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

|.92|.84|1..|

|.31|629|48.|

|4.8|...|.29|

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

|..5|498|2..|

|98.|...|.46|

|124|763|958|

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

|8..|...|..4|

|.19|846|.3.|

|.46|...|8..|

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

7 posts
• Page **1** of **1**

I am relatively new at this and have probably done 200 puzzles of increasing difficulty in the last 2 months. This is the first one I have been stuck on and I don't want to move on until I understand how to solve it. I have been staring at it for the past two days and am getting nothing. Can someone just give me the next logical step? I don't need the whole solution - I just want to understand the next step. Thanks.

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

|.92|.84|1..|

|.31|629|48.|

|4.8|...|.29|

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

|..5|498|2..|

|98.|...|.46|

|124|763|958|

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

|8..|...|..4|

|.19|846|.3.|

|.46|...|8..|

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

- shurd12
**Posts:**21**Joined:**07 March 2006

Assuming your candidate list looks like this:

There is a discontinuous XY Chain:

5-(r3c2)-6-(r4c2)-7-(r5c3)-3-(r5c7)-7-(r8c7)-5

Which allows you to exclude the 5 at r3c7.

From there you can solve it with nothing more complicated than an XY Wing.

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

| 567 9 2 | 35 8 4 | 1 67 357 |

| 57 3 1 | 6 2 9 | 4 8 57 |

| 4 56 8 | 135 1357 157 | 356 2 9 |

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

| 36 67 5 | 4 9 8 | 2 17 137 |

| 9 8 37 | 125 15 125 | 37 4 6 |

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

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

| 8 57 37 | 1259 135 125 | 56 169 4 |

| 25 1 9 | 8 4 6 | 57 3 257 |

| 235 4 6 | 1359 1357 157 | 8 19 125 |

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

There is a discontinuous XY Chain:

5-(r3c2)-6-(r4c2)-7-(r5c3)-3-(r5c7)-7-(r8c7)-5

Which allows you to exclude the 5 at r3c7.

From there you can solve it with nothing more complicated than an XY Wing.

- Sped
**Posts:**126**Joined:**26 March 2006

Thanks for the quick reply. Your candidates match mine except I had a 3 in r7c4. Did I miss something? Anyway, I'm going to have to do some research to understand what an XY chain is and what it means if it is "discontinuous". Anything you can point me to for info on this? Thanks again.

Stan

Stan

- shurd12
**Posts:**21**Joined:**07 March 2006

shurd12 wrote:Thanks for the quick reply. Your candidates match mine except I had a 3 in r7c4. Did I miss something? Anyway, I'm going to have to do some research to understand what an XY chain is and what it means if it is "discontinuous". Anything you can point me to for info on this? Thanks again.

Stan

The 3 in r7c4 was removed by a technique called 'coloring' by Simple Sudoku. I think it's also called a forcing chain, but I'm a bit hazy on the terminology. Basically, there are conjugate relationships on 3s covering much of the board. If you follow them out, you'll see that either r7c4 or r1c4 must be a three. Therefore the 3 at the intersection of row 7 and column 4 can be excluded.

A nice explanation of XY Chains can be found here:

http://forum.enjoysudoku.com/viewtopic.php?t=2966

- Sped
**Posts:**126**Joined:**26 March 2006

OK, I've waded through 30 pages of reference material and am starting to get the magnitude of this whole endeavor. If you don't mind walking me through this, I have a few questions: I see the chain you described, but how and why did you focus on that particular chain. There are many possibilities for similar chains. And, at the end of the chain, why did you stop? It could have continued. And, how does this chain lead you to conclude that the 5 in r3c7 should be eliminated? Thanks in advance.

Stan

Stan

- shurd12
**Posts:**21**Joined:**07 March 2006

When I've exhausted all other techniques, I go looking for XY chains. They're often there, and get easier to pick out with practice.

I guessed at the starting cell for the chain. I'm sure I tried a bunch of possible chains till I found one that worked. I stopped the chain where I did because I was looking for a chain that ended in 5 (the same thing it started with) and in which the starting and ending cells both shared a group with a cell where a 5 might be excluded.

The chain started with a 5 leading into r3c2 and meandered until it hit a cell with a 5 leading out of it.. in this case r8c7. Any cells sharing a group with both the starting cell and the ending cell can have its 5s excluded.. in this case the 5 at r3c7.

The exclusion works because setting r3c7=5 forces values in the cells in the chain which lead to a contradiction. r3c7=5 leads to r8c7=7, r5c7=3, r5c3=7, r4c2=6, and r3c2=5, which is impossible because r3c2 and r3c7 cannot both be 5. Therefore r3c7 cannot be 5.

I guessed at the starting cell for the chain. I'm sure I tried a bunch of possible chains till I found one that worked. I stopped the chain where I did because I was looking for a chain that ended in 5 (the same thing it started with) and in which the starting and ending cells both shared a group with a cell where a 5 might be excluded.

The chain started with a 5 leading into r3c2 and meandered until it hit a cell with a 5 leading out of it.. in this case r8c7. Any cells sharing a group with both the starting cell and the ending cell can have its 5s excluded.. in this case the 5 at r3c7.

The exclusion works because setting r3c7=5 forces values in the cells in the chain which lead to a contradiction. r3c7=5 leads to r8c7=7, r5c7=3, r5c3=7, r4c2=6, and r3c2=5, which is impossible because r3c2 and r3c7 cannot both be 5. Therefore r3c7 cannot be 5.

- Sped
**Posts:**126**Joined:**26 March 2006

7 posts
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