print.
We will learn them on a one-star grid, where there is nothing to keep track of, and step up to two stars once the method is in hand.
Each row and each column holds exactly the number of stars the puzzle asks for — one, two or three. Never more, never fewer.
Each heavily outlined region holds that same number. There are always as many regions as there are rows.
Stars may not sit side by side, one above the other, or corner to corner. Every star stands alone.
A star claims all eight cells around it — the four beside it and the four diagonals. Marking those cells with a dot the moment you place a star is the single most useful habit in the game.
A dot means no star here. It is not part of the answer; it is your working, and it is what turns a hard puzzle into an easy one.
The whole game at its smallest: 4 rows, 4 columns, 4 regions, one star in each. Check the three rules on the answer before going any further — every row, column and region has exactly one star, and no two of them touch, not even at a corner.
Small grids are tight. This is the only four-by-four Star Battle there is, once you count turning it round and mirroring it as the same puzzle. Real ones start where there is room to think.
A real 6×6 puzzle — one star per row, per column and per region. It takes 36 deductions, and not one of them is a guess. Here are six moments along the way. The shaded cells are the argument being made; the outlined cells are what it decides. One picture, one reason.
3 cells ruled out. The shaded region's free cells all lie in one row, so it takes that row's star — the rest of the row is out.
3 cells ruled out. The shaded region's free cells all lie in one column, so it takes that column's star — the rest of the column is out.
4 cells ruled out. The shaded region's free cells all lie in one column, so it takes that column's star — the rest of the column is out.
5 cells ruled out. The shaded region's free cells all lie in one column, so it takes that column's star — the rest of the column is out.
1 star placed. This row has only as many free cells left as stars it still needs, so each of them is a star.
All 36 deductions made. Every row, column and region has its star, no two of them touching — and not one guess along the way.
If you get stuck, stop hunting for stars and start hunting for dots. Almost every deduction rules a cell out; the stars appear on their own once enough cells are gone.
Nothing in the rules changes except one number. Every row, column and region now holds two stars instead of one, and stars still may not touch. Every deduction below works exactly as it did — it simply counts to two.
The shaded region holds both of its stars, and they need not be anywhere near each other. A row’s two stars often belong to different regions, and a region’s two stars often lie in different rows — so count each thing separately.
One habit does change. With one star a unit closes the moment you place its star. With two it stays open, so keep track of what each row, column and region still owes rather than treating it as finished.
These are the whole method, in the order they get harder. Our puzzles are graded by the hardest one a solve actually requires, so the label on a chapter is a promise about the reasoning rather than a guess at how long you will take. Every diagram below is a real position from a real grid, with the cells the argument is about shaded.
A star forbids all eight cells around it — the four beside it and the four corners. And the moment a row, column or region holds all the stars it is allowed, every other cell in it is empty.
Stars may not touch, not even at a corner, and no row, column or region may hold more than its quota.
When to reach for it. Dot the eight neighbours the instant you place a star. It is the cheapest move in the game and it never has to be undone.
A real 8×8 position, 31 moves in. Shaded: what the argument is about. Row 8, column 7 is empty.
Count what a row, column or region still owes, then count the free cells it has left. When those two numbers are equal, every one of those cells is a star.
The stars have to go somewhere, and there is nowhere else left.
When to reach for it. Check it on whatever you have just dotted — that is where it usually becomes true.
A real 8×8 position, 29 moves in. Shaded: what the argument is about. Row 8, column 4 is a star.
If every cell a region has left lies in one row, that region's stars must stand in that row. The row's quota is therefore spoken for, and every other cell in it is empty — however far away it sits and whatever region it belongs to. The same argument works down a column.
The region must place its stars, and it can only reach that one line.
When to reach for it. Hunt for narrow regions before anything else. Most puzzles open with one.
A real 8×8 position, on the very first move. Shaded: what the argument is about. Row 1, column 1 is empty.
Take one region on its own and work out where its stars could actually stand, remembering that they may not touch each other. A cell that appears in no legal arrangement is empty; a cell that appears in every one of them is a star.
Counting free cells is not the only constraint on a region — not touching squeezes it much harder, and a cramped region often has only one shape of answer.
When to reach for it. Worth doing on any region down to four or five free cells, and on any region that has to hold two stars in a narrow space.
A real 9×9 position, on the very first move. Shaded: what the argument is about. Row 7, column 6 is a star.
Suppose the cell you are looking at held a star. Dot its eight neighbours as you always would, then look at the rows, columns and regions those neighbours belong to. If any of them can no longer fit the stars it still owes, the supposition was wrong: the cell is empty.
A star's real cost is paid by its neighbours, not by its own unit — so a cell can be ruled out by damage it would do next door.
When to reach for it. Aim it at the tightest unit beside the cell, not at the unit the cell belongs to.
A real 8×8 position, 16 moves in. Shaded: what the argument is about. Row 3, column 2 is empty.
Take two regions together. If all the cells they have left lie in just two rows, and those two rows owe exactly as many stars as the two regions do, then those rows belong entirely to those regions — every other cell in both rows is empty. It reads backwards just as well: two rows whose free cells all lie inside two regions.
Supply equals demand. The two rows can take no star from anywhere else without leaving the two regions short.
When to reach for it. Start counting in pairs when single-region locks have dried up.
A real 8×8 position, 27 moves in. Shaded: what the argument is about. Row 3, column 4 is empty.
The same accounting stretched to three: three regions whose remaining cells lie within three rows, needing between them exactly the number of stars those rows owe. Everything else in the three rows is empty. And, again, the argument reads equally well from the rows to the regions.
Nothing new is being claimed — three units claiming three lines exhaust them exactly as two do.
When to reach for it. The last resort, and the reason an Expert puzzle still needs no guess.
A real 8×8 position, 24 moves in. Shaded: what the argument is about. Row 5, column 4 is empty.
Two cells side by side. If you know a star must be in one of two neighbouring cells, then every cell touching both of them is ruled out — usually four cells in the rows above and below, and you have not even decided which of the two holds the star.
Any two-by-two block holds at most one star. Stars touch diagonally, so a two-by-two square can never hold two. In a two-star puzzle, a region that fits inside two such blocks has both of them spoken for.
Hunt for dots, not for stars. Almost every deduction in Star Battle rules a cell out. The stars appear on their own once enough cells are gone, and a solver who goes looking for stars stalls.
Work in pencil. Dots are the whole method and you will place a great many of them. A pencil and a soft eraser turn a fifteen-minute puzzle into a pleasant one.
The same puzzle you just watched, and its answer. Cover the right-hand grid, work through the left, and you will have solved a Star Battle unaided.
Every puzzle in our books has been checked by exhaustive search to have exactly one answer, and solved again by a program forbidden from guessing. If a puzzle could only be finished by trial and error, it was thrown away rather than printed — and every deduction a book asks of you is taught inside that book, before the first puzzle that needs it.