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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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 Posted: Sat Jan 28, 2012 10:57 pm Post subject: Pattern Game 1/27/12 by dobrichev |
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by dobrichev » Fri Jan 27, 2012 ED=6.0
| Code: | *-----------*
|.92|...|..4|
|7.4|...|...|
|56.|1..|...|
|---+---+---|
|..1|.8.|...|
|...|9.6|...|
|...|53.|6..|
|---+---+---|
|...|..4|.62|
|...|...|1.3|
|8..|...|59.|
*-----------* |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jan 29, 2012 2:47 am Post subject: |
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| I was at a brick wall until I spotted a quad in c8 which had eluded me. An XYZ-Wing (237); r4c7<>7 reduced the grid to a BUG+3. The three BUG killers were 3-7-9. The 37 formed a pseudo cell which forced a 9 in the same row as the killer 9; r3c9<>9. |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Sun Jan 29, 2012 11:24 am Post subject: |
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| Code: | +----------+-----------------+--------------+
| 1 9 2 | 68 (67) 378 | 37 5 4 |
| 7 8 4 | 23 2(5) 3(59) | 39 1 6 |
| 5 6 3 | 1 4 -7(9) | 279 278 89 |
+----------+-----------------+--------------+
| 6 35 1 | 4 8 27 | 279 237 59 |
| 2 35 8 | 9 17 6 | 4 37 15 |
| 4 7 9 | 5 3 12 | 6 28 18 |
+----------+-----------------+--------------+
| 3 1 5 | 7 9 4 | 8 6 2 |
| 9 2 7 | 68 (56) 58 | 1 4 3 |
| 8 4 6 | 23 12 13 | 5 9 7 |
+----------+-----------------+--------------+
9r3c6=(9-5)r2c6=5r2c5-(5=6)r8c5-(6=7)r1c5 => -7r3c6 |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Sun Jan 29, 2012 11:50 am Post subject: |
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| Code: | *--------------------------------------------------*
| 1 9 2 | 68 67 378 | 37 5 4 |
| 7 8 4 |d23 25 359 |c39 1 6 |
| 5 6 3 | 1 4 79 | 279 278 b89 |
|----------------+----------------+----------------|
| 6 35 1 | 4 8 27 | 279 237 59 |
| 2 35 8 | 9 17 6 | 4 37 15 |
| 4 7 9 | 5 3 2-1 | 6 28 a18 |
|----------------+----------------+----------------|
| 3 1 5 | 7 9 4 | 8 6 2 |
| 9 2 7 | 68 56 58 | 1 4 3 |
| 8 4 6 |e23 12 f13 | 5 9 7 |
*--------------------------------------------------*
xy chain
(1=8)r6c9-(8=9)r3c9-(9=3)r2c7-(3=2)r2c4-(2=3)r9c4-(3=1)r9c6 => r6c6<>1 |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Jan 29, 2012 4:22 pm Post subject: |
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A busy puzzle.
| Code: | +-----------------------+
| . 9 2 | . . . | . . 4 |
| 7 . 4 | . . . | . . . |
| 5 6 . | 1 . . | . . . |
|-------+-------+-------|
| . . 1 | . 8 . | . . . |
| . . . | 9 . 6 | . . . |
| . . . | 5 3 . | 6 . . |
|-------+-------+-------|
| . . . | . . 4 | . 6 2 |
| . . . | . . . | 1 . 3 |
| 8 . . | . . . | 5 9 . |
+-----------------------+
c8b3 Locked Candidate 1 <> 1 r56c8
r7 b7 Locked Candidate 1 <> 1 r7c5
r8 b7 Locked Candidate 1 <> 2 r8c456
c8b3 Locked Candidate 1 <> 5 r45c8
c8 Naked Quad <> 2378 r12c8
r3 b3 Locked Candidate 1 <> 8 r3c36
c4 Naked Pair <> 23 r1c4
c6b5 Locked Candidate 1 <> 2 r239c6
c7b3 Locked Candidate 1 <> 3 r4c7
r2 b2 Locked Candidate 1 <> 2 r2c7
<23+7> XYZ-Wing r4c8/r4c6+r5c8 <> 7 r4c7
c8b6 Locked Candidate 1 <> 7 r3c8
c8 Naked Pair <> 28 r4c8
<27+9> XY-Wing r4c6/r3c6+r4c7 <> 9 r3c7
+-----------------------------------------------------+
| 1 9 2 | 68 67 378 | 37 5 4 |
| 7 8 4 | 23 25 359 | 39 1 6 |
| 5 6 3 | 1 4 79 | 27 28 89 |
|-----------------+-----------------+-----------------|
| 6 35 1 | 4 8 27 | 29 37 59 |
| 2 35 8 | 9 17 6 | 4 37 15 |
| 4 7 9 | 5 3 12 | 6 28 18 |
|-----------------+-----------------+-----------------|
| 3 1 5 | 7 9 4 | 8 6 2 |
| 9 2 7 | 68 56 58 | 1 4 3 |
| 8 4 6 | 23 12 13 | 5 9 7 |
+-----------------------------------------------------+
# 32 eliminations remain
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If r1c6<>7 and r2c6<>3, then a BUG remains. This is unacceptable. So, at least one of r1c6=7 and/or r2c6=3 must be true. Either way, r1c6<>3 follows. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sun Jan 29, 2012 7:22 pm Post subject: |
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Initially I found a couple of xy-chains such as:
(9=7)r3c6-(7=6=5=2)r182c5-(2=3=9)r2c47; r2c6<>9
But then I tried the brute force approach; a BUG+6
BUG+6 => r1c7=3
(7)r1c6-(7=3)r1c7
(3)r2c6-r1c6=(3)r1c7
(7)r3c78-(7=3)r1c7
(7)r4c78-(7=2=1=3)r469c6-r1c6=(3)r1c7
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Jan 29, 2012 8:07 pm Post subject: |
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| tlanglet wrote: | I tried the brute force approach; a BUG+6
BUG+6 => r1c7=3
(7)r1c6-(7=3)r1c7
(3)r2c6-r1c6=(3)r1c7
(7)r3c78-(7=3)r1c7
(7)r4c78-(7=2=1=3)r469c6-r1c6=(3)r1c7
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| Code: | after basics
+-----------------------------------------------------+
| 1 9 2 | 68 67 378 | 37 5 4 |
| 7 8 4 | 23 25 359 | 39 1 6 |
| 5 6 3 | 1 4 79 | 279 278 89 |
|-----------------+-----------------+-----------------|
| 6 35 1 | 4 8 27 | 279 237 59 |
| 2 35 8 | 9 17 6 | 4 37 15 |
| 4 7 9 | 5 3 12 | 6 28 18 |
|-----------------+-----------------+-----------------|
| 3 1 5 | 7 9 4 | 8 6 2 |
| 9 2 7 | 68 56 58 | 1 4 3 |
| 8 4 6 | 23 12 13 | 5 9 7 |
+-----------------------------------------------------+
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Hmmm!!! If you eliminate your candidates -- r2c6<>3 and r1c6,r34c78<>7 -- then you have what appears to be a BUG because all of the unsolved cells are bivalues. However, there is a second constraint that's also necessary -- no Singles present when reduced to bivalue cells.
| Code: | Ted's grid after: r2c6<>3 and r1c6,r34c78<>7
+-----------------------------------------------------+
| 1 9 2 | 68 67 38 | 37 5 4 |
| 7 8 4 | 23 25 59 | 39 1 6 |
| 5 6 3 | 1 4 79 | 29 28 89 |
|-----------------+-----------------+-----------------|
| 6 35 1 | 4 8 27 | 29 23 59 |
| 2 35 8 | 9 17 6 | 4 37 15 |
| 4 7 9 | 5 3 12 | 6 28 18 |
|-----------------+-----------------+-----------------|
| 3 1 5 | 7 9 4 | 8 6 2 |
| 9 2 7 | 68 56 58 | 1 4 3 |
| 8 4 6 | 23 12 13 | 5 9 7 |
+-----------------------------------------------------+
Hidden Single: r1c7=7 in [b3]
Hidden Single: r5c8=7 in [b6]
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jan 29, 2012 8:38 pm Post subject: |
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| Quote: | | If r1c6<>7 and r2c6<>3, then a BUG remains. This is unacceptable. So, at least one of r1c6=7 and/or r2c6=3 must be true. Either way, r1c6<>3 follows. |
Danny, same result, but, alternatively, the 37 is a pseudo cell that is part of a 1237 quad in c6; r3c6<>7. |
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Clement
Joined: 24 Apr 2006
Posts: 1113
Location: Dar es Salaam Tanzania
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| Posted: Mon Jan 30, 2012 11:49 pm Post subject: Pattern Game 1/27/12 by dobrichev |
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The xyz-Wing 237 mentioned by Marty ealier opens an XY-Wing 279 pivoted in r4c6; r3c7<>9 reduces the Grid to BUG+2. Either r1c6=7 or r2c6=3.
If r1c6=7; r2c7=9
If r2c6=3; r2c7=9;r2c7<>3. |
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