2-string kite

A 2-string kite is the second of three single-digit patterns that share the same underlying logic. Pick a digit. Find a row where the digit has exactly two candidate cells, and a column where the digit also has exactly two candidate cells. If one cell from the row and one cell from the column share a box, that shared box is the "knot" of the kite. The remaining two cells — one from the row, one from the column, both outside the knot box — are the kite's "tails." The digit can be eliminated from any cell that sees both tails.

The argument

The row's strong link puts the digit in either its in-the-knot cell or its outside-the-knot cell. The column's strong link puts the digit in either its in-the-knot cell or its outside-the-knot cell. The knot box can hold the digit at most once.

Two cases. Case one: the digit is in the knot box, at the cell that completes the row's strong link or the column's strong link (or possibly both, if the two in-the-knot cells coincide). The other strong link's outside-the-knot cell — the tail — must then be the digit. Case two: the digit isn't in the knot at all. Both strong links' outside cells then carry the digit. Either way, at least one of the two tails is the digit. So any cell seeing both tails can't be the digit.

The pattern's name comes from the visual shape: two "strings" — the row strong link and the column strong link — meeting at the knot, with the tails extending outward.

Where it differs from skyscraper and empty rectangle

Skyscraper, 2-string kite, and empty rectangle are three names for variations of the same single-digit pattern. The difference is the geometry of the strong links and the shared cell:

• Skyscraper: two row strong links share a column.
• 2-string kite: a row strong link and a column strong link share a box.
• Empty rectangle: a box's candidates for the digit are confined to a single row and column intersection, paired with a strong link in that row or column.

All three produce the same kind of elimination — the digit removed from cells visible to both "outside" ends. The Sudoku Mountain solver uses one detector that emits one of these three labels depending on the geometry.

When you'll see it

2-string kites are a step rarer than skyscrapers because the row-meets-column geometry is more restrictive than two-rows-share-a-column. They turn up on hard puzzles where simpler techniques have run out, and they're the same technique-strength tier as skyscrapers and empty rectangles — find any one, and the eliminations are always available.