Finned X-Wing

Recommended first: X-Wing

Description

Finned X-Wing is a fish-style candidate elimination technique. It looks like an X-Wing that is almost formed, but on one base line (a row or column) there are one or more extra candidates of the same digit — these extras are the fins.

Compared to a standard X-Wing:

• The green four key points resemble the X-Wing body
• The yellow extra candidate(s) are the fins, which “break” the perfect rectangle
• Because of the fins, eliminations are no longer a full row/column sweep — they are restricted to the fin’s box (the restricted area)

A helpful rule of thumb: the fin’s box is where the safe eliminations happen.
Sometimes there can be more than one fin, but they must lie in the same box for a finned fish.

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Explanation

In the image above, the target digit is 7.
The green cells r1c4, r1c7, r5c4, r5c7 look like a standard X-Wing.
But the yellow candidate 7 in r1c8 is an extra — the fin — so the rectangle is no longer perfect.

Even so, we can still eliminate candidates, and the eliminations are confined to the fin’s box 3 (the restricted area).

Why is that valid? Consider two cases:

1. If the fin r1c8 is NOT 7
   Then in row 1, digit 7 is left only at the two green positions (c4/c7).
   That restores a standard X-Wing, so we can eliminate 7 from other cells in columns c4 and c7 (including the eliminations inside the restricted box).

2. If the fin r1c8 IS 7
   Then the fin’s box already contains a 7.
   So other 7 candidates in that same box (on the cover line) cannot be true and can be eliminated directly.

Either way, those candidates inside the restricted box are impossible, so they are safe eliminations.

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Examples

These images show more finned X-Wing patterns. Use them as references for body (green) / fins (yellow) / eliminations in the fin’s box (red).

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How to Find Finned X-Wing

One-line checklist: find an “almost X-Wing” body, then find extra candidates (fins) on one base line, and only eliminate within the fin’s box.

In a real puzzle:

1. Pick a digit d
2. Start like an X-Wing: find the key body points (two base lines × two cover lines)
3. Check whether one base line has extra candidates for d, and confirm all fins are in the same box
4. Look for eliminations only inside the fin’s box: usually candidates of d on the cover line within that box, excluding the body intersection cells