Slitherlink Puzzle
A 3 tells you no more than a 1 — both leave four possibilities. The 0 is the only clue that settles anything on its own.
Click an edge to draw it, again to mark it crossed out, again to clear it.
A 3 tells you no more than a 1
Every cell has four edges, so a clue of n can be satisfied in exactly C(4, n) ways on its own. Write that out and the ranking is not the one people play by: a 1 leaves four possibilities and a 3 leaves four possibilities. They are equally informative. Everyone hunts for 3s because "three of these four edges are on the loop" sounds decisive — but you still do not know which three, and a 1 constrains you exactly as much from the other direction.
The 2 is the vaguest clue on the board at six ways, despite looking like an unremarkable middle value. And the 0 — the clue that appears to say the least — is the only one that settles anything by itself: all four edges off, no reasoning required. That is why experienced solvers open on the 0s and the corners rather than on the big numbers.
A 4 would be forced too, and it can never appear. Four edges around one cell is a closed square — a loop of its own — and the puzzle demands a single loop. So of the clues that can actually be printed, exactly one of the four is forced.
How much each clue narrows things down
Ways the clue can be met by the four edges of its own cell, before any other reasoning.
| Clue | Ways | What it means alone |
|---|---|---|
| 0 | 1 | all four edges off — completely settled |
| 1 | 4 | four possibilities, and no way to choose between them |
| 2 | 6 | the least you can learn from a single clue |
| 3 | 4 | four possibilities, and no way to choose between them |
| blank | 16 | any subset of the four edges |
| 4 | 1 | forced, but never printed — it is a closed loop on its own |
The rule that catches everyone
Satisfying every clue is not enough. The edges you draw must form one closed loop — not two, not a loop plus a stray line. It is entirely possible to meet every number on the board and end up with two separate rings, and the puzzle is then simply wrong. Every vertex having exactly zero or two lines through it is necessary and does not settle it either: two disjoint rings pass that test perfectly. The check here walks the loop and confirms it accounts for every line drawn.
How to use
- Click an edge to draw it, again to cross it out, again to clear it.
- Each number says how many of that cell's four edges are on the loop.
- Start with the 0s — every one of their edges is off.
- The finished lines must form exactly one closed loop, not two.
Frequently asked questions
What are the rules of Slitherlink?
Draw lines between dots so that each numbered cell has exactly that many of its four edges on the line, and the whole thing forms a single closed loop that never branches or crosses itself. Cells with no number are unconstrained. It is also called Loop the Loop, Fences and Number Line in various places.
Which clue is the most useful?
The 0, and it is the one that looks like it says the least. Each cell has four edges, so a clue of n can be met C(4, n) ways in isolation — and only the 0 has a single possibility, with all four edges off. Every other clue leaves you with a choice, which is why solvers open on the 0s and the corners rather than the big numbers.
Is a 3 more informative than a 1?
No, exactly equally. A 3 leaves four possibilities and so does a 1, because C(4,3) and C(4,1) are both four. "Three of the four edges are on the loop" sounds decisive, but you still do not know which three — and a 1 constrains you precisely as much from the other direction. The intuition that bigger numbers are stronger clues is simply wrong here.
Which clue is the weakest?
The 2, at six possibilities, more than any other. It looks unremarkable because it sits in the middle of the range, and that is exactly why it is the vaguest — there are more ways to choose two edges from four than to choose one or three. A board full of 2s is a hard board.
Why is there never a 4?
Because four edges around a single cell is a closed square, which is a loop all by itself, and the puzzle requires one single loop covering everything. So a 4 could never be part of a valid solution and is never printed. That leaves exactly one forced clue among those you can actually see, the 0.
Can I satisfy every number and still be wrong?
Easily, and this is the rule that catches everyone. Meeting every clue is necessary and not sufficient — you can finish with two separate rings, each perfectly legal locally, and the puzzle is wrong. The single loop requirement is a global condition that no amount of local counting can enforce.
Is checking every dot for zero or two lines enough?
No, and this is the subtle version of the same trap. Two disjoint rings satisfy that test perfectly: every dot has zero or two lines through it. The only reliable check is to walk the loop from one line and confirm it comes back to the start having used every line you drew. That is what this page does.
Does every puzzle here have one answer?
Yes, checked rather than intended. Each generated board is passed to a solver that counts solutions and stops at two, and anything with a second answer is thrown away. Clues are then removed one at a time, each removal kept only if the puzzle is still unique — so the board you see has no clue on it that could have been left off.
How are the puzzles generated?
By growing a random blob of cells and taking its outline as the loop, then reading each cell's clue off that outline. The blob has to be free of pinch points — a dot where four boundary lines meet is a place the loop touches itself, which makes it two loops rather than one. Checking the cells are connected does not catch that; checking every dot does.
What is a good opening strategy?
Find the 0s and cross out all their edges, then look at corners: a 3 in a corner has its two outer edges forced on, and a 1 in a corner has them forced off. After that, adjacent clue pairs do most of the work — a 3 beside a 0 has all three of its other edges forced, and two adjacent 3s force the edge between them plus the two outer parallels.
Why do crossed-out edges matter?
Because knowing where the loop is not is as useful as knowing where it is, and on a 0 it is the only information there is. Marking them explicitly turns "I have not decided" into "I have decided against", which is what stops you re-examining the same edge a dozen times. Clicking an edge cycles through drawn, crossed and blank.
Does this store anything?
Only if you post a time. The puzzle is generated and solved entirely in your browser, nothing is uploaded, and nothing is kept between puzzles unless you choose to put a time on the global board, which sends the name you type and the number.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.