## Help with a 6-star

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### Help with a 6-star

Have gotten it mostly solved but in a bit of a twist now. Would appreciate the next step together with explanation of the rule used to get there.

Current state:

Remaining:

| . 58 58 | . . . | . . . |
| . . . | . 58 . | 18 . 15 |
| . . . | 68 . 568 | 38 . 35 |
|--------------------+------------------+--------------|
| . 378 38 | 78 . . | . . . |
| . . . | 67 . . | 17 . 16 |
| . 378 . | . . 68 | 37 . 36 |
|----------------------+----------------+-------------|
| . . 35 | . 58 358 | . . . |
| . . . | . . . | . . . |
| . 35 . | . . 35 | . . . |

Completed:

| 3 . . | 4 7 1 | 6 2 9 |
| 9 4 6 | 3 . 2 | . 7 . |
| 7 2 1 | . 9 . | . 4 . |
|------------------+-----------------+--------------|
| 6 . . | . 1 9 | 2 5 4 |
| 5 9 2 | . 3 4 | . 8 . |
| 1 . 4 | 5 2 . | . 9 . |
|------------------+-----------------+--------------|
| 4 1 . | 2 . . | 9 6 7 |
| 2 6 9 | 1 4 7 | 5 3 8 |
| 8 . 7 | 9 6 . | 4 1 2 |

Thanks.

P.S. Also any help in making this look prettier in the boxes appreciated as well.
wcfreed

Posts: 2
Joined: 01 January 2006

Regarding formatting, you can type [ code] at the start and [ /code] at the end of your text (remove the space after the opening bracket) and it'll keep your spacing correct. You'll end up with something like this:
Code: Select all
`| . 58  58 | .  .  .   | .  . .  | | . .   .  | .  58 .   | 18 . 15 | | . .   .  | 68 .  568 | 38 . 35 | |----------+-----------+---------| | . 378 38 | 78 .  .   | .  . .  | | . .   .  | 67 .  .   | 17 . 16 | | . 378 .  | .  .  68  | 37 . 36 | |----------+-----------+---------| | . .   35 | .  58 358 | .  . .  | | . .   .  | .  .  .   | .  . .  | | . 35  .  | .  .  35  | .  . .  | Completed: | 3 . . | 4 7 1 | 6 2 9 | | 9 4 6 | 3 . 2 | . 7 . | | 7 2 1 | . 9 . | . 4 . | |-------+-------+-------| | 6 . . | . 1 9 | 2 5 4 | | 5 9 2 | . 3 4 | . 8 . | | 1 . 4 | 5 2 . | . 9 . | |-------+-------+-------| | 4 1 . | 2 . . | 9 6 7 | | 2 6 9 | 1 4 7 | 5 3 8 | | 8 . 7 | 9 6 . | 4 1 2 | `

Regarding next step, if you don't understand the terms I'm using, go here and here to learn the techniques.

You have an XWing on 3s in columns 7 and 9, and can remove the 3 from r6c2.
Then the next step is what I BELIEVE is known as chains:

start with r6c2. If you place a 7 there, then r6c7 must be 3, r3c7 must be 8 and r3c4 must be 6. However, if you put the 8 in r6c2 instead, then r6c6 becomes 6, r5c4 is 7, r4c4 is 8 and r3c4 becomes 6. No matter what value is used in r6c2, the value of r3c4 is always 6. So that's your next placement, which will allow you to solve the rest of the puzzle.
Shazbot

Posts: 220
Joined: 24 September 2005

Thanks for the help, I am just starting to get into the advanced techniques like xwing and forcing chains. I see the xwing fine now, but I am wondering how you determined to start with the particular square to look at the chains, or did you try several until you found one that worked? Also, there are many other squares available from that chain, again did you try them all or was the path you described "obvious" in some way?

Thanks again.
wcfreed

Posts: 2
Joined: 01 January 2006

Here's an alternative, shorter chain that you might find easier to spot:
r3c6=5 => r6c6=6 => r6c9=3 => r3c9=5, which contradicts the original assumption. With 5 eliminated from r3c6, we're left with just a single candidate for the value in Box 2, after which the puzzle is solved easily.

I found the chain with a computer solver but the chain is short enough to be found by humans - search on the forum for some of the advice offered by Jeff with regard to bivalue/bilocation graphs.

PS Note that in the original candidate grid, the 3s in Row 4 all lie in Box 4, which eliminates the 3 from r6c2 without an X-Wing.
rubylips

Posts: 149
Joined: 01 November 2005