Grouped Single Digit Chains: Grouped Skyscraper, Grouped 2-String Kite, Grouped Turbot Fish
Grouped Single Digit Chains are extended versions of the Single Digit Chains techniques. This article covers three grouped techniques: Grouped Skyscraper, Grouped 2-String Kite, and Grouped Turbot Fish. They share the same core principles as regular single digit chains, but the strong link endpoints are extended to multi-cell groups within a box.
In regular strong links, endpoints are single cells. In grouped strong links, endpoints can be multiple cells within the same box forming a group. When a candidate appears in a row/column only within a specific box, those cells act as a single unit and form a strong link relationship with other positions.
Before reading this article, we recommend understanding regular Single Digit Chain techniques.
Understanding Grouped Strong Links
Let's understand the difference between grouped and regular strong links:
The logic of a grouped strong link is: if all cells in the group are NOT the candidate, then the single cell at the other end must be that candidate; and vice versa. The group participates in reasoning as a whole unit - as long as one cell in the group is true, the entire group is considered "true."
General Elimination Rule
The elimination rule for grouped single digit chains is the same as regular single digit chains:
Elimination Logic
If two strong links (which can be grouped strong links) are connected through a weak link,
Then cells that can see both outer endpoints of the two strong links can eliminate that candidate.
Note: When an outer endpoint is a group, the eliminated cell must be able to see all cells in the group.
Grouped Skyscraper
Grouped Skyscraper is an extended version of the Skyscraper technique. It features two parallel strong links where at least one is a grouped strong link (with a group endpoint).
Example Analysis
Observe the distribution of candidate 7:
- If R7C8=7 → Row 7 is determined
- If R7C8≠7 → R7C2=7 (strong link) → R4C2≠7 (weak link) → R4C7 or R4C9=7 (grouped strong link)
In either case, R7C8 and group R4C7,R4C9 must contain at least one 7.
- R5C8: Same column as R7C8, same box as R4C7,R4C9 → Eliminate candidate 7
Grouped Skyscraper: Digit 7, R7C8-R7C2 (Row 7 strong link) connects with R4C2-R4C7,R4C9 (Row 4 grouped strong link) via Column 2 weak link.
Action: Eliminate candidate 7 from R5C8.
Grouped 2-String Kite
Grouped 2-String Kite is an extended version of the 2-String Kite technique. It features one row strong link and one column strong link where at least one is a grouped strong link.
Example Analysis
Observe the distribution of candidate 8:
- If R1C1=8 → Row 1 is determined
- If R1C1≠8 → R1C8 or R1C9=8 (grouped strong link) → R3C7≠8 (weak link) → R7C7=8 (strong link)
In either case, R1C1 and R7C7 must contain at least one 8.
- R7C1: Same column as R1C1, same row as R7C7 → Eliminate candidate 8
Grouped 2-String Kite: Digit 8, R1C1-R1C8,R1C9 (Row 1 grouped strong link) connects with R3C7-R7C7 (Column 7 strong link) via Box 3 weak link.
Action: Eliminate candidate 8 from R7C1.
Grouped Turbot Fish
Grouped Turbot Fish is an extended version of the Turbot Fish technique. It features one box strong link and one row/column strong link where at least one is a grouped strong link.
Example Analysis
Observe the distribution of candidate 6:
- If R3C1 or R3C2=6 → Group endpoint is true
- If neither R3C1 nor R3C2 is 6 → R1C3=6 (grouped strong link) → R7C3≠6 (weak link) → R7C4=6 (strong link)
In either case, group R3C1,R3C2 and R7C4 must contain at least one 6.
- R3C4: Same row as group R3C1,R3C2, same column as R7C4 → Eliminate candidate 6
Grouped Turbot Fish: Digit 6, R3C1,R3C2-R1C3 (Box 1 grouped strong link) connects with R7C3-R7C4 (Row 7 strong link) via Column 3 weak link.
Action: Eliminate candidate 6 from R3C4.
Grouped vs Regular Techniques Comparison
| Regular Technique | Grouped Technique | Key Difference |
|---|---|---|
| Skyscraper | Grouped Skyscraper | Endpoint can be a multi-cell group within a box |
| 2-String Kite | Grouped 2-String Kite | Row or column strong link endpoint can be a group |
| Turbot Fish | Grouped Turbot Fish | Box or row/column strong link endpoint can be a group |
How to Find Grouped Single Digit Chains?
Steps to find grouped single digit chains:
- Groups must be within the same box
- Eliminated cells must see all cells in the group, not just one of them
- Grouped techniques extend regular techniques, revealing more elimination opportunities
- Master regular Single Digit Chain techniques first before learning grouped versions
Technique Summary
Key points for applying Grouped Single Digit Chain techniques:
- Core Extension: Extend strong link endpoints from single cells to multi-cell groups within a box
- Elimination Rule: Cells that see both outer endpoints (including all cells in groups) can eliminate the candidate
- Use Cases: Supplementary method when regular single digit chains can't find eliminations
- Difficulty: Harder to spot than regular single digit chains, but more powerful
Grouped Single Digit Chains are advanced versions of Single Digit Chains. Recommended learning order:
Single Digit Chains → Grouped Single Digit Chains → X-Cycle
Mastering these techniques will help you handle most chain reasoning scenarios.
Start a hard difficulty Sudoku game and try to discover Grouped Single Digit Chain patterns! Since manual searching is complex, consider using the solver's hint feature to familiarize yourself with these patterns first.