Link is a game by nmskr where you have to make a single loop that satisfies all the numbers to win.

How to Play

Tap an edge to place a line. Tap the edge again to remove it. Hold the edge to mark it with an X. Tap the 2 arrow symbol cycle to reset the board. The numbers indicate how many lines are bordering the cell. You win if all conditions are met:

  • The line makes a single loop.
  • The line never makes a branch.
  • There is no isolated lines in the level.
  • All numbers are satisfied.

The game will automatically highlight currently unsatisfied numbers, as well as vertices that are either dead-ends or branches.

Basic Logic

All of these logic will be based on the original slitherlink logic.

  • If a line has only one path to take, extend that line with that 1 path.
  • If theres an explicit path that leads to a dead end if you take the path, that path has no lines.
  • A 0 always doesn't have a line.
  • A 1 clue on a corner doesn't have a line on the edges bordering the corner, since if one is filled, the loop can't end and has to extend, breaking the 1 clue.
  • Inversely, a 3 clue on a corner must have a line on the edges bordering the corner, since if one is empty, the other one is empty and it will break the 3 clue.
  • 2 3 clues that share an edge has:
    • the line placed in the common edge, otherwise, it makes a closed link.
    • two combinations (if not counting the closed link) that form an S-shape, taking the common lines and X's:
  • 2 3 clues that share a vertex must have lines in the outer corners, if there is no line to the outer corner, a 3 clue cant be satisfied.
  • A line with exactly one vertex adjacent to a 3 will tell that the edges adjacent to that 3 but not touching the line are all lines, otherwise branching lines will form. (Top-left image)
    • The line is forced to enter the 3 clue. Therefore, the line which touches it but isn't in the edge of the 3 is X'd out. (See bottom-left image)
  • A 2 clue can have lines separated from each other, keep in mind.

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