2-String Kite

Hard

A conjugate pair in a row and one in a column intersect in a box; cells seeing both free ends can have the digit eliminated.

How It Works

For a digit, a conjugate pair exists in one row and another in one column. If one end of each pair is in the same box, the two free ends form a virtual conjugate pair. Any cell seeing both free ends can have the digit eliminated.

Example

1	2	369	158	4	3	1	8	6
27	9	1	579	8	4	2	37	5
3	6	259	138	469	5	7	4	9
2	378	4	256	137	1	3	9	5
6	259	378	4	289	5	1	7	3
47	3	256	37	145	8	5	6	8
8	469	5	248	367	9	4	8	6
149	278	6	159	248	6	7	5	9
356	148	279	146	359	7	8	3	5

Key cells of the techniqueCells where elimination is appliedCandidate to be placedEliminated candidate (crossed out)

Digit 7: Row 3 conjugate at C1,C8; Column 5 conjugate at R3,R9. The ends R3C1 and R3C5 share Box. Free ends: R3C8 and R9C5 → Eliminate 7 from cells seeing both.

Practice with a Real Puzzle

This 9×9 puzzle is solver-verified to require this technique on its solution path.

Medium26 givens

1	2	369	158	4	3	1	8	6
27	9	1	579	8	4	2	37	5
3	6	259	138	469	5	7	4	9
2	378	4	256	137	1	3	9	5
6	259	378	4	289	5	1	7	3
47	3	256	37	145	8	5	6	8
8	469	5	248	367	9	4	8	6
149	278	6	159	248	6	7	5	9
356	148	279	146	359	7	8	3	5

1	2	369	158	4	3	1	8	6
27	9	1	579	8	4	2	37	5
3	6	259	138	469	5	7	4	9
2	378	4	256	137	1	3	9	5
6	259	378	4	289	5	1	7	3
47	3	256	37	145	8	5	6	8
8	469	5	248	367	9	4	8	6
149	278	6	159	248	6	7	5	9
356	148	279	146	359	7	8	3	5

1	2	369	158	4	3	1	8	6
27	9	1	579	8	4	2	37	5
3	6	259	138	469	5	7	4	9
2	378	4	256	137	1	3	9	5
6	259	378	4	289	5	1	7	3
47	3	256	37	145	8	5	6	8
8	469	5	248	367	9	4	8	6
149	278	6	159	248	6	7	5	9
356	148	279	146	359	7	8	3	5