Skyscraper

A Skyscraper is a one-digit elimination pattern built from two Strong Links in two parallel houses.

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 contain X.

Therefore candidate X can be removed from any cell that sees both roofs.

The column-based version is identical after swapping rows and columns.

Skyscraper at a glance

row A:   base A -------- roof A
           |
row B:   base B ---- roof B

The two base candidates align in one cover line. The two roofs do not need to align.

The pattern uses only one digit, so it is most naturally found with a candidate filter or digit-first scan.

Why Skyscraper works

Suppose candidate 6 appears exactly twice in row 2:

• base A;
• roof A.

And exactly twice in row 7:

• base B;
• roof B.

The two bases share the same column.

Because each row has exactly two candidate 6s, each pair forms a Strong Link.

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 sees base A in the shared column and cannot also be 6.

Row 7's Strong Link then forces roof B = 6.

Those two branches cover every possibility.

So:

roof A is 6 or roof B is 6.

Any candidate 6 that sees both roofs is impossible.

Step-by-step board example

A reliable Skyscraper proof sequence is:

1. filter one candidate digit;
2. find two rows with exactly two positions for that digit;
3. confirm one endpoint from each row shares a column;
4. label those aligned candidates as the base side;
5. label the unmatched endpoints as roofs;
6. prove at least one roof must be true;
7. eliminate the digit only from common peers of both roofs.

For a column-based Skyscraper, transpose the same reasoning.

Why the source rows or columns must be conjugate pairs

The proof depends on each source house having exactly two candidate positions for the digit.

If a source row has three candidates, then making one candidate false does not force the other chosen endpoint true. A third possibility remains.

That breaks the Strong Link and therefore breaks the standard Skyscraper proof.

This source-completeness check is more important than how closely the pattern resembles a skyscraper drawing.

Column-based Skyscraper

Everything works symmetrically with rows and columns reversed.

For a column-based pattern:

• column A contains exactly two X candidates;
• column B contains exactly two X candidates;
• one endpoint from each pair lies in the same row;
• the unmatched endpoints are the roofs.

Candidate X can be eliminated from cells that see both roofs.

A good solving habit is to search both orientations whenever one digit has several conjugate pairs.

How to find a Skyscraper

Skyscraper is a classic digit-first technique.

1. Choose one candidate digit

Filtering everything else reduces visual noise dramatically.

2. Record row conjugate pairs

Look for rows containing exactly two positions for the chosen digit.

For example:

r2 → c3 / c8
r7 → c3 / c5

3. Compare endpoint columns

Both pairs use c3. Those two c3 candidates form the aligned side.

4. Identify the roofs

The unmatched endpoints are r2c8 and r7c5.

5. Intersect the roof peer regions

Search for candidates of the same digit that see both roofs.

6. Repeat with column conjugate pairs

Transpose the search to avoid missing the opposite orientation.

Skyscraper vs X-Wing

Both patterns begin with two same-digit Strong Links in parallel houses.

The difference is how the opposite endpoints align.

X-Wing

Two base rows use the same two columns.

Both sides align, producing a size-2 Fish.

Skyscraper

The two rows share only one endpoint column.

The other endpoints lie in different columns and become the roofs.

This makes Skyscraper an excellent pattern for learning to stop thinking of sparse candidate structures as perfect rectangles.

Skyscraper and Sashimi X-Wing

The same candidate arrangement can be described from more than one advanced framework.

A Skyscraper can be viewed as a special Turbot pattern and can also be related to Sashimi X-Wing structures.

For human solving, the named Skyscraper pattern is often the simplest explanation because its two conjugate pairs and roof elimination are easy to verify directly.

The later Finned/Sashimi Fish expansion will explain that Fish terminology separately rather than forcing it into this Guide.

Skyscraper as a short X-Chain

Skyscraper is also a short one-digit chain.

Its logic can be expressed through alternating Strong and Weak Links between candidate X positions.

The important endpoint conclusion is:

at least one roof must be true.

That is exactly the kind of conclusion used by X-Chains: if one of two chain endpoints must contain the digit, that digit can be removed from candidates that see both endpoints.

This is why Skyscraper belongs naturally beside:

• Two-String Kite;
• Empty Rectangle;
• Turbot Fish;
• X-Chain.

The named pattern is the easy-to-recognize special case. Chain language provides the general framework.

Skyscraper vs Two-String Kite

Both use:

• one digit;
• two Strong Links;
• a Weak-Link connection between one endpoint from each;
• a common-peer elimination from the opposite endpoints.

The difference is where the Strong Links live.

Skyscraper

Two row links or two column links.

Their connecting endpoints align in a column or row.

Two-String Kite

One row Strong Link plus one column Strong Link.

Their connecting endpoints lie in the same box.

This structural comparison is more useful than memorizing the names independently.

Skyscraper vs Turbot Fish

Turbot Fish is a broader four-candidate X-Chain pattern.

Skyscraper is one named geometry that fits that logic.

So a solver may legitimately describe the same deduction as:

• a Skyscraper;
• a Turbot-style pattern;
• a short X-Chain.

When several labels are possible, these Guides prefer the simplest recognizable named pattern first and use the chain interpretation to explain why it generalizes.

A valid Skyscraper can be unproductive

The two conjugate pairs may form the correct structure while no external candidate sees both roofs.

That means the pattern has no elimination at the current state.

Do not remove candidates merely because the shape exists.

The target is part of the solving move.

Common Skyscraper mistakes

Using a source row or column with more than two candidates

Then the required Strong Link does not exist.

Choosing two pairs with no aligned endpoint

A standard Skyscraper needs one shared cover line on the base side.

Treating both sides as needing alignment

If both sides align, check X-Wing instead.

Eliminating from a cell that sees only one roof

The target must see both possible true roofs.

Eliminating from the aligned bases automatically

The proof establishes an either/or relationship between the roofs, not a blanket elimination around the base side.

Mixing digits

All four structural candidates and the target use the same digit.

A practical Skyscraper recognition drill

Filter one digit and write down its conjugate pairs.

For rows:

r2 → c3/c8
r7 → c3/c5

The repeated c3 reveals the aligned base.

The unmatched endpoints c8 and c5 are the roofs.

Then ask:

Does any candidate X see both roofs?

If yes, you have a productive Skyscraper elimination.

FAQ

Does Skyscraper use only one digit?

Yes. All structural candidates and eliminations involve the same candidate digit.

Why is it called Skyscraper?

Common diagrams resemble two towers of different heights. The name is only a visual mnemonic; the conjugate-pair logic defines the technique.

Do the roofs need to see each other?

No. A target candidate must see both roofs.

Is Skyscraper an X-Wing?

No. X-Wing has both sides aligned. Skyscraper has one aligned side and two unmatched roof endpoints.

Is Skyscraper a Turbot Fish or X-Chain?

It can be represented as both a Turbot-style pattern and a short X-Chain. The named Skyscraper is a convenient recognizable special case.

Can a Skyscraper eliminate more than one candidate?

Yes. Every candidate of the pattern digit that sees both roofs can be removed.

What to learn next

Learn Two-String Kite, which uses one row Strong Link and one column Strong Link connected through a box.