How to Play Slitherlink: seven rules for solving the loop
Slitherlink looks like it needs guessing and does not. Every puzzle here has exactly one solution, counted by a solver that shares no code with the builder — and puzzles it could not finish counting are thrown away rather than assumed unique. So every step can be reasoned out, starting with these.
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Every dot has zero or two lines
This is the rule that does most of the work. A dot with one line must get a second; a dot with two is finished, so every other edge at it is crossed. Reading dots rather than cells is what turns a stalled puzzle around.
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A 0 crosses all four of its sides
Cheap and immediate. Mark every side of a 0 as empty before anything else — the crosses this produces are what make the neighbouring clues decidable.
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A 3 in a corner takes both outer sides
A 3 in the corner of the grid must use the two sides against the border, because the loop cannot leave the board. The same reasoning fixes a 3 next to an already-crossed edge.
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A 1 in a corner crosses both outer sides
The mirror of the previous rule. A corner 1 cannot use either border side, because using one would force the other and give it two. Both are crossed at once.
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Two 3s side by side share their edge
Adjacent 3s always use the edge between them, plus the two outer edges parallel to it. This shape appears constantly and resolves five edges at a time.
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Two 3s diagonally always take their outer corners
When two 3s touch corner to corner, the two outer edges at each of them are used. It is the second most useful pattern after the adjacent pair.
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The loop must be a single closed circuit
Numbers can be satisfied by two separate rings, and that is not a solution. When a line is about to close a small loop early while edges remain elsewhere, that edge is wrong.
A puzzle is only published if the count came out at exactly one, and puzzles where the count did not finish are discarded — an unfinished search proves nothing. So being stuck always means a deduction is still on the board.