Trial, and Why This Site Refuses It

It finishes every board ever made, which is the problem with it. Here is how to do it properly if you meet one elsewhere, and why nothing here will make you.

How a trial actually works here

Pick an undecided segment and provisionally decide it — drawn, or crossed out. Follow the consequences with every ordinary argument until either the board finishes or something breaks: a square with more sides than its number, a square that can no longer reach its number, a dot with three lines, a line that stops dead, a ring closed with work left outside it. If it breaks, that decision was wrong, and the opposite one is a permanent, sound result.

Slitherlink is unusually good at punishing a wrong trial quickly, which is the one thing that makes the technique bearable here. Deciding a segment changes two dots and two squares immediately, and each of those changes more, so a false branch tends to collapse within four or five moves rather than wandering for pages. Choose a segment touching a dot that already has a line, or a side of a 3, and you will normally know within seconds.

The discipline is entirely in the bookkeeping. Everything derived under a trial is provisional and has to come off again if the trial fails, so it must be visibly separable from what you knew before — a second colour on paper, or the undo button here, which is exactly what it is for. A solver who cannot cleanly unwind a trial will eventually leave a consequence of something false on the board, and that is far worse than being stuck.

Before — nothing ordinary applies

After — one segment, proved by contradiction

This board has exactly one answer and no reasoned route to it — the kind this site grows, grades and then discards. Eight ordinary moves have been made and everything above has run out: no zero left, no dot with one way out, no number that counting settles, no corner and no ring near closing. Supposing one segment drawn breaks the board, so it is crossed out. Sound, and thoroughly unsatisfying.

what it decides what it wrote

Why trial cannot be one of the levels

Because it works on everything without exception. Any board with a unique answer can be finished by deciding, following and unwinding, repeatedly if necessary, so "needs a trial" is a statement about the solver’s patience rather than about the board. A scale whose top rung fits every board is not measuring anything at all.

It is also what a generator falls back on when it has stopped checking. Grow a loop, read the numbers off it, carve numbers away for as long as the answer stays unique, and you get boards that have exactly one answer and no reasoned route to it. That is the defect behind almost every review of a loop puzzle app that calls a board impossible. The board is not impossible. It has simply stopped being a puzzle, and the app cannot tell, because it never asked.

The position below is one of those boards, produced deliberately for this page by carving for uniqueness alone. Eight ordinary moves have been made — a zero, the dot rule twice over, a corner, a pair of threes — and then everything ordinary runs out at once. Only a trial will move it.

Meeting one somewhere else

Trial into the most constrained segment you can find, keep the provisional marks visibly separate, and stop the instant you hit a contradiction rather than pressing on to see how bad it gets. One resolved segment is a complete result — go straight back to the cheap arguments, because that segment will have changed two dots and two squares and something will now be forced.

Nesting a second trial inside the first is the point to stop. Two layers of provisional marks on one board is where mistakes are made rather than found, and a board demanding it was built by a program that never asked whether anyone could follow the result.

Where this sits on the ladder

Rung 1Counting a cell
A number with its sides already drawn has none left to give; a zero gives none at all.
Rung 2Following the line
Every dot carries no line or exactly two, so a line that arrives has to leave again.
Rung 3The corner cases
A corner dot has only two segments to offer, which settles a 1, a 2 or a 3 sitting in it.
Rung 4Threes together
Two threes side by side, or corner to corner, decide their outer sides before anything is drawn.
Rung 5No early closing
A segment that would seal a short ring with numbers still unsatisfied can never be drawn.
Rung 6Assumption
Draw a segment, follow it until the board breaks, and rub it out again.

Common questions

Is trial and error allowed in slitherlink?

The logic is watertight — something that leads to a broken rule was false. What it is not is a measure of anything, since it cracks every board there is, so needing it means the board went unchecked rather than that it is tough.

Will any loop here ever make me guess?

Never. Each loop is put through the reasoning solver before it goes anywhere near a page, and one that could only be finished by trial is thrown out and another grown in its place.

Why do some loop puzzle apps produce boards that feel impossible?

Because they carve numbers away while checking only that the answer stays unique. Unique and humanly reachable are different properties, and testing the first without the second ships boards that can only be finished by trial.