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

| 56 348 a148 | 7 145 4-1 | 36 2 9 |

|b14 2 9 | 3 8 6 | 7 14 5 |

| 56 34 7 | 2 145 9 | 36 14 8 |

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

| 8 6 2 | 9 14 7 | 5 3 14 |

|c14 5 3 |d14 6 8 | 9 7 2 |

| 7 9 14 | 5 2 3 | 8 6 14 |

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

| 3 48 48 | 6 9 2 | 1 5 7 |

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

| 9 7 5 |e14 3 f14 | 2 8 6 |

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

OK this is the X chain position marked in cells abcdef.

Assume r1c3 is not 1.

Then r2c1 must be 1 (only 2 1's in Box 1)

so r5c1 must not be 1

so r5c4 must be 1 (only 2 1's in Row 5)

so r9c4 must not be 1

so r9c6 must be 1 (only 2 1's in Row 9).

Now, if you start by assuming r9c6 is not 1, then you can follow a similar chain of reasoning by following the cells in the reverse order (fedbca), and you'll find that r1c3 must be 1.

The net result of all this is that

at least one of cells a and f (r1c3 and r9c6) must be 1. They might both be 1 but they can't both be not 1.

Since r1c6 sees both of these cells it can't be 1.

The standard notation for this is (1) r1c3 = r2c1 - r5c1 = r5c4 - r9c4 = (1) r9c6 => - 1 r1c6.

This is an example of what is called an alternating inference chain (AIC for short), which is just a set of alternating True/False inferences.

Here are some links to sites that discuss this topic.

http://www.sudokuwiki.org/Alternating_Inference_Chainshttp://hodoku.sourceforge.net/en/tech_chains.php#xHope this helps, Leren