sweetbix wrote:Are you saying that you can see the forcing chain as a pattern straight off, the same as Xwing? I have to go through it step by step and this seems like trial and error unlike Xwing where I can see the implications without checking every step.

It doesn't matter if the individual solver -- carbon or silicon based -- can see the pattern instantly or must search for it by her/his/its favorite method. A novice might require trial and error to locate and x-wing and prove to herself that it does what we claim it does.

If you find a xy-type forcing chain by drawing lines between the bivalue cells and labeling them, then looking for a closed loop that has a single repetion of lables, you can make the exclusion not only without using a method anything like trial and error. You don't even have to know *why* this method works. One doesn't have to trace back every step to the basic axioms in order to do calculus.

Here's an example:

- Code: Select all
` 3 . 1 | 9 7 2 | 4 . 8 `

. 9 . | 1 8 . | . 3 7

8 . 7 | 5 3 . | 2 9 1

-------+-------+------

9 2 5 | 4 1 8 | 3 7 6

4 7 3 | 6 2 9 | 8 1 5

6 1 8 | 3 5 7 | 9 2 4

-------+-------+------

1 8 . | 7 9 3 | . . 2

7 3 . | . 4 5 | 1 . 9

. . 9 | . 6 1 | 7 . 3

- Code: Select all
` `

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

| 3 [56] 1 | 9 7 2 | 4 [56] 8 |

| 25 9 24 | 1 8 46 | 56 3 7 |

| 8 46 7 | 5 3 46 | 2 9 1 |

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

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

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

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

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

| 1 8 46 | 7 9 3 | 56 456 2 |

| 7 3 26 | 28 4 5 | 1 [68] 9 |

| 25 [45] 9 | 28 6 1 | 7 [48] 3 |

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

At this point, there are (at least) two clear choices.

[EDIT: typo corrected in bold](I) There is an xy-type forcing chain aka "nice loop" in the 5 cells marked in brackets. Either value of r9c2 forces r1c2=

6.

If you merely searched for all possible xy-type forcing chains they way you'd search for x-wings, your search would be longer and more tedious -- but it would only be different by degree, not by quality. A search is a search.

However, this loop can also be found by drawing labeled edges between all bivalue cells. Then, the search is *shorter* than one for an x-wing, as there are only a few loops to check -- and knowing that at least one edge of the loop must join two cells in either row 7, column 8 or box 9 (because these three groups contain the last tri-value cell) shortens the search to a few seconds. Often, knowing where to look can allow you to do it in your head without drawing lines in simpler puzzles like this one once you get the hang of it. There are those of us who feel this is one of the most enjoyable parts of solving a Sudoku. I no longer think in terms of "all values of cell x lead to cell y=z", but instead just look at the labels. Starting from r9c2 and traveling counterclockwise:

[45]---(4)---[48]---(8)---[68]---(6)---[56]---(5 or 6, your choice)---[56]---(5)---[45]

The consecutive (6)s eliminate a 6 from r1c8.

The consecutive (5)s eliminate a 5 from r1c2.

I no longer have to remember why I can make the exclusion or convert it into a pair of "if this, then this" implication chains.

(II) Look at r7c8 in the candidate diagram. It is the only cell that has three possible values. This means you can solve this in one fell swoop using

BUG avoidance.

[EDIT: switched to more appropriate link]All you need to know is:

-- All but one of the undecided cells have exactly two candidates.

-- One undecided cell has exactly three candidates.

-- Therefore, the candidate that appears exactly three times in the row, column and box containing the tri-value cell must be placed in the tri-value cell.

Now, very little in the way of *search* is required to recognize the existance of a BUG -- nothing that could be labeled as trial and error. But at the same time, I would be hard pressed to be able to follow all of the implications. I just know it works. This pattern is just easier to recognize that an odd shaped 5 cell forcing chain. Different by degree, not quality.