My experience with sudoku is only 2 weeks old. Here is an example of this technique.

The candidates of the unknown cells are:

- Code: Select all
`*-----------------------------------------------------------*`

| 9 478 478 | 5 148 17 | 3 6 2 |

| 2 5 3 | 9 46 67 | 8 1 47 |

| 6 478 1 | 2 48 3 | 9 5 47 |

|-------------------+-------------------+-------------------|

| 47 6 9 | 17 3 2 | 14 8 5 |

| 1 247 2457 | 6 57 8 | 24 3 9 |

| 3 28 258 | 4 9 15 | 12 7 6 |

|-------------------+-------------------+-------------------|

| 5 3 27 | 17 127 4 | 6 9 8 |

| 8 9 26 | 3 256 56 | 7 4 1 |

| 47 1 467 | 8 67 9 | 5 2 3 |

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

Applying this technique, I am able to identify 2 open chains of sudo "7". Sudo "7" means that we are propagating with the candidate "7" along the chain links.

Chain 1: (9,1)(4,1)(4,4)(7,4), these are all conjugate links, ie.

when (9,1)=7, (4,1)<>7, (4,4)=7 and (7,4)<>7, or

when (9,1)<>7, (4,1)=7, (4,4)<>7 and (7,4)=7

Either way, the open ends of the chain (9,1) & (7,4) has a conjugate relationship; therefore it is also a conjugate link.

Chain 2: (9,1)(4,1)(4,4)(5,5), these are all conjugate links, ie.

when (9,1)=7, (4,1)<>7, (4,4)=7, (5,5)<>7, or

when (9,1)<>7, (4,1)=7, (4,4)<>7, (5,5)=7

Either way, the open ends of the chain (9,1) & (4,5) has a conjugate relationship; therefore it is also a conjugate link.

In the conjugate link, one of the 2 cells must hold a "7". Any other possibilities of "7" that lie on the intersection (connected by a row, column or box) of this conjugate link must be false and can be safely excluded.

With chain 1, (7,3) lies on the intersection of the chain link (9,1)(7,4). Therefore, (7,3) must not be "7" because either (9,1) or (7,4) must be "7". It follows that (7,3) must be "2".

With chain 2, (9,5) lies on the intersection of the chain link (9,1)(5,5). Therefore, (9,5) must not be "7" because either(9,1) or (5,5) must be "7". It follows that (9,5) must be "6".

From here, I would like to introduce the idea of like link. Contrary to conjugate link, the 2 cells in a like link has a like relationship where both cells must be x or both cells must not be x.

In this grid, one more open chain of sudo "7", can be identified with a like link. Although no elimination of "7" can be resulted from this chain, it is listed below for observation purposes:

Chain 3: (9,1)(4,1)(4,4)(1,6)(2,6)(2,9)(3,9), where all of links are conjugate links except for (4,4)(1,6) which is a like link, ie.

when (9,1)=7, (4,1)<>7, (4,4)=7, (1,6)=7, (2,6)<>7, (2,9)=7, (3,9)<>7, or

when (9,1)<>7, (4,1)=7, (4,4)<>7, (1,6)<>7, (2,6)=7, (2,9)<>7, (3,9)=7.

Either way, the open ends of the chain (9,1)(3,9) has a conjugate relationship; therefore it is also a conjugate link. From here, any possibilities of "7" that lie on the intersection of this conjugate link must be a false and can be safely excluded.

Without this like link, it is impossible to form the conjugate link (9,1)(2,9) at the open ends of the chain. Like link is not easy to spot. However, the location of its 2 cells can be anywhere in the 9x9 grid.

Cheers

George