Two-String Kite

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A Two-String Kite is a same-digit two strong link chain. Its two strong links come from conjugate pairs in one row and one column. When drawn on the board, those two strong links are perpendicular.

For a given candidate digit, if you can find one conjugate-pair strong link in a row and another in a column, and choose one node from each so that those chosen nodes lie in the same box and therefore form a weak link, then the pattern is a Two-String Kite. The two unchosen nodes are the endpoints of the chain. Any candidate that forms weak links with both endpoints can be eliminated.

For example, look at digit $5$ in the board below. There is one conjugate pair in row $R3$ and another in column $C5$, so we get two perpendicular strong links. At the same time, $R3C6$ and $R1C5$ lie in the same box and form a weak link. This gives a two-strong-link chain with endpoints $R3C2$ and $R9C5$. By alternating-inference-chain logic, those endpoints also act as a strong link, so one of them must be true. Candidate $5$ in $R9C2$ forms weak links with both endpoints, so it can be eliminated.

This is a very neat example of a Two-String Kite. Here, the two perpendicular strong links cross, giving the pattern its familiar kite shape. However, the technique requires only that the strong links be perpendicular; they do not have to cross.

For example, in the next board, digit $4$ forms two perpendicular strong links: one between $R6C3$ and $R6C5$, and the other between $R4C2$ and $R7C2$. Since $R4C2$ and $R6C3$ lie in the same box, they form the weak link, so the endpoints are $R6C5$ and $R7C2$. That lets us eliminate candidate $4$ from $R7C5$.

Here is another common form of the Two-String Kite.