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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Tue Dec 23, 2008 12:06 am Post subject: Set G Puzzle 67 |
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| 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 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Tue Dec 23, 2008 1:23 am Post subject: |
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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  |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Dec 23, 2008 4:48 am Post subject: |
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| 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
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| Posted: Tue Dec 23, 2008 7:37 am Post subject: |
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| 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
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| Posted: Tue Dec 23, 2008 9:07 am Post subject: |
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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
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| Posted: Tue Dec 23, 2008 1:15 pm Post subject: |
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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: 3854
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| Posted: Tue Dec 23, 2008 5:58 pm Post subject: |
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| 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 ...
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Asellus: You had fun with this one, didn't you!  |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Tue Dec 23, 2008 6:22 pm Post subject: |
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| Quote: | | Craig, you might want to verify the second ER on <3>. |
I Erred with my Er - and got lucky. |
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