Star Battle rules › Guide
Star Battle 2×2 Rule: Explained with Examples
A 2×2 block in Star Battle can contain at most one star because every pair of its cells touches at an edge or corner. It may contain zero. Counting can prove that a particular block must contain exactly one.
This applies to any 2×2 square, even when it crosses colour-region borders. A counting block is not an extra puzzle region. The examples below are local illustrations, not complete puzzles; dots mark empty cells.
1. Why two stars cannot fit
Put a star in the top-left cell. The top-right and bottom-left share its edges; the bottom-right shares its corner. All three are forbidden, so a second star cannot fit. The argument works whichever cell gets the first star.
2. Why a block can be empty
There is no rule requiring a star in every 2×2 square. A local patch may be empty because its rows, columns and regions place their stars elsewhere. Turning “at most one” into “exactly one” needs additional information.
3. Four stars with room for only four blocks
These are two adjacent rows of a 10×10 two-star board. Together they need four stars. Split them into five disjoint 2×2 blocks. If the leftmost block is already empty, only four blocks remain, each holding at most one star. Therefore every remaining block must contain exactly one star.
The blocks must not overlap, and together they must cover every available cell in the area being counted. Overlapping blocks could count the same star twice.
4. Turn a forced block into a forced cell
Keep the same four-block count. In the second block, R1C4, R2C3 and R2C4 are empty. Since that block must hold one star, its remaining cell R1C3 is a star. Without the counting proof, those three dots alone would not force it.
5. Five available blocks do not all need stars
If all five blocks are available, the two rows still need only four stars. At least one of the five disjoint blocks will be empty. Capacity exceeds demand, so the 2×2 argument alone cannot identify which four blocks are occupied.
6. Adjust the count for one-star puzzles
On a one-star board, including Queens-style puzzles, two rows need only two stars. Even with the first block empty, four available blocks do not each need a star. The spacing limit is unchanged; the row quota changes the conclusion.
Before using a 2×2 deduction
- Check whether the puzzle uses one or two stars per unit.
- Cover the counted area with disjoint blocks; do not omit available cells.
- Prove that required stars equal the available blocks' total capacity.
- Apply row, column, region and no-touch constraints after every forced mark.
Practise two-star Star Battle →
Use the complete two-star walkthrough for broader pair reasoning, or try printable Star Battle puzzles with answers.
Rule reference
The underlying spacing rule is stated in Grandmaster Puzzles' Star Battle rules. The capacity arguments and diagrams here are original illustrations.