What "medium" means here
Our solver replays every board one forced mark at a time and scores the effort each deduction takes. A medium puzzle lands between 400 and 1,800 on that scale. The number describes a specific experience: the direct moves — ringing stars, completing lines, spotting a region trapped in one row — take you a good way in and then stop. Somewhere in the middle of the board there is at least one place where nothing is forced by a single observation, and you have to combine two constraints to find the next mark.
That is the whole definition of medium. Not more cells, not stranger shapes; one or two moments that ask for a second kind of thinking. We still generate these boards with compact regions of at least four cells, just with a little less tidiness than the easy tier, because slightly looser regions are what create those moments without creating a dozen of them.
The wall, and why it's the point
Every medium solver knows the feeling. You open the board, the first eight or ten marks fall in a pleasant rhythm, and then — nothing. Every row you check has three or four open cells. Every region has room. You start to wonder whether the puzzle is broken, or whether it is time to guess.
It isn't, and it isn't. The wall is the puzzle. Everything before it was the setter clearing the table; the wall is the one move they actually built the board around. Learning medium is really learning to recognise the wall for what it is, feel a flicker of interest instead of frustration, and reach for the one tool that goes through it.
The moves you need
The easy-tier foundations, plus the two that go through the wall.
1. Count a band
Pick any two adjacent rows. Between them they hold exactly four stars — that is the rule. Now look at the regions that fit entirely inside those two rows. If two of them do, they need four stars between them, which is the band's whole quota. Every other cell in those two rows — the cells belonging to regions that poke in from outside — can be X'd. You have just made progress without placing a single star. The same argument works on any pair of adjacent columns, and it is the move that breaks nearly every medium wall.
1 The top two rows hold exactly four stars — and these two regions, which fit entirely inside them, also need exactly four.
2 Those regions consume the whole quota, so every other cell in the two rows is X'd.
2. Let a region claim its line
After a few X's, a region's remaining open cells may all sit in one row or one column — even though you don't yet know which two will be the stars. That region has claimed the line. No other region can use it, so the row or column is X'd everywhere outside the region. This is the counting idea seen from the other side: instead of asking what the rows need, you ask what the region has been squeezed into.
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.
3. Then sweep for completions
A count or a claim rarely places a star directly. What it does is hand you a few X's, and those X's close a row or a region somewhere else. The instant you have made a counting move, sweep the whole board for lines with two cells left or two stars in — that is where the payoff actually lands.
1 Three of this region's five cells are already X'd — only two remain open.
2 A region needs exactly two stars, so both open cells must be stars. Rows and columns work the same way.
Go deeper: the strategy guide covers counting and the star claim with more examples, and the counting technique article works through the arithmetic in detail.
A typical medium solve
Easy, then the wall, then easy again.
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1
The opening: the free marks
It starts like an easy board. Trapped regions, a sliver or two, the first stars and their rings of X's. Take everything the board offers here, but don't be lulled — a medium opening is deliberately generous so that the wall lands harder.
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2
The wall: count your way through
The forced moves stop, usually a third of the way in. Don't scan for stars — you won't find one. Instead, go band by band: every pair of adjacent rows, then every pair of columns, totalling the regions inside each. One of them will give you three or four X's. Then sweep for completions.
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3
The finish: the cascade
Once the wall is down, the board usually tips straight into forced moves and finishes itself. Some medium boards have a second, smaller wall; treat it exactly like the first.
When you get stuck
First rule out a missed X: check every star's eight neighbours and every completed line. If the board is genuinely quiet, you are at the wall, and the way through is systematic rather than clever:
- Take rows 1 and 2. Which regions fit entirely inside them? What do those regions need? Compare it to four. Move to rows 2 and 3, and so on down the board, then do the same for columns.
- Look at each region's open cells. Have any been squeezed into a single row or column? If so, that region owns the line — clear it outside the region.
- Look for a region with only three open cells in a straight line. Its stars must be the two ends, and the middle is an X.
- After any of these, sweep for completions before looking for the next count.
If none of that moves the board, the free step-by-step solution for every daily medium names each deduction in order. Find the step where it diverges from your board — that is the count you missed, and it will usually be one of the two moves above.
When to move up
You are ready for hard when the wall has stopped being a wall — when you hit the quiet patch, think "band," and find the count within a minute. Hard boards remove the generous opening and ask you to read regions against each other from the very first move. If you would rather stay, the medium tier has months of boards in the archive, and the printable Medium book puts twenty of them on paper. Coming up from easy? Welcome — the rules are the same, only the thinking changes.