TECHNIQUES FOR SOLVING SLITHERLINK PUZZLES

SLITHERLINK puzzles seem to have possibly a greater number of solution strategies than any other puzzle. They are presented in the following with examples, but without justification. A little doodling with pencil and paper will soon convince you of the correctness of these strategies.

When specific cells need to be referred to in this discussion, they will be designated as C4-R3 which means the 4th cell in row 3.

For a description of SLITHERLINK puzzles, refer to  Building Slitherlink Puzzles 


   
LEFT HAND GRAPHIC.
Zero segments. Any cell which contains a 0 may have all four pending line segments removed.
Threes in line. Whenever two threes are adjacent either vertically or horizontally, three pending line segments may be converted to full, and two may be permanently removed.

RIGHT HAND GRAPHIC.

Threes diagonally. Whenever two threes are adjacent diagonally, four pending line segments may be converted to full.
Remove pending lines. Whenever two full line segments touch at a point, any pending lines which also touch that point may be removed. Note also that a pending line which does not meet another pending line may also be removed.


   
LEFT HAND GRAPHIC.
Lonely three. Whenever a cell containing a three has a corner where only two line segments meet, those two line segments can be converted to full lines.
Lonely one. Whenever a cell containing a one has a corner where only two line segments meet, those two sides can be removed.
Two and one in a corner. Whenever a cell containing a two has a corner where only two line segments meet, and also has an adjacent cell containing a one, then three full line segments can be inserted and three may be removed as revealed in the left hand graphic.
Insert Pending Line. The pending line segment at cell C5-R3 can be inserted along with two other pending line segments.

RIGHT HAND GRAPHIC.

Contact with a three. Refer to C4-R2. A line segment has been inserted which contacts this cell at a corner having only two pending line segments. Only one of them can be inserted, so the other two line segments of this cell must be inserted.



   
LEFT HAND GRAPHIC.
Contact with a one. Look at C1-R4. A full line has contacted a one cell. One of the pending line segments at this point must be inserted, so the other two pending line segments of this cell can be removed.

RIGHT HAND GRAPHIC.

Must not complete loop. The last remaining pending line segment in C3-R4 would complete a premature loop if it were to be entered. It must therefore be removed. The same situation applies in the case of C4-R2.



Adjacent ones at boundary. This situation happens quite regularly. The pending line segment between the two ones may be removed.