GridWits
Expert tier Technique 18 of 20 Used by Smart Hint

Cross-Line Consistency

This row or column has only a few orderings left — any one that would leave some other row or column with no way to finish is out, and a value used by none of the survivors can be struck.

How it works

  1. 1Column 1 carries no sign of its own, so Line Consistency never even looks at it — yet its four cells still have only six orders their candidates allow.
  2. 2Write each order into the column and then read the REST of the board, which is the only way the ∧ in column 2 gets to speak.
  3. 3Just one order dies. Put 4-1-3-2 down column 1 and column 2's bottom cell is left holding only 4, so the cell above it must be 2 — and the ∧ then needs the cell above THAT to be under 2, when 2 is the smallest it has left.
  4. 4That was the only order with a 4 on top, so strike 4 from the top-left. The sign that killed it lies outside the line being enumerated, which is exactly what Line Consistency cannot reach.
1 3 4 1 3 4 2 3 4 1 2 3 1 2 3 4 2 3 2 3 4 2 3 4 1 2 3 4 2 4 2 4 3 1
  • Candidates this technique rules out
  • Smaller → larger — The arrow follows the direction imposed by the inequality sign.
  • Cells read together — The connecting line shows which cells combine to make the deduction.
  • Conclusion — The coloured candidate, or the final arrow when it lands outside the pattern, shows the result.
Next in the ladder Jellyfish →

A value's candidate cells across four rows (or columns) line up in the same four columns (or rows) — eliminate it everywhere else in those columns or rows.