Start with the corners and dead ends
4-minute read
Open a room in Fill the Space and the middle looks like the hard part: it’s where everything has to fit together. It’s usually the easy part. A cell in the middle of an empty room can be covered by almost any piece, in several ways. The cells that decide a room are the ones few pieces can reach: corners, the cells beside a notch, and the little dead ends that appear as you play.
A reach map
Here’s a way to see it. Take the warm-up room from Fill the Space #2 (September 24, 2026): a four-by-four square with four pieces in the tray, a T, a small L of three cells, an S standing on end and a P-shape of five. Now write in each cell how many of those pieces could cover it somewhere. Pieces don’t turn, so each one has only a few legal spots.
Every middle cell scores 4: any piece can get there. The corners are where the room narrows. Two of them score 3, and two score only 2. Those two are where to start.
Two corners, one shared piece
The top-left corner can only be covered by the T, sitting flat along the top edge, or by the P-shape, standing in the corner. The bottom-right corner can only be covered by the small L or, again, the P-shape. The P appears in both lists, and it can’t be in two places, so test it.
Put the P in the top-left corner. Now look at the bottom-left corner below it: its only open neighbour is the cell to its right, and no piece left in the tray can cover it from there. Dead. Put the P in the bottom-right corner instead, and the top-right corner and the cell beneath it are cut off the same way. Dead again.
So the P goes neither place. The T takes the top-left corner and the small L takes the bottom-right. Two corners settled, half the pieces placed, and not a single drop wasted. The other two pieces have one way left to go.
The obvious obstacle isn’t always the tight spot
Some rooms have a pillar in the middle, a single blocked cell the pieces must flow around. It looks like trouble. Here’s the reach map for the pillar room from the same day: six pieces, 29 cells.
The cells touching the pillar score between 4 and 6: most of the pieces can reach them. The tightest cell in the room is the bottom-left corner, with 3. The pillar shapes the solution, but the corner is where the choices run out first. Trust the count over the look of the room.
Dead ends you make yourself
The room changes every time you drop a piece. The most important cells to watch are the ones you create: a single empty cell with walls on three sides. A piece can only fill it with a part that pokes in from the open side, and often nothing left in the tray has one.
Before you let go of a piece, glance at the cells around where it lands. If it leaves a one-cell dead end, ask which remaining piece fits into it. If the answer is none, don’t let go: move it away and look again. Lifting a piece and putting it back where it was costs nothing, but moving it later does.
In short
- Middle cells are flexible. Corners, notches and dead ends are not.
- Count how many pieces can reach each awkward cell, and start with the smallest count.
- When the same piece is the answer for two tight cells, test it in each. Often it belongs in neither.
- Check every drop for the dead ends it leaves behind.
The Hint on every archive page uses exactly this count: it marks the cell the fewest pieces can reach.
Next guide: Count before you drop