Timeouts and “no solution”

The solver gives one of four answers, Solved, No solution, Out of time or, rarely, No answer. Solved and No solution are exact verdicts on the board as you entered it. Out of time and No answer mean the search ended without a verdict.

What happens when you press Solve puzzle

The solver runs an exact search with no guessing. It turns the board into rules and asks Z3, a constraint solver compiled to WebAssembly, for paths that satisfy all of them.

Every cell gets exactly one color (at most one, if filling isn't required). A dot connects to exactly one neighbor of its color, and every other cell of a path to exactly two. An answer that meets those rules can still contain a stray closed loop of one color. When the solver finds one, it adds a rule excluding that loop and searches again; the processing panel counts these as Disconnected loops excluded. Once an answer has no loops, the solver checks it again with separate code before showing it, which is why a solved board says it was checked independently. It stops at the first answer and doesn't look for others.

The first solve downloads the solver itself, about 7.5 MiB compressed and 33 MiB unpacked, and checks its size and checksum before use. You'll see Downloading the solver and Unpacking and checking the solver. Later solves usually load it from your browser's cache.

Why board size isn't difficulty

Search time depends on how much freedom the paths have, more than on the number of cells. A large board crowded with dots and narrow corridors leaves few choices. A smaller board with a few colors and wide open areas lets every path wander, which allows a huge number of candidate answers, many with loops that each cost another search.

A board with no solution can take longer than one with a solution, because reporting No solution means ruling out every arrangement.

The time limit

Open the menu (the three dots at the top right) and choose Solver settings. Under Time limit, pick 10 s, 30 s or 60 s. The default is 30 seconds, and it returns to 30 when you reload the page. As the dialog says, Most boards solve in about a second. Large boards may need longer.

The limit covers building the rules and searching, not the download.

Out of time

Out of time comes with The solver stopped after 30 s. That doesn't mean the board is unsolvable. It doesn't mean the board has a solution either.

If the limit was under 60 seconds, tap Try for 60 s. It raises the limit and starts again.
If 60 seconds wasn't enough, tap Fix the dots and check the board. A misread board can be slow to rule out.
A board that runs out of time on a phone may solve on a faster computer.

No answer means Z3 stopped for a reason other than the time limit, and the message under it gives that reason. Check the board and try again.

Stop and processing details

While the solver works, the main button reads Stop processing, and the panel above the board has a Stop button. Either one ends the work at once and leaves your board as it was, with Stopped. Your image stayed on this device.

Processing details in that panel opens the numbers. Operation statistics lists the board size, playable cells, constraints, search checks and loops excluded, the Search time limit and, while running, Search budget remaining (not an ETA). Time by stage shows where the time went. A search has no meaningful percentage, so the panel says Search progress has no reliable percentage.

Why a board comes back “No solution”

The message reads These dots can't all be connected under the fill rule. A missed or extra dot is the usual cause. The verdict is exact for the board you entered, so the question is whether that board matches your game. Tap Fix the dots and check these, most likely first.

A dot in the wrong cell. The color list can't flag this, because every color still has two dots. On a board that must be filled, moving one dot of a solvable board a single step up, down, left or right always makes it unsolvable. Color the cells like a checkerboard. A path whose dots sit on the same shade covers one more cell of that shade than of the other, and on a filled board those differences must add up to the difference between the two shades' cell counts. One step changes a dot's shade and breaks the total. See Checkerboard parity, and the example in Fixing detection mistakes.
A wrong grid size. One row or column too few or too many shifts every dot past it.
A missing or extra pair. The color list can't flag a pair missed completely, or an extra pair read from glare or drawn paths.
Unmarked holes. The solver tries to fill every cell that isn't a hole. Mark your game's gaps with #.
The fill rule. If your puzzle doesn't require every cell to be filled, turn off Every cell must be filled in Solver settings. The size label above the board then adds fill not required.

If the board matches your game exactly, the puzzle as entered has no answer. That happens with boards typed in by hand or copied with a mistake.