A Skyscraper is a one-digit pattern built from two conjugate pairs in two rows or two columns.
For a row-based Skyscraper:
- row A contains exactly two candidates X;
- row B contains exactly two candidates X;
- one candidate from each row lies in the same column;
- the two remaining candidates are the roofs.
At least one roof must be X.
So candidate X can be removed from every cell that sees both roofs.
Quick pattern
base A ----- roof A
|
base B ----- roof BThe bases align in one column.
The roofs do not need to align.
Why one roof must be true
Take digit 6.
Row 2 has:
- aligned base A;
- roof A.
Row 7 has:
- aligned base B;
- roof B.
Both rows form Strong Links because each has exactly two candidate 6s.
Now consider base A.
If base A is false
Row 2's Strong Link forces roof A = 6.
If base A is true
Base B shares the same column and cannot be 6.
Row 7's Strong Link then forces roof B = 6.
Either way:
- roof A is 6;
- or roof B is 6.
Therefore a candidate 6 that sees both roofs is impossible.
Step-by-step board example
Column-based Skyscraper
Transpose the pattern.
Two columns each contain exactly two candidates for X.
One endpoint from each pair shares a row.
The other endpoints are the roofs.
Candidate X can be eliminated from common peers of those roofs.
Skyscraper vs X-Wing
They begin similarly: two same-digit conjugate pairs.
X-Wing
Both sides align.
The pairs use the same two opposite units.
Skyscraper
Only one side aligns.
The unmatched endpoints become the roofs.
This difference is enough to change the elimination rule.
Skyscraper as a short X-Chain
A Skyscraper is not just a special shape.
It can be represented as a four-candidate X-Chain / Turbot-style structure.
That is useful pedagogically because:
- the named pattern is easy to spot;
- the chain explanation proves why it works;
- later X-Chains generalize the idea beyond a fixed geometry.
How to find Skyscrapers
1. Choose one digit
2. Find row conjugate pairs
Rows with exactly two candidate positions.
3. Compare endpoint columns
Do two pairs share one column?
4. Mark the free endpoints
Those are the roofs.
5. Search for a common peer
Any candidate X seeing both roofs can be eliminated.
Then repeat with columns as the starting units.
Common mistakes
Using rows with more than two candidates
Then the row endpoints do not form the required Strong Link.
Choosing two pairs with no aligned endpoint
No Skyscraper.
Eliminating from a cell that sees only one roof
The target must see both.
Eliminating from the aligned base automatically
The proof guarantees one of the roofs is true.
Calling a complete X-Wing a Skyscraper
If both sides align, use the simpler Fish explanation.
Recognition drill
With one digit filtered, record conjugate pairs:
r2 → c3/c8
r7 → c3/c5The shared c3 reveals the base.
The unmatched c8 and c5 are the roofs.
FAQ
Why is the technique called Skyscraper?
The visual arrangement resembles two towers of different heights in common diagrams. The aligned-base / two-roof logic matters more than the name.
Does Skyscraper use one digit?
Yes.
Is Skyscraper an X-Chain?
It can be represented as a short X-Chain.
Do the roofs need to see each other?
No. The elimination target must see both roofs.
What to learn next
Learn Two-String Kite, which uses one row conjugate pair and one column conjugate pair connected through a box.