3-String Kite
3-String Kite chains three strong links in mixed houses — rows, columns, and blocks — on the same candidate. Consecutive links share a bridge cell, and the chain forces at least one of the two unlinked endpoints to hold the digit, eliminating it from any cell that sees both.
What is a 3-String Kite?
3-String Kite is a single-digit pattern built from three strong links that run through a mix of house types — rows, columns, and blocks — where a particular candidate appears in exactly two cells in each house. The six cells form three pairs, and one cell from each neighbouring pair shares a house with its partner. Those shared-house cells are the bridges: because each pair of bridge cells sees each other, they can't both hold the digit. Since each strong link must place the digit in one of its two cells, and the bridges can't supply both ends of the chain, at least one of the two outer endpoints — the roof — has to contain the digit. Any cell outside the pattern that shares a house with both roof cells can't also hold the digit, so it gets eliminated.
How to spot it
3-String Kite is a natural extension of the two-link 2-String Kite, so you find it the same way — by scanning one digit at a time, but this time across a mix of house types. Pick a candidate digit and look for rows, columns, and blocks where it's restricted to exactly two cells. When you find three such houses, check whether one cell from each neighbouring pair shares a house with the next — a block, a row, or a column. If they do, you've got a 3-String Kite chain: the shared-house cells are the bridges, and the two cells at the ends of the chain are the roof. The elimination lands on any cell that sees both roof cells — same row, same column, or same block as each. These patterns are rarer than two-link kites, but they turn up in harder puzzles once the easier strong-links techniques have been exhausted, and they're worth checking whenever you can trace three conjugate pairs on the same digit through a mix of house types.
The logic
Each strong link is a house where the digit has exactly two candidate cells, so one of them must be the digit. In a 3-String Kite chain, one candidate from each neighbouring pair sits in a shared house — the bridge. Because the two bridge cells see each other, at most one of them can be the digit. If the first bridge cell is the digit, the second link's digit falls on its roof cell, and the chain stops there. If the first bridge cell is not the digit, the first link's digit falls on its other cell, which is also a bridge to the next link — and the same reasoning carries forward. Tracing the chain link by link, every case forces at least one of the two outer roof cells to contain the digit, so any cell that sees both roof cells can't also hold it. The same reasoning applies regardless of which combination of house types the three links live in.