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Set G Puzzle 67

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Dec 23, 2008 12:06 am    Post subject: Set G Puzzle 67 Reply with quote

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

Play this puzzle online at the Daily Sudoku site
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Tue Dec 23, 2008 1:23 am    Post subject: Reply with quote

Found a five step solution; did not try to reduce number of steps. Every step was a different technique.

Quote:

An ER <3>, x-wing <8>, xyz-wing <468>,some version of a m-wing to delete a critical <4> which open up a xy-wing to do the deed.

Ted Smile
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Marty R.



Joined: 12 Feb 2006
Posts: 5061
Location: Rochester, NY, USA

PostPosted: Tue Dec 23, 2008 4:48 am    Post subject: Reply with quote

My first three moves were the same as Ted's, in a different sequence, but the last two were W-Wings.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Tue Dec 23, 2008 7:37 am    Post subject: Reply with quote

Code:
.---------------------.---------------------.---------------------.
| 9      5      6     | 348    1      348   | 7      2      38    |
| 8      1      3     | 9      2      7     | 6      4      5     |
| 2      4      7     | 5      38     6     | 38     1      9     |
:---------------------+---------------------+---------------------:
| 46     3      9     | 1      7      48    | 2      5      468   |
| 1      2      8     | 346    5      349   | 49     7      46    |
| 46     7      5     | 468    4689   2     | 489    3      1     |
:---------------------+---------------------+---------------------:
| 3      6      4     | 2      89     5     | 1      89     7     |
| 57     9      2     | 34678  3468   1     | 345    68     34    |
| 57     8      1     | 3467   3469   349   | 345    69     2     |
'---------------------'---------------------'---------------------'


here is a two step solution.

w-wing (4,6) removes 4 from r6c7.
then that opens up the w-wing (8,9) removes 9 from r6c5
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Tue Dec 23, 2008 9:07 am    Post subject: Reply with quote

Just for the sake of interest, it can be done with 2 Deadly Pattern steps. First, note the 6-cell 46 DP in r46c1|r56c4|r45c9. This creates the strong inference:
DP[(3)r5c4=(8)r4c9|r6c4]
Then we have the short AIC:
(6)r5c4 - DP[(3)r5c4=(8)r4c9|r6c4] - ALS[(8)r6c7=(4)r56c7] - (4=6)r5c9 - (6)r5c4; r5c4<>6

For those not into AICs, the explanation is: If r5c4 is <6> then it's not <3>. So, either or both of r4c9 and r6c4 must be <8> to avoid the DP. Thus, r6c7 is not <8> and the resulting 49 locked pair means r5c9 is <6>. So, r5c4 cannot be <6>.

This brings us to a 34 UR in r15c46:
Code:
+--------+------------------+--------------+
| 9  5 6 |a348    1    a348 | 7    2  #3-8 |
| 8  1 3 | 9      2     7   | 6    4   5   |
| 2  4 7 | 5      38    6   | 38   1   9   |
+--------+------------------+--------------+
| 6  3 9 | 1      7     48  | 2    5  c48  |
| 1  2 8 | 34     5    a349 |b49   7   6   |
| 4  7 5 | 68     689   2   | 89   3   1   |
+--------+------------------+--------------+
| 3  6 4 | 2      89    5   | 1    89  7   |
| 57 9 2 | 34678  3468  1   | 345  68  34  |
| 57 8 1 | 3467   3469  349 | 345  69  2   |
+--------+------------------+--------------+

The 3 UR cells marked "a" form an 89 pseudocell. Along with "b" and "c", this is an XY-Wing that eliminates <8> from r1c9.
(8)r1c9 - 34UR[(8)r1c46=(9)r5c6] - (9=4)r5c7 - (4=8)r4c9 - (8)r1c9; r1c9<>8

This can be done even more concisely by noting that r1c9=3 and/or r5c7=4 destroy the UR, which means: 34UR[(3)r1c9=(4)r5c7]. The AIC is then:
(8)r1c9 - 34UR[(3)r1c9=(4)r5c7] - (4=8)r4c9 - (8)r1c9; r1c9<>8

In descriptive language: If r1c9=3, the UR is destroyed. If r1c9=8, then r5c7 must be <4> to destroy the UR and r4c9 is thus <8>. So r1c9 cannot be <8>.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Tue Dec 23, 2008 1:15 pm    Post subject: Reply with quote

Are we doing the same puzzle? All I did was find an ER on <3> which led to another ER on <3>. This provided a basic elimination of <3> in R3C7.

Two steps (one really).
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Tue Dec 23, 2008 5:58 pm    Post subject: Reply with quote

cgordon wrote:
Are we doing the same puzzle? All I did was find an ER on <3> which led to another ER on <3>. This provided a basic elimination of <3> in R3C7.

Two steps (one really).

Craig: You might want to verify the second ER on <3>.

Asellus wrote:
Just for the sake of interest ...

Asellus: You had fun with this one, didn't you! Very Happy
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Tue Dec 23, 2008 6:22 pm    Post subject: Reply with quote

Quote:
Craig, you might want to verify the second ER on <3>.

I Erred with my Er - and got lucky.
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