Cross-Line Forcing
Same as Cross-Line Consistency, but each ordering is also followed through: fill in every value it forces outright, and rule it out if that leaves some other row or column unfinishable.
How it works
- 1Row 3's candidates allow ten orders. Write each one in and look straight away for a line that has died, and two of them go — but every candidate still survives in some order that is left, so Cross-Line Consistency strikes nothing here.
- 2So follow through first: after writing an order in, fill every cell it forces outright, the way you would without thinking about it.
- 3Both of the orders that put 2 in row 3's second cell then complete the top row as 4-3-2-1 and 1-3-2-4 — each with a 3 to the left of the < and a 2 to its right.
- 4Neither order broke a rule when you wrote it; what it forced two moves later did. So the second cell of row 3 is not 2 — and this is the deepest reasoning the solver does that still runs forwards, which is why boards needing it are graded Extreme.
- 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.