Kite

Prerequisite: Chain Basics

Description

Kite is a single-digit candidate elimination technique: focus on one digit d.

You find two candidates for d in one row, and two candidates for d in one column, with one pair “tied together” by being in the same box.
Then any candidate d that can see both endpoints can be eliminated.

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Explanation

In the image above, the target digit is 4.
The chain is r4c2 → r4c9 → r6c8 → r8c8. The red candidate is digit 4 in r8c2, and the two endpoints (r4c2, r8c8) are highlighted in blue.

Why can we eliminate it? A short contradiction is enough:

• Assume r8c2 = 4 (the red candidate is true)
• r8c2 can see both endpoints, so r4c2 ≠ 4 and r8c8 ≠ 4
• Two strong links are forced to “fill in” 4: on row 4, r4c9 = 4; on column 8, r6c8 = 4
• But r4c9 and r6c8 are in the same box, so they can’t both be 4 → contradiction

Therefore, r8c2 cannot be 4, and the red candidate 4 can be eliminated.

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Examples

The next two images are more kite examples. Use them as references:

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How to Find a Kite

One-line checklist: two-in-a-row + two-in-a-column + a box tie → eliminate where both endpoints are seen.

In a real puzzle:

1. Pick a digit d
2. Find a row (or column) where d appears in exactly 2 candidate cells (a strong link)
3. Find a perpendicular column (or row) where d also appears in exactly 2 candidate cells (another strong link)
4. Check that one candidate from each pair lies in the same box (the “knot”)
5. The remaining two candidates are the endpoints: eliminate d from any cell that can see both endpoints