Pieces don’t turn
3-minute read
In Fill the Space, a piece goes into the room exactly as it sits in the tray. You can slide it anywhere, but you can’t turn it or flip it. New players sometimes read that as a handicap. It’s the opposite: it’s the rule that makes a room solvable by thinking rather than by trial and error.
Fewer shapes, fewer places
Mathematicians who study these shapes, called polyominoes, count them two ways. If you’re allowed to turn and flip a piece, there are 5 different four-cell shapes and 12 five-cell ones. If you aren’t, every turned or mirrored version is its own piece: 19 four-cell shapes and 63 five-cell ones. These are called fixed polyominoes, and they’re what Fill the Space uses. A T pointing up and a T pointing down are different pieces, and an L is never a J.
That matters for how many places a piece can go. Take the standard room from Fill the Space #2 (September 24, 2026): a five-by-five square and five pieces.
The seven-cell piece, an arch with one long leg, fits in this room in just 6 spots. If it could turn and flip, it would have 8 orientations and 48 spots to choose from. Locked rotation cuts the search by a factor of eight before you’ve thought about anything else. The same goes for every piece in the tray.
Read the outline, not just the shape
Because a piece can’t turn, its outline tells you a lot about where it goes. Two features are worth spotting.
Gaps. A piece with a gap in its outline, like the arch, can only go where something else fills that gap. The arch’s gap is a single cell under its top bar, between the short leg and the long one. Whatever goes there has to poke up into it from below.
Bumps. A piece with a single cell sticking out, a bump, needs a gap to sit in. Look at the last piece in the tray: a block of four with one extra cell on top. That bump is exactly one cell wide.
Put those together and the room starts to solve itself. The arch’s gap needs a bump from below, and the piece with the bump on top is the natural partner. In the finished room, that’s exactly how they sit: the bump tucked into the arch.
This is the main skill of the game. When you see a gap, look in the tray for a bump that fits it. When you see a bump, look for where its gap is. You don’t have to imagine turning anything, only sliding.
Mirror images are traps
The most common slip is seeing the shape you need and grabbing its mirror image. Two pieces of the same size can look alike in the tray and still be mirror images, an S and a Z, or two P-shapes facing opposite ways, and only one of them will fit. Before you drag, check which side the bump or the notch is on. It takes a second, and it saves an extra drop.
Use the room’s edges
The room’s edges are the other half of the picture. A piece with a flat side fits along a flat wall. A piece with a step in its outline fits against a step in the room, like a notch in the top edge or a pillar in the middle. Match the outline of the piece to the outline of the space, and most pieces have one obvious home.
This room happens to have four different solutions, so the early choices are a little freer than usual. Rooms with one solution are stricter, and the outline reading matters even more there. For a step-by-step example, see how to solve a room.
Next guide: The checkerboard trick