An X-Wing with one extra candidate cell, the "fin." Eliminations are restricted to cells that also see the fin.
A Finned X-Wing is what happens when you almost have a perfect X-Wing, but one row (or column) has an extra candidate cell, the "fin." In a regular X-Wing, a digit appears in exactly two cells in each of two rows, and those cells share the same two columns, allowing broad eliminations. The fin breaks this symmetry.
Despite the imperfection, the pattern is still useful. The logic works by considering two possibilities: either the standard X-Wing holds (and eliminates as usual), or the fin cell contains the digit (and eliminates from its own peers). The intersection of these two cases (cells that would be eliminated in both scenarios) can still be safely eliminated.
This makes Finned X-Wing more common than regular X-Wing but with fewer eliminations. You will encounter it frequently in Extreme-level puzzles.
Start by looking for an almost-X-Wing: a digit appears in exactly two cells in one row (the "base"), and in two or three cells in another row. The extra cell in the second row is the fin.
Identify the two columns that would form the X-Wing (the columns shared by the base and the non-fin cells in the cover row). The fin cell is in the same row but a different column.
Now consider: if the fin cell does NOT contain the digit, the remaining cells form a standard X-Wing and you can eliminate from both shared columns. If the fin cell DOES contain the digit, it eliminates the digit from its peers. The cells that lose the digit in BOTH cases are the safe eliminations, specifically, cells in the shared columns that also see the fin cell (share its box).
Example 1: Finned X-Wing
Look at digit 1 in rows 5 and 7. In row 5, digit 1 appears as a candidate in R5C3 and R5C4, a clean pair. In row 7, digit 1 appears in R7C1, R7C3, and R7C4. If only R7C3 and R7C4 had digit 1, we would have a perfect X-Wing in columns 3 and 4. R7C1 is the fin, the extra cell.
Green circles mark digit 1 in the pattern cells. The fin (R7C1) is in box 7. Only cells in columns 3-4 that also share box 7 with the fin can be eliminated. R8C3 and R9C3 meet this criteria, they are in column 3 and in box 7.
Eliminate digit 1 from R8C3 and R9C3. R9C3 reduces to {7}, a Naked Single.
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