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

| 1 b579 29 | 28 259 6 | 4 379 3578 |

|a45 b459 8 | 3 159 7 | 6 2 a15 |

| 27 6 3 | 248 1259 14 | 59 179 1578 |

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

| 45 145 15 | 7 3 2 | 8 6 9 |

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

| 9 2 6 | 5 18 18 | 7 34 34 |

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

| 267 b1579 29 | 24 67 45 | 3 8 457-1 |

| 367 8 15 | 9 67 345 | 2 147 1457 |

| 23 b57 4 | 1 28 38 | 59 79 6 |

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

Here is a slightly more instructive example from today's puzzle.

ALS XZ Rule: X = 4, Z = 1: (1=4) r2c19 - (4=1) r1279c2 => - 1 r7c9; stte

The way this works is as follows : The first ALS has two cells marked a in the diagram. They happen to be both bi-value cells but they don't have to be.

Between them they contain 3 digits 145. Now suppose 1 in r2c9 was false. The two a cells would become a naked pair and would have to contain just 4 and 5 - in particular r2c1 would be 4.

Now look at the second ALS - this has 4 cells marked b and between them they contain 5 digits 14579.

Now if r2c1 is 4, as we have supposed, the 4 in r2c2 would be false. Since this is the only 4 in the b cells they would be reduced to a naked quad with 4 digits 1579. Since r7c2 has the only 1 in the second ALS, it would have to be True there.

So you can eliminate 1 from r7c1 and the puzzle solves with singles from there.

The important thing to understand when forming chains of ALSs is the way the restricted common digit works - in this example it is 4. In general, all of the restricted common digits in the first ALS must see all of the restricted common digits in the next ALS in the chain. In this example there were only 2 ALSs in the chain and one instance of the restricted common digit in each ALS, but more complex chains can be formed, with, say, 3 ALSs and more than one instance of a restricted common digit in some of the ALSs.

Thus endeth the lesson

Here is a link to another good teaching site's ALS section

http://www.sudokuwiki.org/Almost_Locked_SetsBoth sites I've mentioned have good graphical worked examples and are definitely worth studying if you want to learn more.

Leren