Reading Empty Cells: The Clues That Are Not There

Silence Speaks Volumes

In a Slitherlink grid, a cell without a number is not "blank." It is simply a cell with a constraint of "0, 1, 2, or 3 lines." While less specific than a "3," it is still constrained by the rules of the universe (the Loop).

They Are Not Wildcards

Beginners treat empty cells as "anything goes" zones. Experts treat them as "connectors." The lines must pass through them to get from Point A to Point B.

Vertex Propagation

The most common way to solve an empty cell is via its vertices.
Remember the Vertex Rule: "A vertex has 0 or 2 lines."
If an empty cell is surrounded by determined edges, check its corners.
Example: An empty cell has a line entering its top-left corner. That line MUST exit the corner. If the top edge is blocked (X), the line must go down the left edge. You just deduced a line on an empty cell!

  Line enters empty cell via vertex:

  ·═══· × ·              ·═══· × ·
       (empty)    →       ║  (empty)
  ·   ·   ·              ·   ·   ·

  Line came in from top.  Top-right is ×.
  Vertex needs 2 lines.   So it MUST exit
                          down the left side!

Indirect Constraints

Empty cells next to numbered cells inherit constraints.
If a "3" forces a line on the shared edge with an empty cell, that empty cell now has a line. Now check the empty cell's vertices. Does that line have to turn?
Often, a "3" will force a chain of lines to snake through a series of empty cells because of vertex rules.

  Chain through empty cells:

  ·───·   ·   ·   ·
  │ 3 │(e) (e) (e)       (e) = empty cell
  ·───·═══·═══·═══·
  The 3 forces its bottom edge.
  Vertex logic forces the line to
  snake through all empty cells →

The "Canal" Effect

In hard puzzles, you often find "canals" of empty cells running between clusters of numbers. The loop often has to use these canals to connect the clusters.
If you have a narrow path of empty cells bordered by Xs (or board edges), the loop is forced to travel through it like water in a pipe. You can often draw lines straight through multiple empty cells just because there is "nowhere else to go."

  Canal effect — forced path:

  · × · × · × ·
  ║  (empty)   ║    ← Xs above and below
  ·═══·═══·═══·       force a straight
  ║  (empty)   ║       "pipe" through
  · × · × · × ·       the canal!

Strategy Summary

Don't skip empty cells when scanning the board.
1. Check their vertices for forced "in-out" moves.
2. Check if they form a "bottleneck" or canal between regions.
3. Use coloring (inside/outside) to determine if the empty cell is part of the interior or exterior.