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Two-String Kite ​

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A Two-String Kite is a two-strong-link chain, a type of AIC (alternating inference chain). Its strong links come from conjugate pairs in one row and one column. When drawn on the board, the two links are perpendicular.

How to spot it ​

  • For each candidate x from 1 to 9, examine its conjugate-pair strong links in rows and columns.
  • Find one conjugate pair in a row and another in a column, so that their strong links are perpendicular.
  • If one cell from each conjugate pair lies in the same box, candidate x can be eliminated from any cell that sees both of the other two cells.
Two-String Kite diagram

How it works ​

  • Let the two conjugate-pair strong links for candidate x be [A]━[B] and [C]━[D]. If B and C share a box, they see each other and form the weak link [B]┉[C], producing the two-strong-link chain [A]━[B]┉[C]━[D]. By the rules of an AIC, the end nodes A and D also have a strong relationship: at least one of them must be true.
  • If A does not contain x, then B must contain x. This prevents C from containing x, which in turn forces D to contain x. The same reasoning works in reverse: if D does not contain x, then A must contain x.
  • Therefore, candidate x can be eliminated from any cell that sees both A and D.

Examples ​

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On the board above, candidate 5 forms two perpendicular conjugate pairs, one in row R3 and the other in column C5. Candidate 5 occurs in exactly two cells in each house, producing two strong links. Cells R3C6 and R1C5 share a box and form a weak link, giving a two-strong-link chain with end nodes [R3C2:5] and [R9C5:5]. At least one end node must be true, so candidate 5 can be eliminated from R9C2, which sees both end nodes.

This is an idealized Two-String Kite: its perpendicular strong links also cross, giving it the simplest kite-like shape. The technique only requires the strong links to be perpendicular, however; they do not have to cross.

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On the board above, candidate 4 forms perpendicular strong links between R6C3 and R6C5, and between R4C2 and R7C2. Cells R4C2 and R6C3 share a box and form the weak link, leaving [R6C5:4] and [R7C2:4] as the end nodes. Candidate 4 can therefore be eliminated from R7C5.

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

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