A puzzle that's been troubling me...

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A puzzle that's been troubling me...

Postby SocioSudoku » Sat May 06, 2006 10:04 pm

Hey all! Does anyone have any idea how to continue this puzzle? I can't seem to find what to do next.

Clean puzzle:

Code: Select all
. 4 7 | . . 1 | . . 2
5 . . | . . . | 4 . .
9 . . | . 4 . | . 1 5
------+-------+------
. 3 . | . 5 2 | . . .
. . . | 7 . 4 | . . .
. . . | 1 8 . | . 9 .
------+-------+------
2 7 . | . 6 . | . . 1
. . 1 | . . . | . . 4
3 . . | 2 . . | 5 7 .


With pencil marks:

Code: Select all
68    4      7    | 5     39     1     | 389   368    2 
5     1      368  | 3689  2      36789 | 4     368    3789
9     268    2368 | 368   4      3678  | 378   1      5
------------------+--------------------+-------------------
7     3      689  | 69    5      2     | 1     4      68
1     2689   2689 | 7     39     4     | 2368  5      368
4     256    256  | 1     8      36    | 2367  9      367
------------------+--------------------+-------------------
2     7      589  | 4     6      3589  | 389   38     1
68    5689   1    | 389   7      3589  | 3689  2      4
3     689    4    | 2     1      89    | 5     7      689


If the answer is ridiculously obvious, could you give me a hint rather than just tell me what I'm missing?
Last edited by SocioSudoku on Sat May 06, 2006 10:53 pm, edited 2 times in total.
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Re: A puzzle that's been troubling me...

Postby ronk » Sat May 06, 2006 11:24 pm

SocioSudoku wrote:If the answer is ridiculously obvious, could you give me a hint rather than just tell me what I'm missing?

Look for "locked candidate" in column 8 ... but it gets tougher after that.
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Postby Hud » Sun May 07, 2006 1:20 am

It seems like there should be a number in the original puzzle at R3C6. That would make the puzzle symmetrical, and possibly solvable.
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Postby SocioSudoku » Sun May 07, 2006 2:02 am

Sorry, there's definately no original number in r3c6, but I did accidentally add a pencil-marked number at r7c4. It actually is symmetric. I'll edit the original post to reflect this. Thanks!

Got the locked candidate (the six, right?). I'll edit the original so people don't tell me about that particular thing. Thanks for the responses!
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Postby RW » Sun May 07, 2006 8:01 pm

SocioSudoku wrote:With pencil marks:

Code: Select all
68    4      7    | 5     39     1     | 389   368    2 
5     1      368  | 3689  2      36789 | 4     368    3789
9     268    2368 | 368   4      3678  | 378   1      5
------------------+--------------------+-------------------
7     3      689  | 69    5      2     | 1     4      68
1     2689   2689 | 7     39     4     | 2368  5      368
4     256    256  | 1     8      36    | 2367  9      367
------------------+--------------------+-------------------
2     7      589  | 4     6      3589  | 389   38     1
68    5689   1    | 389   7      3589  | 3689  2      4
3     689    4    | 2     1      89    | 5     7      689



Interesting puzzle... Some staring at the pm grid revealed:

If r4c4=6 => r4c3=9
If r4c4=9 => r5c5=3 => r6c6=6 => r6c23=25 => UR in r45c39: r5c3<>68 => r5c3=9

Either way r5c2 and r7c3<>9

That got rid of 2 candidates. I'm sorry I don't have time to solve the whole puzzle right now, but I might get back to it later if someone else doesn't provide a solution first.:)

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Postby ravel » Sun May 07, 2006 8:46 pm

[Edit: made it shorter]
r5c5=3 => r5c9=68
r5c5=3 => r1c5=9 => r2c9=9 => r9c9=68
Since also r4c9=68, this is impossible.

=> r5c5=9, which solves the puzzle.
[Edit 2: corrected typo, thanks to RW]
Last edited by ravel on Tue May 09, 2006 3:32 am, edited 1 time in total.
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Postby tarek » Mon May 08, 2006 9:55 am

I just wanted to highlight this nice elimination from the candidate grid provided:
Code: Select all
*-----------------------------------------------------------------*
| 68     4      7     | 5     ^39     1     | 389    368    2     |
| 5      1     *368   |*3689   2     -36789 | 4     *368    3789  |
| 9      268    2368  | 368    4      3678  | 378    1      5     |
|---------------------+---------------------+---------------------|
| 7      3      689   | 69     5      2     | 1      4      68    |
| 1      2689   2689  | 7      39     4     | 2368   5      368   |
| 4      256    256   | 1      8      36    | 2367   9      367   |
|---------------------+---------------------+---------------------|
| 2      7      589   | 4      6      3589  | 389    38     1     |
| 68     5689   1     | 389    7      3589  | 3689   2      4     |
| 3      689    4     | 2      1      89    | 5      7      689   |
*-----------------------------------------------------------------*
Eliminating 3 from r2c6(ALS-XZ A=3689 in r2c3, r2c8, r2c4 B=39 in r1c5  x=9 z=3, a classic WXYZ wing)

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Postby RW » Mon May 08, 2006 7:22 pm

Interesting Ravel, when I had a second look at the puzzle I almost instantly found a very nice solution, but then I saw that you already posted it... Seems we work in quite the same way.:)
(btw, should be r5c5)

I'd prefer to write it as one trail though:

if r5c5=3 => r45c9=68 => r9c9=9 => r1c7=9 => r1c5=Empty cell

But how you express the solution is not important, as long as the puzzle is neatly solved.

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Postby Myth Jellies » Tue May 09, 2006 8:12 am

Code: Select all
68    4      7    | 5    A39     1     |B389   368    2 
5     1      368  | 3689  2      36789 | 4     368   C3789
9     268    2368 | 368   4      3678  | 378   1      5
------------------+--------------------+-------------------
7     3      689  | 69    5      2     | 1     4     D68 
1     2689   2689 | 7    -39     4     | 2368  5     D368
4     256    256  | 1     8      36    | 2367  9      367 
------------------+--------------------+-------------------
2     7      589  | 4     6      3589  | 389   38     1
68    5689   1    | 389   7      3589  | 3689  2      4
3     689    4    | 2     1      89    | 5     7     D689

AIC/ALS
A3 = A9 - B9 = C9 - D9 = D(3&6&8)
AIC shows A=3 and/or D=3&6&8. Note that if D=3&6&8 then r5c9 must equal 3, therefore cells which see both r1c5 (A) and r5c9 (D) cannot be a 3.
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