A row conjugate pair and a column conjugate pair for the same digit, connected through a shared box.
A Two-String Kite uses two conjugate pairs of the same digit (one in a row and one in a column) that are linked through a shared box. A conjugate pair means there are exactly two cells in that unit where the digit can go. The "kite" metaphor comes from the shape: two strings (the pairs) tied together at the box, with a tail pointing to the elimination target.
The logic is chain-based: if the digit goes in one end of the row pair, it forces the column pair and vice versa. The cell that can see both "free" endpoints of the two strings (the endpoints not connected through the box) cannot contain the digit, because one of those endpoints must hold it.
Two-String Kite is one of the single-digit chain techniques, along with Skyscraper and Empty Rectangle. It appears frequently in Extreme puzzles and is worth learning to spot quickly.
Pick a digit. Find a row where that digit has exactly two candidate positions (a conjugate pair). Call these cells A and B. Then find a column where the same digit also has exactly two positions. Call these C and D.
Check whether one cell from the row pair and one from the column pair share a box. For example, B and C are in the same box. This box connection is the "knot" of the kite.
Now look at the other two endpoints, A (from the row pair) and D (from the column pair). Any cell that can see both A and D cannot hold the digit. The reasoning: if the digit goes in B, then C is forced (column pair), so D cannot have it. If the digit does NOT go in B, it must go in A (row pair). Either way, a cell seeing both A and D sees at least one cell that holds the digit.
Example 1: Two-String Kite
Look at digit 5. In row 7, digit 5 appears only in R7C1 and R7C9, a conjugate pair (one must be 5). In column 2, digit 5 appears only in R3C2 and R9C2, another conjugate pair. R7C1 and R9C2 are connected through box 7.
The free endpoints are R7C9 and R3C2. R3C9 sees both: it shares row 3 with R3C2, and shares column 9 with R7C9. If R7C1 = 5, then R7C9 ≠ 5, but R3C2 must be 5 (column pair forces R9C2 off, then R3C2 on). If R7C1 ≠ 5, then R7C9 = 5. Either way, R3C9 sees a 5.
Eliminate digit 5 from R3C9.
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