Regions inside lines

Page 3 of How to Solve Star Battle Puzzles.

This is the move for one-star boards that stop moving after the basic ones. Queens and Meowdoku are one-star Star Battle puzzles, so it works there too.

Regions inside lines says: if N regions are completely inside N rows, those regions use all the stars of those rows. So rule out every other square of those rows. The same goes for N regions inside N columns.

When N is 1, this is Region inside a line. Here N is 2 or more.

In the app's hints, 35% of 8×8 and 69% of 10×10 one-star puzzles have a step where this is the only move that applies. If a puzzle has stopped, look here first.

Two regions in two rows

Look at the top rows of this puzzle.

An 8×8 one-star puzzle. Look at rows 1 and 2.

Regions inside lines: These 2 regions are inside 2 rows. They hold all the stars of those rows. Rule out the rest of those rows.

The region at columns 4 and 5 and the region at columns 6 to 8 are inside rows 1 and 2. They use both stars of those two rows, so the squares of rows 1 and 2 outside them get dots. The new dots are in blue.

Count it step by step. Rows 1 and 2 need two stars. One region has all its open squares in these two rows. A second region does too. Each region needs one star, so they supply two stars. That is every star the two rows need. The squares of any other region in rows 1 and 2 cannot hold a star.

No single region is inside one row here. Each of the two regions covers both rows. The move works because you count regions against rows.

Three regions in three rows

It works with more regions, too.

Regions inside lines: These 3 regions are inside 3 rows. They hold all the stars of those rows. Rule out the rest of those rows.

Three regions are inside rows 1 to 3. They use all three stars of those rows, so the other squares of those rows get dots. The new dots are in blue.

The same idea, seen from the other side

Count the other way and you get the mirror image. Suppose N rows or columns have all their open squares inside N regions. Those lines use all the stars of those regions. So rule out every other square of those regions. It is the same count, taken from the lines instead of the regions.

What to look for

Small regions. A region of two to six squares is the likely candidate. List the rows and the columns that each one is inside.
A count that matches. List the regions that are inside rows 1 to N. If there are exactly N of them, you have the move.
Both directions. Do the check for columns too.

Practice on puzzles like these in our Star Battle Puzzles app, for iPhone, iPad, Mac and Android.

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