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
- 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.
- 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.
- 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.
- 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.
- 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.