page_title: Slitherlink
section_title: Rules for squares with 3
hierarchical_section_title: Slitherlink / Solution methods / Exactly 2 or 0 lines at each point / Rules for squares with 3
caption_attribution_description: English: A partial Slitherlink game demonstrating the lines and blanks that can be marked when two 3s are adjacent.
context_page_description: Slitherlink is a logic puzzle developed by publisher Nikoli.
context_section_description: If a 3 is adjacent to a 0, either horizontally or vertically, then all edges of that 3 can be filled except for the one touching the 0. In addition, the two lines perpendicular to the adjacent boxes can be filled.
  If two 3s are adjacent to each other horizontally or vertically, their common edge must be filled in, because the only other option is a closed oval that is impossible to connect to any other line. Second, the two outer lines of the group (parallel to the common line) must be filled in.  Thirdly, the line through the 3s will always wrap around in an "S" shape.  Therefore, the line between the 3s cannot continue in a straight line, and those sides which are in a straight line from the middle line can be X'd out.
  If a 3 is adjacent to a 0 diagonally, both sides of the 3 that meet the 0's corner must be filled.  This is because if either of those sides were open, the line ending in the corner of the 0 would have no place to go. This is similar to the 3-in-a-corner rule.
  Similarly, if a 3 has a corner with Xs in both directions going away from that corner, then both sides of the 3 that meet that corner must be filled. This is because if one of those two sides of the 3 were open, the other would have to be filled (because the 3 can only have one open side) but would meet 3 Xs at that corner, which is impossible because each point on the grid must have exactly 2 or 0 lines.
  If a line reaches a corner of a 3, there must be lines on both sides of the 3 that said corner is not adjacent to, because if the 3's sole empty space were not adjacent to it, the corner would have three lines connected to it.  Furthermore, the segment leading away from the 3 at the corner reached by the line must be empty;  if it were filled, neither of the remaining 2 undetermined sides of the 3 would be able to contain a line.
caption: Two adjacent 3s.
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