...posted this to figure out what it was...

Edit: [yes i know its a xy-chain.] {also called W-wing}(thanks ronk)

that exsits between two pairs

where one set is locked into a house that has two polar opposite end points that are also bivalves

where the end points are identical to each other and not alinged in the same house.

the elimination acts similar to that of a skyscraper.

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*-----------------------*

|. . .|. . .| . . .|

|X X X|. AB .|. BC .|

|. . BC|. AB .| X X X|

*-----------------------*

OR

- Code: Select all
`|Ab . .| Ab . . | . . . |`

|BC . .| X X X | . . . |

|X X X | BC . . | . . . |

- Code: Select all
`thanks paul for the puzzle!`

.---------------.-------------.----------------.

| 6 18 4 | 3 5 2 | 9 7 18 |

| 9-5 189 2 | 4 7 18@ | 58@ 3 6 |

| 3 7 58@ | 6 9 18@ | 48-5 14-5 2 |

:---------------+-------------+----------------:

| 4 2 9 | 5 3 6 | 1 8 7 |

| 7 5 1 | 2 8 4 | 3 6 9 |

| 8 6 3 | 7 1 9 | 2 45 45 |

:---------------+-------------+----------------:

| 2 48 578 | 1 6 578 | 458 9 3 |

| 1 389 578 | 89 4 3578 | 6 2 58 |

| 59 3489 6 | 89 2 358 | 7 145 1458 |

'---------------'-------------'----------------'

there is two examples of this function at work:

(5=8)R3C3 - (1|8) R3C6 = (1|8)R2C6 - (8=5)R2C7

=> R2C1, R3C78<>5

OR:

(5=8)R3C3 - (1|8)R1C2 = (1|8)R1C9 - (5=8)R2C7

=> R2C1, R3C78<>5