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# 🧩 Exact Cover

Band 10 — The Uranus transformer. Cover each element exactly once.

Elements: 7
Ready
Sets available (each must be used at most once, each element covered exactly once)

### Algorithm: Knuth's Algorithm X (Dancing Links)

Depth-first search that chooses an uncovered element, tries each set covering it, and recursively covers remaining elements. Dancing Links implements the matrix as circular doubly-linked lists for O(1) row/column removal.

### Why This Matters

The Exact Cover transformer (Uranus) is the Omnitranslator — it finds the unique covering that explains all data. Sudoku, tiling, and the 72-band translation all reduce to exact cover.