Star Battle strategy: regions, rows and counting

A star battle looks like a colouring book and plays like a game of bookkeeping. You place one star in every row, column and outlined region, no two stars touch, and almost every move you make is not a star at all but a mark saying “no star here”. This guide covers the five techniques our solver uses to rate Star Battle puzzles and to write hints, in the order the three levels introduce them. If you have not played yet, the rules and controls are on How to play.

What the rules add up to

On a grid of size n there are n rows, n columns and n regions, and exactly n stars. Every square belongs to one row, one column and one region, so every star does triple duty: it is the only star of its row, of its column and of its region at the same time. That is why a single star rules out so much of the board, and why counting works so well in the harder puzzles.

The touching rule is the easiest one to forget. Stars may not share an edge or a corner, so a star in the middle of the grid rules out all eight squares around it, including the four diagonal ones.

On Point Paper you tap a square once for a mark and twice for a star, and you can drag across several squares to mark them all at once. Placing a star does not mark anything around it for you: doing that yourself is part of the puzzle, and it is the habit that makes the other techniques visible.

What Easy puzzles need

Easy puzzles (6×6 and 7×7 on the site) can be solved with three techniques. None of them needs more than one row, column or region at a time.

Clear around a star

As soon as a star is placed, mark every open square in its row, its column and its region, plus the squares touching it. The hint for this step reads like “The star at row 5, column 5 rules out 12 squares”. It sounds too obvious to count as a technique, but skipping it is a very common reason for getting stuck: the next deduction is often hiding behind a mark you haven’t made yet.

Tip: clear in a fixed order (row, column, region, then the ring of neighbours) so that you never leave one out.

Single

When a row, column or region without a star has only one open square left, the star goes there. The rule behind it is simply that every unit needs its star and has nowhere else to put it. After each round of marks, look for the unit you just emptied most: it is usually the one that has run out of room.

Claim

A claim links a region to a single line. If every open square of a region lies in one row, the region’s star is in that row. The row can hold only one star, so it is this region’s, and every other open square of the row is empty. The same holds for columns. It also works the other way round: if all the open squares left in a row belong to one region, that row supplies the region’s star, and the region’s squares outside the row are empty.

Every region on the site has at least three squares, so Easy puzzles open with a claim rather than a ready-made star. Scan the regions first for ones that are a straight bar, especially short ones along the edges. The hint for this step says “This region fits only in row 6” or “Row 1 fits only in one region”.

The step that follows shows how the three techniques feed each other. The corner region is now a single, so its star goes at row 5, column 5, and clearing around it marks twelve more squares.

What Medium puzzles need

Medium puzzles (8×8 on the site) add one technique. It is the first one that asks you to imagine a star before placing it, but only for a moment and only to see what it would rule out.

Blocking

Pick a row, column or region with only a few open squares left. Now look for a square outside it that touches or lines up with every one of those open squares. A star there would rule them all out, and the unit would have nowhere to put its own star. So that square is empty. The hint calls this “This square can’t hold a star” and shades the unit that would be left without one.

A few shapes come up again and again, and they are worth knowing by sight:

• Two open squares side by side. The two squares directly above them and the two directly below touch both, so all four are empty. Turn it round for a vertical pair.
• Three open squares in a line. Only the square above the middle one and the square below it touch all three.
• An L of three squares. The square that would complete the 2×2 block touches all three. Near an edge or combined with a shared row, as in the figure, you often get more.

Tip: blocking works just as well on rows and columns as on regions. A row whose last open squares are two neighbours rules out the four squares above and below them, whichever regions those belong to.

What Hard puzzles need

Hard puzzles (9×9 and 10×10) add the set argument. It is counting rather than looking, and once it clicks it is often the fastest way into a large grid.

Set argument

A claim says that one region inside one row takes that row’s star. The set argument is the same idea for groups. If two regions lie entirely inside two rows, those two regions need two stars, and the two rows hold exactly two stars between them. The regions use them both, so every other square in those two rows is empty. Three regions inside three rows, or four inside four, work the same way, and so do columns.

The argument also runs in the other direction. If the open squares of two rows all fall inside two regions, those rows supply both regions’ stars, and the regions’ squares outside the rows are empty. It even works between rows and columns: two rows whose open squares all lie in the same two columns use up both of those columns’ stars. Hints name these steps plainly, for example “These two regions fill rows 8 and 9” or “Rows 1 and 2 fit only in two regions”.

Tip: look at the edges first. Regions tucked into a corner or along one side of the grid are the ones most likely to sit inside a narrow band of rows or columns. Then sweep a band of two or three rows across the grid and ask how many regions fit completely inside it. Whenever the count of regions equals the number of rows, you have a set.

A good solving routine

The site’s solver always uses the easiest technique that makes progress, and that order works well for people too:

1. Clear around every star you have placed. Do this before anything else, every time.
2. Look for singles: a row, column or region with one open square left.
3. Check each region for a claim, then each row and column the other way round.
4. Try blocking on the units with the fewest open squares left.
5. Count bands of rows and columns against the regions inside them.

Go back to step 1 as soon as anything changes. Most steps in a Hard puzzle are still clears and singles; the harder techniques are just what gets you moving again.

Common mistakes

• Forgetting the diagonals. Stars that meet at a corner are touching. When a star is placed, mark all eight neighbours, not only the four beside it.
• Placing a star to see what happens. A wrong star can survive for many moves. If you want to test an idea, keep it in your head: blocking is exactly that test, made safe.
• Marking squares because they look unlikely. Only mark what you can prove. A single false mark can make a later claim or set look valid when it isn’t.
• Counting regions that are almost inside a band. For a set argument, every open square of every region in the group must be inside the rows or columns. One stray square anywhere else, and the count no longer holds.
• Ignoring rows and columns. Regions catch the eye, but a row with two open squares left is just as useful for singles, claims and blocking.

If you do go wrong, a hint will say so instead of building on it, and Check outlines the entries that don’t match the solution. For using hints so they teach rather than tell, see Getting started with logic puzzles. Then open an Easy star battle and try naming each step before you make it.