Game Overview:

Star battle is a puzzle with unfilled squares shown in white and the grid divided into several irregular regions. The goal is to match the specified number of stars in each row, column, and region of the grid.

Clicking on a white space places a star. Clicking on a star space changes it to a black space, denoting an empty space/where a star cannot be. Clicking on a black space changes it to a white unfilled space.

Definitions specific to Star Battle

Puzzle number: the number of stars to be placed in each column, row and region, and satisfying it means you have placed the correct number of stars.

Rules

Here are the direct rules to the puzzle:

1. Blank spaces have to be a star or an empty space
2. A row/column/region must satisfy the puzzle number
3. Two stars may not touch each other (be directly adjacent vertically, horizontally, or diagonally)

LEGUP Proof Rules

Case Rules

Star or Empty

Create a branch where a specific square is a black empty square in one branch and has a star in the other (Rule #1).

Contradiction Rules

Too Many Stars

A specific row/column/region has more stars than the puzzle number (Rule #2).

Too Few Stars

A specific row/column/region has fewer stars than the puzzle number and there are not enough empty spaces to make up the difference (Rule #2).

Clashing Orbit

There are multiple stars directly adjacent to each other (Rule #3).

Direct Rules

Surround Star

The remaining unknown space around a known star must be a black space. (Rule #3)

Columns Within Regions

If a number of regions entirely contain an equal number of columns, or a potentially non-equal number of columns with an equal number of missing stars, all of the stars for those regions must lie in those columns. Mark the rest of those regions as black and empty.

Rows Within Regions

If a number of regions entirely contain an equal number of rows, or a potentially non-equal number of rows with an equal number of missing stars, all of the stars for those regions must lie in those rows. Mark the rest of those regions as black and empty.

Regions Within Columns

If a number of columns entirely contain an equal number of regions, or a potentially non-equal number of regions with an equal number of missing stars, all of the stars for those columns must lie in those regions. Mark the spaces in those columns that are not in those regions as black and empty.

Regions Within Rows

If a number of rows entirely contain an equal number of regions, or a potentially non-equal number of regions with an equal number of missing stars, all of the stars for those rows must lie in those regions. Mark the spaces in those rows that are not in those regions as black and empty.

Columns Within Rows

If a number of rows entirely contain an equal number of columns, or a potentially non-equal number of columns with an equal number of missing stars, all of the stars for those rows must lie in those columns. Mark the rest of those rows as black and empty.

Rows Within Columns

If a number of columns entirely contain an equal number of rows, or a potentially non-equal number of rows with an equal number of missing stars, all of the stars for those columns must lie in those rows. Mark the rest of those columns as black and empty.

Blackout

If a region/row/column is finished, i.e. has enough stars, then fill out the rest of that region/row/column with black spaces to indicate that stars cannot be placed there.

Finish With Stars

If a region/row/column has exactly enough empty spaces left to fulfill the puzzle number, finish it by adding stars to those spaces.

Empty Adjacent

If all the possible spaces in a region/row/column would require adjacent spaces to not have stars to meet the puzzle number, add black spaces to indicate that stars can't be placed there.