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leocar
Joined: 04 Mar 2010 Posts: 12
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Posted: Thu Jun 03, 2010 9:25 am Post subject: Difficult puzzle |
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Hi, I came across this puzzle but got stuck very early. Can someone please help me with the next step as I am at a loss. Thank you.
Leo
Code: |
+----------------+-------------+----------------+
| 7 48 9 | 1 2 6 | 48 5 3 |
| 1 68 5 | 47 3 47 | 2689 2689 689 |
| 46 2 3 | 8 9 5 | 467 467 1 |
+----------------+-------------+----------------+
| 356 9 167 | 456 8 134 | 467 467 2 |
| 568 1567 4 | 2 56 19 | 3 6789 5689 |
| 2 356 68 | 4569 7 349 | 4689 1 5689 |
+----------------+-------------+----------------+
| 4689 467 678 | 679 1 2 | 5 3 689 |
| 3689 367 2678 | 5679 56 789 | 1 2689 4 |
| 5689 156 1268 | 3 4 89 | 2689 2689 7 |
+----------------+-------------+----------------+
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keith
Joined: 19 Sep 2005 Posts: 3355 Location: near Detroit, Michigan, USA
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Posted: Thu Jun 03, 2010 12:15 pm Post subject: |
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The next step is a hidden pair in B4. After that, I don't know.
Keith |
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Steve R
Joined: 24 Oct 2005 Posts: 289 Location: Birmingham, England
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Posted: Thu Jun 03, 2010 1:54 pm Post subject: |
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You can place 3 in r8c2 using the contradiction:
r8c2 ≠3 => r8c1 = 3 => r4c1 ≠ 3 => r4c6 = 3 => r4c3 =1 => r5c2 =7 => r9c2 = 1 => r6c2 =5 => r8c2 = 3.
This gives
Code: | +---------------------------------------------+
| 7 48 9 | 1 2 6 | 48 5 3 |
| 1 68 5 | 47 3 47 | 2689 2689 689 |
| 46 2 3 | 8 9 5 | 467 467 1 |
-----------------------------------------------
| 3 9 17 | 5 8 14 | 467 467 2 |
| 568 17 4 | 2 6 19 | 3 789 589 |
| 2 56 68 | 49 7 3 | 489 1 589 |
-----------------------------------------------
| 4689 467 678 | 679 1 2 | 5 3 689 |
| 689 3 2678 | 5679 5 789 | 1 2689 4 |
| 5689 156 1268 | 3 4 89 | 2689 2689 7 |
+---------------------------------------------+ |
There are now conjugates with respect to 6 in b1 and c9. As they line up in r2, 6 can be eliminated from r7c1. It may also be eliminated from r8c1 using the contradiction
r8c1 = 6 => r8c4 ≠ 6 => r7c4 = 6 => r7c9 ≠ 6 => r2c9 = 6 => r2c2 = 8 => r3c1 = 6
We now have
Code: | +-------------------------------------------+
| 7 48 9 | 1 2 6 | 48 5 3 |
| 1 68 5 | 47 3 47 | 2689 2689 689 |
| 46 2 3 | 8 9 5 | 467 467 1 |
---------------------------------------------
| 3 9 17 | 5 8 14 | 467 467 2 |
| 58 17 4 | 2 6 19 | 3 789 589 |
| 2 56 68 | 49 7 3 | 489 1 589 |
---------------------------------------------
| 489 467 678 | 679 1 2 | 5 3 689 |
| 89 3 2678 | 679 5 789 | 1 2689 4 |
| 5689 156 1268 | 3 4 89 | 2689 2689 7 |
+-------------------------------------------+ |
when 4 can be placed in r7c1 using the contradiction
r7c1 ≠ 4 => r7c2 = 4 => r5c2 = 7 => r9c2 = 1 => r9c1 = 5 => r3c1 = 6 => r7c1 = 4.
The rest is intermediate rather than easy but you don’t need any more chains unless you wish to use them.
Steve |
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