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Games/Link.md
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[[/uploads/linknmskr.png]]
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## How to play
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Tap an edge to place a line, tap the edge again to remove it, hold the edge to mark the edge with an X, tap the 2 arrow symbol cycle to reset the board, the numbers indicates how many lines are boardering the cell, numbers can only be satisfied if the boardering lines matches the number of the building type. You win if all conditions are met:
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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.
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The numbers indicate how many lines are bordering the cell. You win if all conditions are met:
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* The line makes a single loop.
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* The line never makes a 3 way branch.
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* The line never makes a branch.
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* There is no isolated lines in the level.
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* All numbers are satisfied.
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The game will automatically highlight currently unsatisfied numbers, as well as vertices that are either dead-ends or branches.
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## Basic Logic
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All of these logic will be based on the original [slitherlink](https://www.conceptispuzzles.com/index.aspx?uri=puzzle/slitherlink/techniques) logic.
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* If a line has only one path to take, extend that line with that 1 path.
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[[/uploads/link-tips-a.png]]
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* If theres an explicit path that leads to a dead end if you take the path, that path has no lines.
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[[/uploads/link-tips-b.png]]
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* A 0 always doesn't have a line.
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* A 1 clue on a corner doesn't have a line on the edges boardering the corner, since if one is filled, the loop cant end and has to extend, breaking the 1 clue.
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* A 3 clue on a corner must have a line on the edges boardering the corner, since if one is empty, the other one is empty and it will break the 3 clue.
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* 2 3 clues that share an edge and has other non-0 clues in the grid must form the classic pattern because you need to place the line in the middle first because it makes a closed link if not, then if the line of the top and bottom are not given, then one of the 3 clues will fail.
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* A 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.
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* A line that is adjacent to the 3 will tell that the edges adjacent to that 3 and opposite of the line are all lines, because if its not met, there will be branching lines.
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* A 2 clue can have lines separated from each other, keep in mind.
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* Anytime you see the 4 clue, its just a 1 cell loop surrounding the loop. (Assuming the puzzle isn't impossible)
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* 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.
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[[/uploads/link-tips-c.png]]
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* 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.
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[[/uploads/link-tips-d.png]]
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* 2 3 clues that share an edge has:
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* the line placed in the common edge, otherwise, it makes a closed link.
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* two combinations (if not counting the closed link) that form an S-shape, taking the common lines and X's:
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[[/uploads/link-tips-e.png]]
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* 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.
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[[/uploads/link-tips-f.png]]
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* 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)
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* 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)
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[[/uploads/link-tips-g.png]]
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* A 2 clue can have lines separated from each other, keep in mind.
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