Star Battle: regions that own rows
If a region fits inside one row, that row’s two stars are the region’s. Dot the rest of the row. Two regions inside two rows work the same way.
How it works
Every region needs two stars. If all of a region’s squares are in one row, both of its stars are in that row.
Every row holds exactly two stars. So the row’s two stars are the region’s two stars, and no other square of the row can have one. Dot them all.
The same counting works for bigger groups. Two regions inside the same two rows need four stars there, and two rows hold exactly four. So every star in those rows belongs to one of the two regions.
Columns, and the reverse
Everything here works for columns too. Regions C and H below both fit in columns 7 and 8, so the other squares of those columns are dotted.
It also works in reverse. If a row’s open squares all lie inside one region, the region’s two stars are in that row, and the region’s squares outside the row are dotted.
Why it is only counting
Two rows hold four stars. Two regions need four stars. If the regions can only put their stars in those rows, there is nothing left over for any other square there.
Count stars on both sides and the dots follow. Three regions in three rows is the same argument with six stars.
Worth memorizing
A region inside one row owns that row’s two stars.
Dot the rest of the row.
k regions inside k rows own all 2k of their stars.
Dot everything else in those rows.
Same for columns, and in reverse.
A row inside one region clears the rest of the region.
Practice
0 of 3 rightRegion A lies in row 1. How many squares can you dot?
Which two regions fit together inside rows 7 and 8?
Regions C and H both fit in columns 7 and 8. How many other squares of those columns can you dot?