2-String Kite Sudoku Technique, With a Worked Example

A 2-String Kite is a single-digit pattern built from one row where a digit has exactly two spots and one column where the same digit has exactly two spots, with one end of each sitting in the same box. Because those two ends share a box, at most one of them holds the digit, so one of the far ends must, and any cell that sees both far ends can lose it.

To spot one, pick a digit, list the rows and columns where it has only two candidates, and look for a row pair and a column pair that each put one cell into the same box (using four different cells). The target is always a single cell: the one where the row of one far end crosses the column of the other.

How the 2-String Kite works

This position comes from a real puzzle in our library. Look only at the digit 2.

• Row 5 has two cells that can be 2: R5C1 and R5C8. This is the first string.
• Column 9 has two cells that can be 2: R6C9 and R9C9. This is the second string.
• R5C8 and R6C9 are both in box 6, so they cannot both be 2. This is the knot that ties the strings together.

Follow both cases. If R5C8 is not 2, row 5 needs its 2 in R5C1. If R6C9 is not 2, column 9 needs its 2 in R9C9. At least one of the two knot cells is not 2, so at least one of the far ends, R5C1 or R9C9, is a 2.

R9C1 sees R5C1 down column 1 and R9C9 along row 9. Whichever far end is the 2, R9C1 would clash with it, so 2 comes out of R9C1.

The payoff here is immediate. Column 1 had only two spots for 2, R5C1 and R9C1. With R9C1 gone, R5C1 is a hidden single and takes the 2.

Puzzle 175758 from the Sudoku Royale library. Givens (row by row, dots are blanks): .........6.....54.83.51.2....59.28....13.7..57.814.6..51.879...4...............7.. The candidates shown are what is left after singles, pointing and claiming, naked and hidden pairs, triples and quads, X-Wing and Swordfish, with nothing else applied.

How to spot a 2-String Kite

1. Pick one digit. Like every kite, skyscraper and fish, this pattern only involves one number.
2. List the row pairs. Note each row where the digit has exactly two candidates, and skip any where both are in the same box (that is a box-line reduction, not a kite string).
3. List the column pairs the same way.
4. Look for a shared box. Take a row pair and a column pair. If one cell of each lands in the same box and the four cells are all different, you have a kite.
5. Find the target. Take the row of the column's far end and the column of the row's far end. The cell where they cross is the target. If it still has the digit, remove it.

The shape looks like a kite on the grid: two long strings running out of one box at a right angle, and the target sitting in the corner that closes the rectangle.

2-String Kite vs skyscraper

Both patterns join two strong links with one weak link on a single digit. A skyscraper uses two parallel links (two rows or two columns) whose ends share a line. The kite uses one row and one column whose ends share a box. The logic is the same, which is why both count as turbot fish, and both are the shortest possible X-Chains.

The practical difference is where you look. Skyscrapers show up when you compare rows with rows. Kites show up only when you compare rows with columns, so a solver who only checks parallel lines will miss them.

Related patterns

• Skyscraper: two parallel strong links on one digit.
• Empty Rectangle: swaps one string for a box where the digit is confined to a cross.
• X-Chain: the general form, with as many strong links as you need.
• Pointing pairs: the box-and-line interaction you should rule out first.

For the full order of techniques, see our list of sudoku techniques in learning order and the overview of advanced sudoku strategies.