2-String Kite

A 2-String Kite is the row-plus-column form of the two-node X-Chain. For one digit, a row strong-inference node and a column strong-inference node form (A=B)-(C=D); the dash is a weak inference through their shared box. The chain proves A OR D, allowing eliminations from candidates that see both endpoints.

What is a 2-String Kite?

Write the Kite as (A=B)-(C=D). A=B is a strong link (XOR) in a row and C=D is a strong link (XOR) in a column: each house must place the digit on at least one represented side. The connected sides B and C lie in one box and cannot both contain the digit, giving the weak inference (NAND) B-C. In strmckr's signature system the node sides may be singleton or properly justified grouped alternatives.

How to spot it

For one digit, find a justified row strong inference and a justified column strong inference. Check whether one side of the row node and one side of the column node share a box and conflict universally; that is the weak inference. The unconnected sides A and D are the endpoints. Remove the digit only from a target that sees every candidate represented by both endpoints.

The logic

If A is false, the row strong link makes B true. The box weak inference B-C makes C false, and the column strong link makes D true. Therefore A OR D is true, possibly both. A candidate that conflicts with both endpoints can be removed. This is the Type 1 same-digit elimination. The Skyscraper has the same two-node theorem but uses two parallel row nodes or two parallel column nodes instead.