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Module 5 · Advanced PatternsLesson 23 of 28

Skyscraper & Two-String Kite

Recognize two common short single-digit patterns built from conjugate pairs.

Outcome

You can recognize two common short one-digit chain patterns, identify their Strong Links and connecting Weak Link, and eliminate the digit from common peers of the forced endpoints.

Intro copy

Skyscraper and Two-String Kite look different.

Logically, they do nearly the same job:

Two Strong Links are connected so that at least one free endpoint must be true.

This lesson teaches the shared inference first, then the two geometries.

Step 1 — The shared engine

Show two Strong Links on digit 6.

Connect one endpoint from each with a Weak Link.

Prompt:

Can the two connected endpoints both be true?

No.

Therefore at least one is false.

Each false connected endpoint forces its opposite Strong-Link endpoint true.

Conclusion:

At least one free endpoint is true.

Learner removes candidate 6 from a cell seeing both free endpoints.

Now reveal:

This is the logic behind both Skyscraper and Two-String Kite.

Part 1 — Skyscraper geometry

Arrange:

  • two row conjugate pairs;
  • one endpoint from each pair in the same column.

Label:

  • aligned endpoints = bases;
  • other endpoints = roofs.

Prompt:

Which cells are the forced free endpoints?

Learner selects roofs.

Then:

Remove candidate 6 from cells seeing both roofs.

Guided Skyscraper

Learner:

  1. filters one digit;
  2. finds two row Strong Links;
  3. identifies shared base column;
  4. marks roofs;
  5. eliminates from common peers.

Include a complete X-Wing as a distractor:

Both sides align here. Which simpler technique applies?

Correct: X-Wing.

Part 2 — Two-String Kite geometry

Show:

  • one row conjugate pair;
  • one column conjugate pair.

Move one endpoint of each into the same box.

Prompt:

What creates the Weak Link between these endpoints?

Correct:

They share a box.

The opposite endpoints become free ends.

Learner eliminates from their common peer.

Guided Kite

Learner identifies:

  • row string;
  • column string;
  • box connection;
  • free endpoints;
  • target.

Step 4 — Pattern classification

Show six mini-diagrams:

  1. Skyscraper;
  2. Two-String Kite;
  3. X-Wing;
  4. invalid pair with no Strong Link;
  5. invalid Kite with box endpoints in different boxes;
  6. valid structure with no elimination.

Learner classifies each before solving.

Practice

Difficulty progression:

  • Strong Links pre-drawn;
  • candidate digit highlighted;
  • no link drawing;
  • multiple conjugate pairs as distractors.

Hint ladder

  1. “Follow one digit.”
  2. “Find conjugate pairs.”
  3. “Can two Strong Links be connected by one Weak Link?”
  4. “Identify the free endpoints.”
  5. “Find a candidate seeing both.”

Completion

Two Skyscrapers, two Kites, and all classification cards.

Next

Strong and Weak Links

You have used the inference visually. Next name the link types explicitly and use them without a fixed pattern shape.

Reference

Read Skyscraper and Two-String Kite for their full proofs.