GridWits

Cross-Line Forcing

Extreme Used by Smart Hint

Same as Cross-Line Consistency, but each arrangement is also followed through: fill in every height it forces outright, and rule it out if that leaves some other row or column unfinishable.

3 5 4 2 5 3 1 2 5 1 2 3 1 4 5 2 1 4 3 4 2

How it works

  1. The same position Cross-Line Consistency worked on, and the same opening move: list every filling of the clued row that matches its clue.
  2. Cross-Line Consistency then tests each filling AS IT STANDS — does some crossing line already have no way to finish? Sometimes the damage isn't visible that early.
  3. Forcing goes one step further before judging. Pencil the filling in, then run the cheap techniques on top of it: every Naked Single it creates, every Hidden Single, everything those in turn force.
  4. Now re-check the crossing lines. A filling that looked survivable often turns out, three forced placements later, to leave some row or column unfinishable — and it can be thrown out too.
  5. Whatever survives all that, the rule is unchanged: a height appearing in none of the surviving fillings is struck.
  6. This is the most expensive constructive rung in the game, which is exactly why it's tried last. Everything cheaper first; widen the net only when nothing else moves.