Patches looks like a drawing game, but it is solved by elimination. Every clue has a short list of rectangles that could be its patch, and solving means crossing entries off those lists until each clue has one left. This page shows how to do that quickly, using real boards from our puzzle pool. It assumes you know the rules; if not, start with how to play Patches.
The order of operations
Most boards fall to the same routine. Run it in this order, and go back to the top every time you place a patch:
- Find the forced clues. Look for a clue whose shape and number allow only one rectangle, or whose position leaves only one. Place those first.
- Treat everything as a wall. Every other clue and every placed patch is a barrier. Recheck the clues next to whatever you just placed.
- Look at cells, not clues. Pick an empty cell, especially a corner, and ask which clues could possibly reach it. If only one can, that clue's patch covers it.
- Budget the area. When a region is walled off, the patches inside it must add up to exactly its number of cells.
- Find the cells every option shares. If all of a clue's remaining rectangles cover the same cell, no other clue can use that cell.
Steps one to three solve most Easy and Medium boards on their own. Steps four and five are what Hard boards are made of.
Find the clue with only one home
A clue with a shape and a number is a small multiplication problem. List the rectangles with that many cells, keep the ones with the right proportions, and throw out any that would run off the board. Some combinations collapse to a single answer before you even look at the neighbors:
- A Square with a number is always one size. Square 4 is 2×2, Square 9 is 3×3, Square 16 is 4×4.
- A Wide or Tall clue with a prime number has one shape. Wide 5 can only be 5×1, and Tall 3 can only be 1×3.
- Big numbers on a small board lose options to the edges. On a 6×6, a Wide 8 must be 4×2 because 8×1 does not fit, and a Freeform 9 must be 3×3 for the same reason.
- A clue in a corner has only one position for any given width and height, so a numbered Square in a corner is placed the moment you see it.
Here is a real 6×6 Medium, the same size and difficulty as the daily puzzle. Three clues show a number; the other three show only a shape.
Start with the Tall 8. Eight cells, taller than wide: 1×8 does not fit on a board six rows high, so it has to be 2 wide and 4 tall. The clue is in the top row, so the patch starts at the top edge, and it can cover either columns 1–2 or columns 2–3.
The right-hand position would take in the Wide 8 clue, and a patch can hold only one clue, so the Tall 8 goes in the first two columns, rows 1 to 4. The Square 4 in the bottom row works the same way. A 2×2 touching the bottom edge can cover columns 4–5 or columns 5–6, and columns 4–5 would swallow the Square clue in row 5, so it takes columns 5–6.
With the Tall 8 in place, the Wide 8 has nowhere else to go. It must be 4×2, and every 4-wide position that reaches into the first two columns now overlaps the Tall 8. The position one row higher was never possible, because it would contain the Wide clue on the right edge. The only survivor runs across rows 3 and 4, from column 3 to column 6.
Every clue is a wall
Notice what did the work in those deductions. It was not the clue being placed but the other clues nearby. A patch holds exactly one clue, so every other clue on the board is a wall the current patch cannot cross. Patches you have already placed are walls too. Whenever you place a patch, recheck the clues next to it: its edges are new walls, and a neighbor often loses all but one option at that moment. That is exactly what happened to the Wide 8.
Ask which clue can reach each cell
This is the most useful technique in Patches, and the one new players skip. Instead of asking where a clue can go, pick an empty cell and ask which clues could ever cover it. Every cell must belong to some patch, so if only one clue can reach a cell, that clue's patch includes it.
Back on the Medium board, look at the top band: the empty cells of rows 1 and 2 to the right of the Tall 8. The two Square clues at the bottom are cut off by the Wide 8, and the placed patches cannot move. Only the Wide clue on the right edge can reach any of those cells.
Its patch must cover all eight cells of that band, from column 3 to column 6 across two rows. That is a 4×2 rectangle, wider than tall, just as the clue demands. The clue never told you its size; the board did.
The bottom-left corner falls the same way. The Square clue in the corner can only be 1×1 or 2×2, since anything bigger would run into the Wide 8. The two cells in column 2 below the Wide 8 can only be reached by that corner Square, so it must be the 2×2. The last four cells form a 2×2 around the other Square clue.
Corners are the best cells to ask about. A corner can only be covered by a patch that stretches all the way into it, and usually only one or two clues are close enough to do that.
Budget the area
A 6×6 board has 36 cells, an 8×8 has 64 and a 10×10 has 100, and the patches have to add up to exactly that. The same bookkeeping works on any region your placed patches have walled off: the patches inside it must add up to its cell count.
- One clue in a closed region takes the whole region, and the region has to be a rectangle that suits the clue.
- Numbered clues must add up to the region's size. If they cannot, one of the patches around the region is wrong.
- A shape-only clue gets whatever is left once the numbered clues are counted. That turns a shape clue into a shape-and-size clue.
On Medium boards about half the clues show only a shape, and on Hard boards most clues have no number at all, so budgeting is how you get the missing numbers back.
Hard boards: Freeform clues and missing numbers
Hard boards give you fewer, vaguer clues. Most are Freeform, which accepts any rectangle, and many carry no number. Here is a real 6×6 Hard with only four clues.
Start with the number that has the fewest rectangles. Nine cells can be 1×9, 9×1 or 3×3, and only 3×3 fits on a 6×6. The Freeform 9 is in the bottom-left corner, and a 3×3 has one position in a corner, so it is placed.
Now ask the cell question about the top-left corner. The Freeform 12 in the top row cannot reach it without also containing the blank Freeform beside it, and the Tall clue in the opposite corner cannot get there without swallowing other clues. The blank Freeform is the only clue that can reach any cell of the top-left 3×3, so its patch is that whole block. It had no number and no fixed shape; it got both from the board.
That leaves the right half: three columns, 18 cells and two clues. A 12-cell rectangle around the Freeform 12 can only be 3 wide by 4 tall or 2 wide by 6 tall; every other one runs off the board or takes in another clue.
You do not need to know which option is right to use them. Both cover the same block of eight cells, columns 4 and 5 in rows 1 to 4, so those cells belong to the Freeform 12 either way and the Tall clue cannot touch them. Now budget: 18 cells, 12 of them for the Freeform 12, leaves exactly 6 for the Tall clue. A tall 6-cell rectangle in the bottom-right corner is either a full-height column one cell wide or a block 2 wide and 3 tall, and the 2×3 would reach row 4 of column 5, one of the shared cells. So the Tall patch is the whole right-hand column, and the Freeform 12 takes the 2×6 beside it.
Edges and corners
- An edge cuts the options. A patch cannot extend past the board, so a clue on an edge can only grow inward, and a clue in a corner can only grow in one direction each way.
- Try the full strip first. When a shape-only Tall or Wide clue sits on an edge, check whether the full-length strip along that edge works. On the Hard board above, the Tall clue's patch turned out to be the entire right column.
- Check every corner early. All four corners have to be covered by something. Work out which clues can reach each one; a corner with a single candidate is a free placement.
Let the board check your work
- Watch the live cell count. While you drag, a small number in the middle of the rectangle shows how many cells it covers, so you can size a numbered patch before you let go.
- Red means a rule is broken. The outline turns red if the rectangle holds no clue or two clues, has the wrong shape, or has the wrong number of cells. Let go and a message tells you which.
- Legal is not the same as right. A patch can follow its clue's rules and still be in the wrong place. If a region becomes impossible to fill, the patch next to it is the likely culprit. Tap it to remove it, or press Undo.