What is a Two-String Kite?
The Two-String Kite is an advanced Sudoku solving technique that uses a chain of strong links to eliminate candidates. It gets its name from the shape formed by the pattern – resembling a kite with two strings attached.
This technique combines elements from a row, a column, and a box to create a logical chain that proves a candidate cannot exist in a specific cell. It's particularly useful when simpler techniques have been exhausted.
The Core Principle
A Two-String Kite is built on the concept of strong links. A strong link exists when a candidate appears in exactly two cells within a house (row, column, or box). If one cell doesn't contain the candidate, the other cell must.
The pattern requires:
- A candidate that appears exactly twice in a row (first "string")
- The same candidate appearing exactly twice in a column (second "string")
- One cell from the row and one from the column sharing the same box (the "kite body")
- The remaining two cells (the "kite tails") that can see a common cell
How to Identify a Two-String Kite
Step-by-Step Process:
- Choose a candidate to analyse (any number 1-9)
- Find a row where this candidate appears in exactly two cells
- Find a column where the same candidate appears in exactly two cells
- Check for box connection – one cell from the row and one from the column must share the same box
- Identify the tails – the other two cells (one from row, one from column) are the "kite tails"
- Find the elimination target – any cell that can see both kite tails can have the candidate eliminated
Understanding the Logic
The Two-String Kite works through a chain of implications:
Logical Chain:
- In the row, the candidate must be in one of two cells (A or B)
- In the column, the candidate must be in one of two cells (C or D)
- Cells B and C share a box – they form the "kite body"
- If the candidate is in B, it cannot be in C (same box)
- If not in C, it must be in D (strong link in column)
- Alternatively, if not in B, it must be in A (strong link in row)
- Therefore, the candidate must be in either A or D
- Any cell that sees both A and D cannot contain this candidate
Analysing the Example
Reading the Diagram
In the example image from SudokuWorldTournament, we can see a Two-String Kite pattern for candidate 7:
The Pattern Components:
- Row 1 (first string): Candidate 7 appears in exactly two cells – R1C1 (circled) and one other cell in the row. This forms a strong link.
- Column 9 (second string): Candidate 7 appears in multiple cells down column 9 (R2C9, R3C9, R4C9, R6C9 – all circled in red). The strong link connects two of these.
- Box connection (green cells): The green-highlighted cells in Box 1 (R1C1 and R1C3) show where the row string connects through the box.
- Pink highlighting: Shows the cells involved in the strong links along the row and column.
The Elimination:
The green checkmarks (✓) indicate the elimination targets. Following the chain logic:
- If 7 is NOT in R1C1, then 7 must be in the other cell of the row string
- If 7 IS in R1C1, it cannot be in R1C3 (same box), forcing 7 into specific cells in column 9
- Either way, 7 must be in one of the two "tail" cells
- Any cell that can see BOTH tails cannot contain 7 – hence the eliminations marked with ✓
The fox mascot at the bottom confirms the technique: "Two-String Kite" – showing that the app has detected and is highlighting this advanced pattern.
When to Look for Two-String Kites
Optimal Conditions:
- After exhausting basic techniques (singles, pairs, pointing)
- When a candidate appears exactly twice in multiple rows and columns
- When X-Wing and Swordfish patterns aren't present
- In puzzles rated as "hard" or "expert" difficulty
Common Mistakes to Avoid
- Weak links: Both strings must be strong links (exactly two candidates)
- Missing box connection: The two strings must connect through a shared box
- Wrong elimination target: Only eliminate from cells that see BOTH tails
- Confusing with Skyscraper: Skyscraper uses two parallel lines; Kite uses perpendicular lines
Related Techniques
The Two-String Kite belongs to a family of chain-based techniques:
- Skyscraper: Two parallel strong links connected at one end
- Turbot Fish: General term for simple chain patterns
- Empty Rectangle: Uses a box with candidates in an L-shape
- X-Chain: Longer chains of alternating strong and weak links
Mastering the Two-String Kite is an excellent stepping stone to understanding more complex chain techniques.
Practice Tips
Building Recognition Skills:
- Mark strong links: When pencil marking, note rows and columns with exactly two candidates
- Look for box intersections: Check if any strong links share a box
- Trace the chain: Follow the logic from one tail to the other
- Verify the elimination: Confirm the target cell sees both tails
- Practice regularly: Two-String Kites appear frequently in hard puzzles