2-String Kite

The 2-String Kite is a visually distinctive pattern that resembles a kite flying in the wind. It uses a box to connect two lines, creating elimination opportunities that neither line could achieve alone.

What is a 2-String Kite?

A 2-String Kite occurs when:

A candidate appears exactly twice in a row (first "string")
The same candidate appears exactly twice in a column (second "string")
One cell from each string shares a box, connecting them
The two non-connected ends are the "kite corners"

The box acts as a pivot, linking the row and column patterns.

Visual Pattern

Imagine a kite shape:

         Col A       Col B       Col C
    ┌─────────────────────────────────────┐
Row 1   │           │  ★ kite   │           │
        │           │  corner   │           │
    ├─────────────────────────────────────┤
        │           │           │           │
Row 3   │  ●────────┼───────────┼────● row  │
        │  box      │           │    string │
    ├─────────────────────────────────────┤
        │  │        │           │           │
Row 5   │  ●        │           │           │
        │  column   │           │           │
        │  string   │           │           │
    ├─────────────────────────────────────┤
        │  │        │           │           │
Row 7   │  ★ kite   │           │           │
        │  corner   │           │           │
    └─────────────────────────────────────┘

Let me draw this more simply:

        Col A   Col B   Col C
Row 1:            X           ← kite corner 1
Row 3:    X               X   ← row string (X at A, X at C)
Row 5:    X                   ← column string continues
Row 7:    X                   ← kite corner 2

Wait, let me clarify the exact pattern:

        Col A   Col B   Col C
Row 1:            X           kite corner 1 (end of column string)
Row 3:    X               X   cell at A is BOTH row string AND column string
Row 6:                    X   kite corner 2 (end of row string)

Actual 2-String Kite:

Row 3 has candidate in exactly 2 cells: A and C
Column A has candidate in exactly 2 cells: Row 1 and Row 3
Cell R3A is the connection point (in both strings)
Kite corners: R1A and R3C

The Logic

Consider candidate 7 in this pattern:

Column A string: 7 is in R1A or R3A Row 3 string: 7 is in R3A or R3C

Case analysis:

If R3A = 7:

Both strings are satisfied
Nothing eliminated yet

If R3A ≠ 7:

Column A string forces R1A = 7
Row 3 string forces R3C = 7

Key insight:

Either R3A = 7
Or BOTH R1A = 7 AND R3C = 7

Elimination: Any cell that sees both R1A and R3C will ALWAYS see a 7 (either R3A has it, or both corners have it).

Therefore, eliminate 7 from cells that see both kite corners.

Step-by-Step Example

Digit 4 appears:

Row 5: columns 2 and 7 (exactly 2 cells)
Column 2: rows 5 and 9 (exactly 2 cells)

Identify the pattern:

Row string: R5C2 — R5C7
Column string: R5C2 — R9C2
Connection point: R5C2 (in both)
Kite corners: R5C7 and R9C2

Find elimination targets: Cells that see both R5C7 and R9C2:

R9C7: shares row 9 with R9C2, shares column 7 with R5C7

If R9C7 contains candidate 4, eliminate it!

Finding the Elimination Zone

The kite corners are typically far apart. Elimination targets must see both:

Common targets:

The cell at the intersection of the corners' row and column
Cells in a box that overlaps both corners (rare due to distance)

Formula: If corners are at R(a)C(x) and R(b)C(y):

Check R(a)C(y) — shares row with first corner, column with second
Check R(b)C(x) — shares row with second corner, column with first

The Box Connection

What makes the 2-String Kite work is the box connection:

┌─────────────────┐
│ Box containing  │
│ the connection  │
│ point           │
└─────────────────┘

The connection point doesn't need to be in any special position within the box. It just needs to be:

Part of the row string (exactly 2 candidates in that row)
Part of the column string (exactly 2 candidates in that column)

2-String Kite vs. Other Patterns

Pattern	Structure	Connection
X-Wing	2 rows × 2 columns	Rectangle corners
Skyscraper	2 rows, 1 shared column	Base column
2-String Kite	1 row + 1 column	Shared cell
Turbot Fish	2 strong links	Various

The 2-String Kite is unique in using one row AND one column, connected at a single cell.

How to Find 2-String Kites

Method 1: Strong Link Search

Find rows with exactly 2 candidates for a digit
Find columns with exactly 2 candidates for the same digit
Check if any row cell equals any column cell
If yes, verify the complete pattern

Method 2: Box-Based Search

Pick a box
For each candidate, check:
- Does the containing row have exactly 2 instances?
- Does the containing column have exactly 2 instances?
If both, you may have a kite connection point

Method 3: Candidate Mapping

For each digit with few placements:

Map all strong links (2-candidate units)
Look for row-column intersections
Verify and find eliminations

Kite Variations

Horizontal-Vertical Kite

Row string horizontal, column string vertical (most common):

        .   X   ← column string end
        .   │
    X───────X   ← row string (connection at right)

Box-Corner Kite

Connection point sits in box corner:

┌───────────────┐
│ X───────X     │   ← row string
│ │             │
│ X             │   ← column string
└───────────────┘

Extended Kite

Strings span multiple boxes:

X . . . . . . X   ← row string
│
│
X                 ← column string

Practice Exercise

Find the 2-String Kite and elimination:

Digit 8:

Row 2: columns 4 and 8 only
Column 4: rows 2 and 6 only

Answer

Pattern:

Row 2 string: R2C4 — R2C8
Column 4 string: R2C4 — R6C4
Connection: R2C4
Kite corners: R2C8 and R6C4

Elimination targets: Cells seeing both corners:

R6C8: shares row 6 with R6C4, shares column 8 with R2C8

Action: Eliminate 8 from R6C8 if present.

Common Mistakes

Mistake 1: Non-strong links

Both strings must have EXACTLY 2 candidates. If a row has 3 cells with the candidate, it's not a valid string.

Mistake 2: Missing the connection

The strings must share a cell. If they don't intersect, it's not a kite.

Mistake 3: Wrong corners identified

The corners are the NON-shared cells, not the connection point.

Mistake 4: Incomplete elimination search

Always check both potential intersection points of the corners.

Why "Kite"?

If you draw lines:

From corner 1 to the connection point
From the connection point to corner 2
From corner 1 directly to corner 2

You get a triangle that resembles a kite shape, with the strings forming two sides.

Quick Reference

2-String Kite pattern:

1 row with exactly 2 candidates
1 column with exactly 2 candidates
1 cell shared by both (connection point)
2 cells not shared (kite corners)

Elimination rule:

Find cells that see both kite corners
Eliminate the candidate from those cells

Logic:

Either the connection point has the digit
Or both corners have the digit
Either way, cells seeing both corners see the digit

When to look:

After X-Wing and Skyscraper fail
Digits with few remaining placements
Strong links visible in perpendicular directions