A Two-String Kite is a one-digit pattern built from:
- one row conjugate pair;
- one column conjugate pair;
- one endpoint from each pair sharing the same 3×3 box.
The two endpoints that are not inside that connecting box are the free ends of the kite.
At least one free end must contain the digit.
So the digit can be removed from any candidate that sees both free ends.
Quick structure
Why Two-String Kite works
Choose candidate 5.
The row contains exactly two 5s:
- row free end R;
- row box end A.
The column contains exactly two 5s:
- column free end C;
- column box end B.
A and B lie in the same box, so they cannot both be 5.
At least one of A/B is false.
If A is false
The row Strong Link forces R = 5.
If B is false
The column Strong Link forces C = 5.
Therefore at least one free end — R or C — is 5.
Any candidate 5 seeing both R and C can be eliminated.
Step-by-step board example
Why the box connection matters
The two inside endpoints need a Weak Link: they cannot both be true.
Sharing a box provides that exclusion.
Without the shared box, both inside endpoints could theoretically be true at the same time and the proof would not force one of the free ends.
The box is therefore not decorative geometry.
It is the logical connection between the two strings.
Two-String Kite vs Skyscraper
Both use:
- one digit;
- two Strong Links;
- a Weak Link between one endpoint from each;
- a common-peer elimination from the opposite endpoints.
Skyscraper
Two row links or two column links.
The connecting endpoints align in a row/column.
Two-String Kite
One row link + one column link.
The connecting endpoints see each other through a box.
This is why both belong naturally next to short X-Chains.
Two-String Kite vs X-Wing
X-Wing is a Fish with two base and two cover sets.
Two-String Kite is better understood as a short chain.
The similar sparse-candidate geometry can make them look related, but the proofs use different frameworks.
How to search for Two-String Kites
1. Filter one digit
2. Mark row conjugate pairs
3. Mark column conjugate pairs
4. Look inside boxes
Can one endpoint of a row pair see one endpoint of a column pair through the same box?
5. Identify the free ends
6. Look for common peers containing the digit
That final common-peer test determines whether the Kite is productive.
Common mistakes
Using a row or column with more than two candidate positions
The strings need Strong Links.
Using connecting endpoints in different boxes
Then the required Weak Link may not exist.
Eliminating from the shared box automatically
The elimination target must see both free ends.
Mixing candidate digits
Both strings use the same digit.
Forgetting that a valid Kite can be unproductive
No common-peer candidate means no move right now.
Recognition drill
When one digit is highlighted:
- circle row conjugate pairs;
- circle column conjugate pairs;
- look where one endpoint from each pair meets inside a box.
Then inspect the opposite endpoints.
FAQ
Why is it called Two-String Kite?
The row conjugate pair and column conjugate pair are the two “strings”; their geometry resembles a kite in common diagrams.
Do the two inside endpoints have to be the same cell?
No. They only need to see each other, typically by sharing the box.
Is Two-String Kite a chain?
Yes. It is a named short one-digit chain pattern.
Which candidates can be eliminated?
The chain digit from cells that see both free endpoints.
What to learn next
Formalize Strong Links, Weak Links, and Chains so Skyscraper and Two-String Kite become examples of a general inference language.