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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Mon Nov 02, 2009 10:54 pm Post subject: Puzzle NR_080 |
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| Code: | NR puzzles can be solved using these techniques:
Basics: Naked/Hidden Single, Naked Pair/Triple, Locked Candidates 1/2
Basics+: Naked Quad, Hidden Pair/Triple/Quad
VH: BUG+1, UR Type 1, X-Wing, XY-Wing
VH+: 2-String Kite, Empty Rectangle, Remote Pair, Skyscraper,
XYZ-Wing, finned X-Wing, UR Type 2/4
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| Code: | +-----------------------+
| 5 8 . | 2 . 4 | . 9 . |
| 7 9 1 | . 8 6 | . . 5 |
| . 2 . | . . . | . 8 . |
|-------+-------+-------|
| 2 . . | . . 1 | . . . |
| . 1 . | . . 9 | . 7 . |
| 4 7 . | 8 2 . | . . 9 |
|-------+-------+-------|
| . . . | . . . | 7 . . |
| 8 . 7 | . 6 . | . 1 . |
| . 3 . | . . 2 | . . 8 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue Nov 03, 2009 7:23 pm Post subject: |
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| Code: | +--------------+-----------------+-----------------+
| 5 8 36 | 2 1 4 | 36 9 7 |
| 7 9 1 | 3 8 6 | 4 2 5 |
| 36 2 4 | 59 59 7 | 36 8 1 |
+--------------+-----------------+-----------------+
| 2 56 9 | 4567 3457 1 | 8 3456 346 |
| 36 1 8 | 456 345 9 | 25 7 2346 |
| 4 7 356 | 8 2 35 | 1 356 9 |
+--------------+-----------------+-----------------+
| 19 456 2 | 1459 3459 8 | 7 3456 346 |
| 8 45 7 | 459 6 35 | 259 1 234 |
| 19 3 56 | 14579 4579 2 | 59 456 8 |
+--------------+-----------------+-----------------+ |
either this chain is true
(3=2)r8c9-(2)r5c9=(2-5)r5c7=(5)r5c45-(5)r6c6=(5)r8c6
which eliminates the 3 in r8c6
or if false, makes the 4 true in r8c9
(4)r8c9-(4=5)r8c2-(5)r9c3=(5)r6c3-(5)r6c6=(5)r8c6
which makes the 3 false in r8c6 again.
so either way the 3 in r8c6 can't exist and solves the puzzle
[(3=2)r8c9-(2)r5c9=(2-5)r5c7=(5)r5c45-(5)r6c6=(5)r8c6] = (4)r8c9-(4=5)r8c2-(5)r9c3=(5)r6c3-(5)r6c6=(5)r8c6; r8c6 <> 3 |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Nov 03, 2009 8:08 pm Post subject: |
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Norm: Your solution appears to be equivalent to a network based on the three candidates in r8c9.
| Code: | (3)r8c9 - (3)r8c6
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(2)r8c9 - r5c9 = (2-5)r5c7 = r5c45 - (5=3)r6c6 - (3)r8c6
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(4)r8c9 - (4=5)r8c2 - r9c3 = r6c3 - (5=3)r6c6 - (3)r8c6
+-----------------------------------------------------------------------+
| 5 8 36 | 2 1 4 | 36 9 7 |
| 7 9 1 | 3 8 6 | 4 2 5 |
| 36 2 4 | 59 59 7 | 36 8 1 |
|-----------------------+-----------------------+-----------------------|
| 2 56 9 | 4567 3457 1 | 8 3456 346 |
| 36 1 8 | 456 345 9 | 25 7 2346 |
| 4 7 356 | 8 2 35 | 1 356 9 |
|-----------------------+-----------------------+-----------------------|
| 19 456 2 | 1459 3459 8 | 7 3456 346 |
| 8 45 7 | 459 6 35 | 259 1 234 |
| 19 3 56 | 14579 4579 2 | 59 456 8 |
+-----------------------------------------------------------------------+
# 66 eliminations remain
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue Nov 03, 2009 10:55 pm Post subject: |
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Danny,
yes, a kraken cell, using a "ttt" like diagram. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Nov 04, 2009 12:37 am Post subject: |
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Normally, I stay away from networks because they are often devastating to a puzzle while providing little insight as logic.
| Code: | network lariat: ???
[(5)r8c6 = r6c6 - r5c45 = (5-2)r5c7 = (2-9)r8c7 = (9)r8c4] = (5)r8c2 - r4c2 = r6c3 - r6c6 = (5)r8c6
+-----------------------------------------------------------------------+
| 5 8 36 | 2 1 4 | 36 9 7 |
| 7 9 1 | 3 8 6 | 4 2 5 |
| 36 2 4 | 59 59 7 | 36 8 1 |
|-----------------------+-----------------------+-----------------------|
| 2 h56 9 | 4567 3457 1 | 8 3456 346 |
| 36 1 8 | c456 c345 9 | d25 7 2346 |
| 4 7 i356 | 8 2 b35j | 1 356 9 |
|-----------------------+-----------------------+-----------------------|
| 19 456 2 | 1459 3459 8 | 7 3456 346 |
| 8 g45 7 | f459 6 a35k | e259 1 234 |
| 19 3 56 | 14579 4579 2 | 59 456 8 |
+-----------------------------------------------------------------------+
# 66 eliminations remain
___________________________________________________________________________________________________
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If r8c6<>5, then r8c7<>5 and r8c4<>5 follow. This forces the (network) strong link (5)r8c6 = (5)r8c2. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Nov 04, 2009 1:39 pm Post subject: |
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ironically,
I like your net better as a diagram
| Code: | (5)r8c2 - (5)r4c2 = (5)r6c3 - (5)r6c6 = (5)r8c6
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(5)r8c4 - (9)r8c4 = (9-2)r8c7 = (2-5)r5c7 = (5)r5c45 - (5)r6c6 = (5)r8c6
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(5)r8c6
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(5)r8c7 - (2)r8c7 = (2-5)r5c7 = (5)r5c45 - (5)r6c6 = (5)r8c6 |
all four of the paths would prove that r8c6 is not a 3, or more obvious that it is a 5.
you can see that if you arrange this correctly into three nodes, you can write it out as a long chain.
| Code: | (5)r8c2 - (5)r4c2 = (5)r6c3 - (5)r6c6 = (5)r8c6
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(5)r8c4 - (9)r8c4 = (9-2)r8c7 = (2-5)r5c7 = (5)r5c45 - (5)r6c6 = (5)r8c6
NODE #1
----------------
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(5)r8c6
NODE #2
----------------
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(5)r8c7 - (2)r8c7 = (2-5)r5c7 = (5)r5c45 - (5)r6c6 = (5)r8c6
NODE #3 |
[NODE #1] = [NODE #2] = [NODE #3]
| Code: | [NODE #1] = [NODE #2] = [NODE #3]
---T---- ----F---- ---T----
if the first and last node is true, this leaves 5 in r8c6, because the first and last nodes eliminate all other 5's in r8.
[NODE #1] = [NODE #2] = [NODE #3]
---F----- = ----T---- = ----F----
if the first and last node is false, then this leaves the middle as being true, placing the 5 in r8c6. |
either way, r8c6 is a 5 and not a 3. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Nov 05, 2009 12:05 am Post subject: |
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| This was a BBDB for me, requiring 10 or so assorted moves ending with an XY-Wing. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Nov 05, 2009 2:03 am Post subject: |
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| Marty R. wrote: | | This was a BBDB for me, requiring 10 or so assorted moves ending with an XY-Wing. |
Marty: Thanks for putting this thread back on solid ground. This puzzle was intended as a BBDB. I'm glad you were successful in dealing with it! I hope others are successful as well. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Thu Nov 05, 2009 1:28 pm Post subject: |
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I just got around to working this puzzle, and after looking at the existing posts, I wonder if I messed up (once again).
I only used three steps:
skyscraper on 5 in r6c36,
w-wing 59 in r3c5 & r9c7 makes 3 deletions, then a pincer transport makes an additional deletion,
another skyscraper 5 in r8c67 completed the puzzle.
Ted  |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Nov 05, 2009 5:55 pm Post subject: |
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| tlanglet wrote: | I just got around to working this puzzle, and after looking at the existing posts, I wonder if I messed up (once again).
I only used three steps:
skyscraper on 5 in r6c36,
w-wing 59 in r3c5 & r9c7 makes 3 deletions, then a pincer transport makes an additional deletion,
another skyscraper 5 in r8c67 completed the puzzle.
Ted |
Since you didn't use NR techniques exclusively, it's possible that you found a shorter solution than the one found by my solver. Since Marty didn't list his steps, it's possible that he encountered the same steps as my solver. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Nov 05, 2009 6:11 pm Post subject: |
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| Quote: | | Since Marty didn't list his steps, it's possible that he encountered the same steps as my solver. |
Danny,
I used these techniques:
Type 4 UR
M-Wing
ER
X-Wing
Skyscraper
Hidden UR
W-Wing
XYZ-Wing
Remote pairs
XY-Wing |
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