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Paladin
Joined: 10 Feb 2006
Posts: 15
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 Posted: Sun Apr 23, 2006 10:11 pm Post subject: Way Beyond Me! |
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The puzzle set forth below came from this address:
http://www.intosudoku.com/viewpuzzle.php?puzzle=.8.....7.4..8.7..2..75.19..2.......6.7.....1.9.......3..97.62..5..3.8..7.6.....4.
Although the puzzle is rated “difficult”, I suspect it may be taken from the “Nightmare” puzzles that appear at sudocue.com. I was only able to solve four cells (r2c2 = 9; r3c8 = 8; r3c9 = 4; r9c1 = 7). I was able to determine, however, that if r3c5 is set at value 2, the entire puzzle collapses. Since my solution was based upon “trial and error”, I wonder if someone could supply a “logical” path for the solution to this puzzle.
The first grid is the original puzzle; the second grid contains my four answers and a simplified grid.
| Code: | +--------------------------------------------+
| . 8 . | . . . | . 7 . |
| | | |
| 4 . . | 8 . 7 | . . 2 |
| | | |
| . . 7 | 5 . 1 | 9 . . |
+--------------+---------------+-------------+
| 2 . . | . . . | . . 6 |
| | | |
| . 7 . | . . . | . 1 . |
| | | |
| 9 . . | . . . | . . 3 |
+--------------+---------------+-------------+
| . . 9 | 7 . 6 | 2 . . |
| | | |
| 5 . . | 3 . 8 | . . 7 |
| | | |
| . 6 . | . . . | . 4 . |
+--------------------------------------------+
+-------------------+---------------------+-------------------+
| 136 8 12356 | 2469 2369 2349 | 1356 7 15 |
| | | |
| 4 9 1356 | 8 36 7 | 1356 356 2 |
| | | |
| 36 23 7 | 5 236 1 | 9 8 4 |
+-------------------+---------------------+-------------------+
| 2 1345 1348 | 149 135789 3459 | 4578 59 6 |
| | | |
| 368 7 3468 | 2469 235689 23459 | 458 1 589 |
| | | |
| 9 145 1468 | 1246 125678 245 | 4578 25 3 |
+-------------------+---------------------+-------------------+
| 138 134 9 | 7 145 6 | 2 35 158 |
| | | |
| 5 124 124 | 3 1249 8 | 16 69 7 |
| | | |
| 7 6 1238 | 129 1259 259 | 1358 4 1589 |
+-------------------+---------------------+-------------------+ |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Apr 23, 2006 11:04 pm Post subject: |
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Paladin,
You are certainly correct. My software says it needs multiple chains to resolve, but I see that r3c5 - <2> breaks it wide open.
Keith |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Mon Apr 24, 2006 2:10 pm Post subject: |
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| Code: | 136 8 12356 | 2469 2369 2349 | 1356 7 15
4 9 1356 | 8 36 7 | 1356 356 2
36 23 7 | 5 236 1 | 9 8 4
-------------------------------------------------------------
2 1345 1348 | 149 135789 3459 | 4578 59 6
368 7 3468 | 2469 235689 23459 | 458 1 589
9 145 1468 | 146 15678 45 | 4578 2 3
-------------------------------------------------------------
138 134 9 | 7 145 6 | 2 35 158
5 124 124 | 3 1249 8 | 16 69 7
7 6 1238 | 129 1259 259 | 1358 4 1589
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Starting with this grid the puzzle can be solved by the following long chain:
r8c8=6 => [r9c9=9 => (r5c9<>9), r8c5=9 (=> r15c5<>9)] => r8c7=1 => r8c7=1 => r1c9=1 =>
=> pair 36 in r13c1 => (r5c1<>36) r5c1=8 (=> r5c5<>8) => r5c9=5 (=> r5c5<>5)
Then you have both a triple 236 in r123c5 and candidates 236 in r5c5 left
=> r8c8<>6 => r8c7=6 |
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