GridWits
Extreme tier Technique 21 of 21 Smart Hint: Skyscrapers and Skyscrapers+

Cross-Line Forcing

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.

How it works

  1. 1The top row has three cells open and four fillings its clues allow: 1-4-3-5-2, 2-4-3-5-1, 3-4-1-5-2 and 3-4-2-5-1.
  2. 2Cross-Line Consistency tries each one as it stands and finds every crossing row and column still finishable, so it has nothing to say here.
  3. 3Forcing writes the filling in FIRST and runs the cheap rungs on top of it. Take 3-4-1-5-2: the second row's last cell is forced to 3, then the fourth row's last to 1, its second to 3, and the second row's third cell to 4.
  4. 4Now the first column can't be finished. Its 4 has nowhere left but the bottom cell, which puts the 5 above it — so the 4 is hidden and only two buildings show, where the clue on top asks for three.
  5. 5That filling is dead, and it was the only one putting a 1 in the top row's third cell. Strike the 1 there.
1 2 3 4 1 2 3 5 1 2 1 2 3 4 5 1 3 4 2 3 1 2 3 5 4 1 2 3 5 1 3 1 2 5 4 1 2 3 1 2 3 4 1 2 5 3 2 2 3 2 3 3 2 1 3 3 4 1 1
  • Height ruled out
  • Relationship — The arrow shows which cells support the deduction.
  • Conclusion — The final arrow lands beside the proved or ruled-out height.