Sudoku-YAdvanced
Skyscraper: two pairs, a useful shared consequence
Two positions in each of two columns can tell you something without choosing either column’s answer first.
Track one digit through two complete units
A Skyscraper connects two pairs of positions for one digit. Each source unit has only two positions; the connecting pair cannot both hold the digit. At least one of the other ends must hold it, so a candidate seeing both ends can be removed. Seeing means sharing a row, column or box.
Our example follows 6
Column 2 allows 6 only at B2/H2; column 8 only at C8/H8. Neither column already has a placed 6. H2 and H8 share row H, so they cannot both be 6. Only this digit is illustrated; other candidates are unspecified.
B7 sees B2 by row and C8 by box. C1 sees B2 by box and C8 by row. Those are our two targets; being close to a line in the drawing is irrelevant.
Check both possibilities
- If B2 is 6, neither B7 nor C1 can be 6.
- If B2 is not 6, H2 must be 6. H8 then cannot be 6, forcing C8 to be 6. That also excludes both targets.
Both cases justify the same removals. We have not determined which end is actually 6, and the elimination does not require that decision.
What if D2 also allows 6?
The old argument fails: rejecting B2 no longer forces H2. For example, D2, H8 and B7 can all hold 6 without sharing a row, column or box. This is a counterexample under our partial conditions. Also check the target relationship: B5 sees B2 but not C8, so it is not covered by the original argument.
Try before revealing
In the original setup, can B5 lose 6 along with B7?
Show explanation
No. B5 cannot see C8, so the case that forces C8 does not exclude B5. Another reason would be needed.
Looking for it while playing
The Classic 9×9 Techniques button now scans Skyscraper and Two-String Kite from your current entries, highlights the evidence and links to these lessons. Strong/Weak Links explain the connections used in those proofs; they are not a standalone elimination. Reading or revealing an answer here never changes your saved game.
First find two-position units for one digit, then verify the connection and common targets. A familiar shape alone is not proof. A valid connection with no removable target does not give a new move.
References and further reading
Read the source explanations and compare them with our examples. Links are references, not endorsements or claims of affiliation.