Fish & Wings
2-String Kite
A 2-String Kite removes one digit using a row and a column where that digit has exactly two places each. One end of the row and one end of the column sit in the same box, so they cannot both hold the digit — and therefore at least one of the two far ends must. The cell in the far end's row of one string and the far end's column of the other sees both, and loses the digit.
What you need to see on the grid
Look for a kite one digit at a time, right after the Skyscraper: both use two strong links, a kite simply takes one row and one column. Four terms carry the method:
- Strings
- The two strong links: a row and a column where the digit has exactly two places. One cell of each string must hold the digit.
- The box ends
- One end of the row and one end of the column, inside the same box. A box holds each digit once, so at most one of them can be it.
- The free ends
- The other end of each string, outside that box. At least one of them holds the digit.
- The target
- The cell in the row of the column's free end and the column of the row's free end. It sees both free ends, so it cannot hold the digit.
How to apply it, step by step
One example runs through all four steps: the digit 4, in a hard puzzle from the app, at the exact point where its hint needs a 2-String Kite. Every diagram shows the whole grid. The cells a step needs are filled in; the others are left blank and hatched, so you know you can ignore them. A digit missing from a drawn cell is already placed in its row, column or box, drawn or not.
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Step 1Find a row and a column where the digit has only two places
Pick a digit and list its places in each row and each column. Keep the rows and columns where it has exactly two: each is a strong link, because one of its two cells must hold the digit.
For 4, row 6 leaves only R6C3 and R6C7, and column 9 only R3C9 and R5C9. Those are the two strings of the kite.
Row 6 and column 9. 4 has two places in each: R6C3 and R6C7, R3C9 and R5C9. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 2 R2 9 R3 R4 7 R5 R6 2 6 8 3 7 9 1 R7 5 R8 6 R9 - Digit already on the grid
- Row or column where 4 has exactly two places
- A place for 4 in a link
- Candidate 4, the digit studied
- Not needed for this step
Filled in: row 6; column 9. The other 64 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 2Check that one end of each sits in the same box
The strings must be tied together: one end of the row and one end of the column in the same box. Here R6C7 and R5C9 are both in box 6. A box holds 4 only once, so R6C7 and R5C9 are not both 4.
The other two ends, R6C3 and R3C9, are the free ends. It does not matter that box 6 has a third place for 4 at R5C7: the argument only needs the two box ends to see each other.
Box 6 ties the strings: R6C7 and R5C9 share it. Numbered in order: free end R6C3, box ends R6C7 and R5C9, free end R3C9. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 2 R2 9 R3 R4 2 6 7 R5 8 R6 2 6 8 3 7 9 1 R7 5 R8 6 R9 - Digit already on the grid
- Row or column where 4 has exactly two places
- A place for 4 in a link
- Chain cell, numbered in order
- Candidate 4, the digit studied
- Not needed for this step
Filled in: row 6; column 9; box 6. The other 60 cells are left blank: they are not needed for this step. Nothing is removed yet: this step only reads the grid.
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Step 3Remove the digit where the free ends' lines cross
If R6C7 is not 4, row 6 puts its 4 on the free end R6C3; if R5C9 is not 4, column 9 puts it on the free end R3C9. One of the two box ends is certainly not 4 — so at least one free end is.
R3C3 sits in column 3 with R6C3 and in row 3 with R3C9: it sees both free ends, so it cannot be 4. It loses 4. That is the only cell a kite can clear; any other cell sees one free end at most.
Technique: 2-String Kite
The two strings and R3C3, where row 3 (free end R3C9) meets column 3 (free end R6C3). 4 leaves R3C3. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 2 R2 9 R3 R4 7 R5 R6 2 6 8 3 7 9 1 R7 5 R8 6 R9 - Digit already on the grid
- Row or column where 4 has exactly two places
- A place for 4 in a link
- Chain cell, numbered in order
- Candidate 4, the digit studied
- Candidate removed
- Not needed for this step
Filled in: row 6; column 9; cell R3C3. The other 63 cells are left blank: they are not needed for this step. Removed: 4 from R3C3.
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Step 4Collect what the elimination unlocks
A kite never places a digit by itself, so look at the cell it just cleared. R3C3 had two candidates, 3 and 4. With 4 gone, only 3 is left: a Naked Single, and the app's next hint in this puzzle.
Technique: Naked Single
Row 3 after the kite. R3C3 has only 3 left. C1 C2 C3 C4 C5 C6 C7 C8 C9 R1 R2 R3 5 3 6 9 2 1 R4 R5 R6 R7 R8 R9 - Digit already on the grid
- The cell that must be 3
- Candidate 3, the digit studied
- Digit placed
- Not needed for this step
Filled in: row 3. The other 72 cells are left blank: they are not needed for this step. Placed: R3C3 = 3.
Common mistakes
Tying the strings with the wrong ends
The two ends that share a box are the ones that cannot both be the digit; the target is built from the other two. Swap them and you clear a cell that may well hold the digit. Name the box ends first, then read the target off the free ends.
Using a line with three places
Each string must be a strong link: exactly two places in its row or column. In the example, box 6 has three places for 4, which is fine because the box only has to stop two cells from both being 4 — but a row or column with three places proves nothing.
Clearing more than the crossing cell
Only the crossing cell sees both free ends. Cells in row 3 or column 3 elsewhere see just one of them, and the other free end may be the one holding the digit, so they keep their candidates.
Recent daily puzzles that needed this technique
Keep going
- SkyscraperTwo two-place columns that share a base row: one roof holds the digit, so cells seeing both roofs lose it.
- Turbot FishTwo strong links on one digit, joined end to end: cells that see both free ends lose the digit.
Learn the move, not just the digit
In a real game, when a 2-String Kite is what opens the next cell, the hint in the app names it and shows the cell it unlocks — the same move as step 4 above.