What "hard" means here
Our solver replays each board move by move and scores the deductions it has to make. A hard puzzle lands between 1,800 and 8,000. Two things push a board into that range. The first is that the free marks are gone: there may be no region trapped in a single line, no three-cell sliver, nothing that a glance resolves. The second is chaining — the board asks for a counting argument, and then for another one that only works because of the X's the first one produced, and then a third.
Hard is also the natural state of the puzzle. When you generate a Star Battle at random and keep only the ones with a single solution, most of what survives is hard or expert. Uniqueness comes from tightness, and tightness makes long chains. In that sense a hard board is the puzzle as it wants to be, before we go looking for the gentler ones.
Finding the thread
On easy and medium boards you start with what is forced. On a hard board, nothing is — so you start with what is tightest. Somewhere on the grid there is a region with the fewest ways to hold its two stars, or a pair of rows with the least slack between what they must hold and what the regions inside them need. That is the thread. Pull it and the board starts to unravel; ignore it and you can stare at the other seventy cells for ten minutes and learn nothing.
The practical version: before you place anything, look at each region in turn and ask how many ways could its two stars fit? A region with two or three legal arrangements is where the puzzle begins. A region with twenty is where it ends.
The moves you need
The medium toolkit, plus three ways of making constraints talk to each other.
1. Clumps and the squeeze
When a row is down to two touching pairs of cells, each pair holds exactly one star — touching cells can't both be stars. That alone tells you nothing about which cell. But any cell that touches both cells of a pair touches that pair's star wherever it lands, and is X'd. A hard board hides these squeezes in rows you thought were still wide open.
1 This row is down to two touching pairs. Touching cells can't both be stars, so each pair holds exactly one.
2 Any cell that touches both cells of a pair touches that pair's star wherever it lands — X them all.
2. The virtual star
Extend the same idea to a region. If you can list every cell where a region's remaining star could legally go, then any cell adjacent to all of those candidates is adjacent to the star no matter where it lands — so it is never a star. Our solver calls this the virtual star rule and leans on it constantly in the hard tier. You don't know where the star is; you know where it isn't allowed to have a neighbour.
1 This region has one star placed and one still to find. After earlier X's, only two cells could hold it, and they don't touch each other.
2 This cell touches both candidates, so whichever one holds the star, it would touch it. It can never be a star.
3. Wider bands
Medium boards break with a two-row count. Hard boards often need three: three adjacent rows hold six stars, and comparing that against the regions caught entirely inside them tells you exactly how many stars are left for the cells that poke in from outside. Sometimes the answer is zero, and a whole strip of the board clears at once.
The bottom three rows form a band holding exactly six stars. The two highlighted regions fit fully inside it and claim four — leaving just two stars for every other cell in the band, an accounting no single row reveals.
And always, the star claim
Every one of the moves above produces X's, and X's squeeze regions into lines. The moment a region's open cells all sit in a single row or column, it claims that line and everything outside it clears. On a hard board this fires again and again, and it is what turns a slow middle game into a cascade.
1 Earlier X's have squeezed this region's open cells into a single column — both of its stars must land there.
2 The region claims the column's two stars, so the column is X'd everywhere outside it.
A typical hard solve
A short survey, a long middle, and a late reward.
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The survey: find the tightest region
Resist placing anything. Read every region and estimate how many ways it could hold two stars. Note the one or two with the fewest. Check the two-row bands for any with no slack. You are choosing where to start, and on a hard board that choice is half the solve.
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The middle: make the constraints interact
Work the tight area. Count its bands, squeeze its clumps, apply the virtual-star rule to the tightest region. Each move yields a few X's and rarely a star; that is normal. Expect to loop — count, sweep for completions, count again — for most of the solve.
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The finish: a late cascade
On a hard board the tipping point comes late, often with two-thirds of the stars placed. Then the claims fire in sequence and the last third fills in under a minute. If you are at fourteen stars and the board is silent, you have not missed an X — you have missed a count. Go back to the bands.
When you get stuck
Being stuck on a hard board is the ordinary condition, not a failure. The question is only whether you are stuck usefully. Try, in order:
- Change your unit. If you have been reading rows, read columns. If you have been reading regions, read two-row bands. Hard boards hide the next move in the axis you are not looking along.
- List the candidates. Pick the tightest region and write out — or picture — every legal placement of its stars. Then look for a cell every placement would touch. That cell is an X.
- Widen the band. Two rows didn't give? Try three. Three didn't? Try the two columns that cross the tight region instead.
- Walk away. Ten minutes off and the board looks different. The move you couldn't see is usually obvious on return.
And when it isn't, the free step-by-step solution for every daily hard names each deduction. Find the first step that differs from your board and read only that one. Then close the solution and finish it yourself — that is where the technique actually sticks.
When to move up
Expert is not a bigger hard. It is a board built to demand the advanced techniques — fish patterns across three or four lines, deep lookahead, several counting arguments held at once — and it runs on its own schedule, one board a day. Move up when you are finishing hard boards without the solution and finding the thread in the first minute or two. If that is not yet where you are, the hard archive is deep, and the printable Hard book is twenty boards for a long weekend. Coming up from medium? The rules haven't changed; only how much you have to hold in your head at once.