The Solver’s Method · Patches
Patches strategy — solve the shape-fill puzzle faster
The short answer
Solve Patches from the outside in and the tightest spot first: attack the corners, dead ends and one-cell-wide strips where a single piece is forced, commit your most constrained piece where it has the fewest homes, and never place a piece that would strand a square no other piece can reach.
Follow the constraint, not the colour
Patches looks like a puzzle about shapes, but it is really a puzzle about constraint. Every board has places where the geometry leaves almost no choice — a corner cell with a single neighbour, a channel one square wide, a notch that only one piece could ever wrap around. Those places are gifts. Wherever a cell can be covered in only one way, you get a placement for free, with no guessing at all.
The mistake most new players make is to start with the piece they like the look of and drop it somewhere roomy in the middle. That feels like progress, but it spends your freedom in the one place you had the most of it, and it often blocks a tight corner you had not looked at yet. The disciplined approach is the opposite: let the board tell you what to place. Find the most constrained cell, work out the only piece that fits it, and put that down first.
Do this repeatedly and a Patches board tends to collapse in a chain. Each forced placement shrinks the region and creates new tight corners, which force the next piece, and so on until the middle — the roomy part you wisely left alone — is all that remains, now small enough to see at a glance. The sections below turn that idea into concrete tactics.
Six tactics that do the work
| Tactic | What to do | Why it works |
|---|---|---|
| 1 Tightest first | Cover the corner, dead end or one-wide strip before anything else. | These cells usually admit one piece in one rotation, so the move is proven, not guessed. |
| 2 Constrain the big piece | Place your largest, most awkward piece where it has the fewest legal homes. | A pentomino has few positions; pinning it early removes the most uncertainty at once. |
| 3 Edges inward | Anchor against the border and corners first, then move toward the open middle. | Edge placements are the most forced; the centre stays flexible until last, where flexibility helps. |
| 4 Guard the singletons | Before committing, check no lone square is about to be cut off. | A stranded one-cell hole cannot be filled by any tromino or larger, and dooms the board. |
| 5 Rotate on purpose | Cycle every rotation of a piece against the gap before ruling it out. | Only some rotations fit a given notch; the right one is easy to miss at a glance. |
| 6 Back out early | If nothing fits a gap, lift your last piece and try a different line. | A dead end means an earlier placement was wrong; undo it before the board is jammed. |
How to read this. Tactics one to three are about order — solve the forced parts before the free parts. Tactics four to six are about safety — keep every remaining region fillable, and undo rather than force when a gap will not close.
Place the largest piece where it is most boxed in
It sounds backwards, but the piece to commit first is usually the one with the fewest options, and on most boards that is the biggest, most irregular piece — a pentomino or an L-shaped tetromino. A small straight tromino can slot into dozens of places, so it is happy to wait. A five-cell zig-zag might have only one or two legal homes on the whole board. Find that home and take it while you still can; a big piece left until last is the one most likely to have nowhere to go.
The way to find its home is to overlay the awkward piece, in each of its rotations, against the board’s most awkward features — the long arm, the deep notch, the corner it seems shaped for. Very often a distinctive piece and a distinctive part of the board are made for each other, and once you see the match the placement is obvious. Anchor the hard piece there, and the rest of the tray, being more flexible, will fit around it.
Never strand a single cell
The most common way to lose a Patches board is not a dramatic mistake — it is quietly leaving a lone square with nothing that can fill it. Because the smallest piece is a tromino of three cells, a one-cell hole is fatal: no piece in the tray is small enough to cover it, and every larger piece would spill over its edges. If you ever find a single isolated empty square, the tiling is already broken and you must lift a piece to reopen room around it.
The habit that prevents this costs almost nothing. Before you drop a piece, glance at the cells it would leave behind — the ones next to it that stay empty. Ask whether each of those remaining pockets is at least three cells and still connected to enough room for a real piece. If a placement would pinch off a square, or split the board into a region smaller than any piece you have left, choose a different cell or a different rotation. Thinking one move ahead about the gaps, not just the piece in your hand, is what separates a smooth solve from a stuck one.
The method on one small board
Take a small six-cell board: a full top row three squares wide, with a two-square column hanging down from its left end and one square poking out to the right of the bottom of that column — an S-shaped region. Your tray holds two pieces: a straight tromino (three squares in a line) and an L-tromino (three squares bent at a right angle). The finished tiling looks like this — the straight tromino is A, the L-tromino is B:
Move one — the tightest cell. The bottom-right square has a single neighbour, the square to its left. It is a dead end, so the piece covering it must bend around the bottom-left corner. That is the L-tromino, and only one rotation fits: it takes the bottom-left square, the square above it and the square to the right. Place B there first.
Move two — what is left. The remaining three squares form the top row, a straight line. Only a straight tromino covers a straight line of three, so A drops in without a decision to make. Two pieces, no gaps, no overlaps, done — and notice we never guessed. We read the tightest corner, let it force B, and A followed. On a full daily board the same chain simply runs longer: each forced piece uncovers the next tight corner until the middle is trivial.
Common mistakes to avoid
Strategy FAQ
Where should I place my first Patches piece?
Start at the most constrained spot on the board — a tight corner, a dead-end cell or a one-cell-wide strip. Those places usually admit only one piece in one rotation, so they are the easiest moves to prove and the safest to commit to first.
Should I place large or small pieces first in Patches?
Place whichever piece is most constrained, which is often the largest. A big piece such as a pentomino has few legal positions, so pinning it down early removes the most uncertainty. Small pieces are flexible and are best saved to fill the gaps that remain.
How do I avoid getting stuck one cell from the end?
Watch for cells that are about to be stranded. Before you place a piece, check that it does not leave a lone square with no piece able to reach it. If it would, choose a different placement or rotation, or lift the previous piece and try another line.
Can rotating a piece help me solve a Patches board?
Yes. Most pieces have two or four distinct rotations, and only some of them fit a given gap. Cycle through each rotation against the space you are filling before deciding a piece does not belong there. Pieces rotate but never flip, so a shape and its mirror image stay different.
Is there always one correct way to tile a Patches board?
No. Some boards can be tiled in more than one valid way. Your aim is any exact tiling that covers every cell once with no overlaps, so you do not have to reproduce the published arrangement — a different valid tiling still counts as solved.
Got the method? Put it to work.
The quickest way to jam a board is to fill the comfortable middle first and only then discover a corner that nothing fits. Solve the forced edges while you still have every piece to choose from; the roomy centre can wait, because roominess is exactly what makes it easy to finish.
Starting in the open centre. A piece dropped in the middle looks like progress but spends your freedom where you had the most of it, and often blocks a tight corner you had not checked. Begin where choice is scarce, not where it is plentiful.
Saving the big piece for last. An irregular pentomino has the fewest homes on the board, so leaving it until the end is the surest way to find it has nowhere to go. Commit awkward pieces early, flexible ones late.
Forgetting to try every rotation. A piece that seems not to fit a notch often fits it perfectly one quarter-turn round. Cycle through all its rotations before deciding it belongs elsewhere — and remember pieces rotate but never flip.
Ignoring the gaps you create. Judge a placement by the space it leaves, not just the space it fills. If it would pinch off a lone cell or a pocket smaller than your smallest piece, it is the wrong move however neat it looks.
Forcing instead of undoing. When a region simply will not close, an earlier placement was wrong. Lift a recent piece and re-examine it; stubbornly forcing pieces around a bad move only buries the mistake deeper.