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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Fri Jan 08, 2010 5:58 pm Post subject: Puzzle 10/01/08 (C) |
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| Code: | +-----------------------+
| 5 . . | . 7 . | . 4 . |
| . 4 . | . . 9 | . . 8 |
| . . 8 | . . . | 9 7 6 |
|-------+-------+-------|
| . . . | 7 . . | . . 5 |
| 1 . . | . 5 . | . 3 . |
| . 5 . | . . 3 | . . . |
|-------+-------+-------|
| . . 1 | . . . | . . 7 |
| 3 . 5 | . 8 . | . 2 1 |
| . 7 4 | 1 . . | 8 9 . |
+-----------------------+
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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: Sat Jan 09, 2010 1:15 pm Post subject: |
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Three moves.
| Quote: | xy-chain: (3=1)r1c7 - (1=5)r2c8 - (5=6)r7c8 - (6=4)r7c6 - (4=1)r3c6 - (1=3)r3c2; r1c2<>2
xy-wing 1-36,
type 1 UR27.
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Ted |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jan 10, 2010 8:52 pm Post subject: |
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| I needed to look at the implications of a potential 27 DP in boxes 46. Every way of killing the DP placed a 3 in r1c7 and that reduced the grid to a BUG+1. |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Sun Jan 10, 2010 10:02 pm Post subject: |
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Two Steps: | Quote: | (3)-r3c5=(3-1)r3c2=(1)r1c2-(1=3)r1c7-(3)r1c4=(3)r7c4
=> r1c4,r7c5<>3
later an xy-wing 168 is needed |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Jan 11, 2010 1:06 am Post subject: |
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| Marty R. wrote: | | I needed to look at the implications of a potential 27 DP in boxes 46. Every way of killing the DP placed a 3 in r1c7 and that reduced the grid to a BUG+1. |
Marty,
I also looked at the UR27, but viewed it as a Type 2 situation that deleted 6 in r5c246. I do not recall why I did not use this move but it was not as fruitful as your analysis of the same conditions.
What I find particularly interesting is that when both your action and the Type 2 action are combined, the UR27 becomes a one stepper 
It is also unusual that one pattern deletes/forces results on more than a single digit.
Ted |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Jan 11, 2010 4:43 am Post subject: |
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| I didn't see anything that I recognized as a Type 2. All four cells had at least three candidates and examining the implications is basically trial and error, except with a pattern as a starting point rather than a guess. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon Jan 11, 2010 7:25 am Post subject: |
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looks like a type 2 to me. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Jan 11, 2010 8:15 am Post subject: |
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There are two UR patterns present in the same cells. I've seen this combination of URs occur several times previously. In this case, a total of five eliminations in [r5].
| Code: | +-----------------------------------------------------------------------+
| 5 136 9 | 368 7 168 | 13 4 2 |
| 7 4 36 | 2 136 9 | 135 15 8 |
| 2 13 8 | 5 134 14 | 9 7 6 |
|-----------------------+-----------------------+-----------------------|
| 49 368 236 | 7 1469 12468 | 126 168 5 |
| 1 68 *27+6 | 4689 5 2468 | *27+6 3 49 |
| 49 5 *27 | 68 16 3 | *27 168 49 |
|-----------------------+-----------------------+-----------------------|
| 8 2 1 | 39 39 46 | 456 56 7 |
| 3 9 5 | 46 8 7 | 46 2 1 |
| 6 7 4 | 1 2 5 | 8 9 3 |
+-----------------------------------------------------------------------+
# 61 eliminations remain
r56c37 <27> UR Type 2 <> 6 r5c246
r56c37 <27> UR Type 4 <> 2 r5c37
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HoDoKu also reports UR Type 3 exists. Boy, is this puzzle fun!
| Code: | Uniqueness Test 3: 2/7 in r56c37 => r5c46<>68 -- < 68 > pair
Uniqueness Test 3: 2/7 in r56c37 => r5c6<>468 -- <4689> quad
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I believe this is why it's recommended that you search for a Type 4 after other UR Types in a possible DP.
I'm unaware that the UR forces r1c7=3. However, a gM-Wing completes the puzzle after my UR eliminations. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon Jan 11, 2010 12:47 pm Post subject: |
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| daj95376 wrote: | There are two UR patterns present in the same cells. I've seen this combination of URs occur several times previously. In this case, a total of five eliminations in [r5].
| Code: | +-----------------------------------------------------------------------+
| 5 136 9 | 368 7 168 | 13 4 2 |
| 7 4 36 | 2 136 9 | 135 15 8 |
| 2 13 8 | 5 134 14 | 9 7 6 |
|-----------------------+-----------------------+-----------------------|
| 49 368 236 | 7 1469 12468 | 126 168 5 |
| 1 68 *27+6 | 4689 5 2468 | *27+6 3 49 |
| 49 5 *27 | 68 16 3 | *27 168 49 |
|-----------------------+-----------------------+-----------------------|
| 8 2 1 | 39 39 46 | 456 56 7 |
| 3 9 5 | 46 8 7 | 46 2 1 |
| 6 7 4 | 1 2 5 | 8 9 3 |
+-----------------------------------------------------------------------+
# 61 eliminations remain
r56c37 <27> UR Type 2 <> 6 r5c246
r56c37 <27> UR Type 4 <2> r5c46<>68 -- <68> pair
Uniqueness Test 3: 2/7 in r56c37 => r5c6<>468 -- <4689> quad
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I believe this is why it's recommended that you search for a Type 4 after other UR Types in a possible DP.
I'm unaware that the UR forces r1c7=3. However, a gM-Wing completes the puzzle after my UR eliminations. |
Danny, either r5c3=6 or r5c7=6 to prevent the DP.
(6)r5c3 - (6=3)r2c3 - (3)r2c7 = (3)r1c7,
(6)r5c7 - r8c7 = r8c4 - (6=4)r7c6 - (4=1)r3c6 - (1)r2c5 = ss[(36)r2c35] - (3)r2c7 = (3)r1c7.
Thus, both conditions to prevent the DP force r1c7=3.
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Jan 11, 2010 6:28 pm Post subject: |
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| tlanglet wrote: | Danny, either r5c3=6 or r5c7=6 to prevent the DP.
(6)r5c3 - (6=3)r2c3 - (3)r2c7 = (3)r1c7,
(6)r5c7 - r8c7 = r8c4 - (6=4)r7c6 - (4=1)r3c6 - (1)r2c5 = ss[(36)r2c35] - (3)r2c7 = (3)r1c7.
Thus, both conditions to prevent the DP force r1c7=3.
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Ted: Thanks for the explanation. Since r5c3=6 is in the solution for the puzzle, I'd already verified that it led to r1c7=3. But, for r5c7=6, I kept coming up with chains that performed r1c7<>3. I feel better now about Marty's r1c7=3. Good catch guys!
Regards, Danny |
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