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sdq_pete
Joined: 30 Apr 2007
Posts: 119
Location: Rotterdam, NL
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 Posted: Fri Nov 09, 2007 12:20 pm Post subject: Nov 9 VH |
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Well, I shall triumphantly announce the X-moves that solved it for me. I leave it to others to point out the ER's and possible short cuts. They were:
| Code: | XY 149 R8C5
X 1 R27
XY 678 R4C6 |
Peter |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Fri Nov 09, 2007 12:39 pm Post subject: |
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Thank you Pete for letting me show the ER.
There are only two 6's in C4. The bottom 6 lines up with a T shaped hinge in Box 7 (bits of the T are missing). Doesn't matter which is the 6 in C4 - there cannot be a 6 in R6C3.
After that it's a breeze.
| Code: |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . 6 | 6 . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| 6 . 6 | 6 . . | . . . |
| . . 6 | . . . | . . . |
+-------+-------+-------+
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re'born
Joined: 28 Oct 2007
Posts: 80
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| Posted: Fri Nov 09, 2007 3:38 pm Post subject: |
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After singles, locked candidates and one naked pair:
| Code: | .---------------------.---------------------.---------------------.
| 8 5 46 | 3 9 1 | 246 7 246 |
| 146 146 3 | 8 7 2 | 469 5 469 |
| 7 2 9 | 4 6 5 | 8 3 1 |
:---------------------+---------------------+---------------------:
| 9 1467 1467 | 2 158 68 | 456 48 3 |
| 5 46 8 | 7 3 9 | 1 24 246 |
| 2 3 16 | 16 58 4 | 59 89 7 |
:---------------------+---------------------+---------------------:
| 14 147 1457 | 19 2 78 | 3 6 4589 |
| 146 8 12456 | 169 14 3 | 7 249 2459 |
| 3 9 2467 | 5 48 678 | 24 1 248 |
'---------------------'---------------------'---------------------' |
there is a skyscraper that eliminates 6 from r8c4, leaving singles to the end. |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Fri Nov 09, 2007 4:11 pm Post subject: |
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cg,
I found the same ER for digit <6> in Box 7, the ERI in R8C3 can see one
of the strong links on <6> in R6, eliminating <6> in R8C4, and the puzzle is solved, so the ER can be used in both ways (a double ER?)
| Code: |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . 6 | 6 . . | . . . |
+-------+-------+-------+
|er er. | . . . | . . . |
| 6 .eri|-6 . . | . . . |
|er er6 | . . | . . . |
+-------+-------+-------+
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George Woods
Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK
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| Posted: Fri Nov 09, 2007 4:43 pm Post subject: A Rose by any other name |
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| cgordon wrote: | Thank you Pete for letting me show the ER.
There are only two 6's in C4. The bottom 6 lines up with a T shaped hinge in Box 7 (bits of the T are missing). Doesn't matter which is the 6 in C4 - there cannot be a 6 in R6C3.
After that it's a breeze.
| Code: |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . 6 | 6 . . | . . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| 6 . 6 | 6 . . | . . . |
| . . 6 | . . . | . . . |
+-------+-------+-------+
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I did this by looking at the two 16 pairs in boxes 4 and 8 as the arms of an W wing- both operating on box 7 (both 16 cannot be 6 else box 7 would have no 6, so one of them must be 1, hence r6c4 cannot be 1 so must be 6....). Logic is almost identical to your's using the ER! I forget to mention that it is not a pure W Wing - but the logic works in spite of the 16 in r8c4 having a 9 attached! If it is not 6 then the pair of 19s deny a 1 to r6c4 |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Fri Nov 09, 2007 4:59 pm Post subject: |
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Johan: I kinda lost you there. For clarity, I only showed the 6's relevant to the ER - but below are all of them. I'm pretty sure for an ER you need a row or column with only 2 candidates - which line up with a L, T or + shaped hinge in a box and another candidate. Don't see any more of those here. Not yet anyway.
| Code: |
+-------+-------+-------+
| . . 6 | . . . | 6 . 6 |
| 6 6 . | . . . | 6 . 6 |
| . . . | . . . | . . . |
+-------+-------+-------+
| . 6 6 | . . 6 | 6 . . |
| . 6 . | . . . | . . 6 |
| . . 6 | 6 . . | 6 . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| 6 . 6 | 6 . . | . . . |
| . . 6 | . . 6 | . . . |
+-------+-------+-------+
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re'born
Joined: 28 Oct 2007
Posts: 80
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| Posted: Fri Nov 09, 2007 5:59 pm Post subject: |
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| cgordon wrote: | I'm pretty sure for an ER you need a row or column with only 2 candidates - which line up with a L, T or + shaped hinge in a box and another candidate. Don't see any more of those here. Not yet anyway.
| Code: |
+-------+-------+-------+
| . . 6 | . . . | 6 . 6 |
| 6 6 . | . . . | 6 . 6 |
| . . . | . . . | . . . |
+-------+-------+-------+
| . 6 6 | . . 6 | 6 . . |
| . 6 . | . . . | . . 6 |
| . . 6 | 6 . . | 6 . . |
+-------+-------+-------+
| . . . | . . . | . . . |
| 6 . 6 | 6 . . | . . . |
| . . 6 | . . 6 | . . . |
+-------+-------+-------+
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Box 5 also has an ER, which would allow you to eliminate 6 from r6c3. |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Fri Nov 09, 2007 6:28 pm Post subject: |
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| Quote: | | For clarity, I only showed the 6's relevant to the ER - but below are all of them |
cg,
The <6> in R6C7 in your posted grid, was not present in my grid because of the naked [16] pair in R6C34, maybe therefore you missed the strong link on <6> in R6? |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Fri Nov 09, 2007 6:38 pm Post subject: |
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| Quote: | | Box 5 also has an ER, which would allow you to eliminate 6 from r6c3. |
Well spotted Bruce !! (Monty Python). I was going to protest - but there is indeed an L shaped hinge in Box 5 which complements the two 6's in R9. |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Fri Nov 09, 2007 7:00 pm Post subject: |
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| Johan: You are also very correct. I didn't see the naked [16] pair in R6. So there are three ERs with bases of [6] pairs in R6, R9 and C4. In retrospect I think Re'borns skyscraper was the simpler way to go. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Fri Nov 09, 2007 11:15 pm Post subject: |
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I hate to spoil things after all that discussion but... re'born's grid is not fully reduced: there's a {248} Locked Set in R9. Here's the grid after basics:
| Code: | +--------------+------------+------------+
| 8 5 46 | 3 9 1 | 246 7 246 |
| 146 146 3 | 8 7 2 | 469 5 469 |
| 7 2 9 | 4 6 5 | 8 3 1 |
+--------------+------------+------------+
| 9 467 1467 | 2 158 68 | 456 48 3 |
| 5 46 8 | 7 3 9 | 1 2 46 |
| 2 3 16 | 16 58 4 | 59 89 7 |
+--------------+------------+------------+
| 14 147 5 | 19 2 78 | 3 6 489 |
| 146 8 2 | 169 14 3 | 7 49 5 |
| 3 9 67 | 5 48 67 | 24 1 248 |
+--------------+------------+------------+ |
Technically, that Skyscraper in R69 eliminates the <6> at R4C6 as well as that at R8C4. (That doesn't matter, though.)
There is also a Skyscraper in R68 that eliminates the <6> at R9C3 and solves the puzzle.
Peter,
Your X-Wing on <1> isn't required; the two XY Wings alone solve the puzzle.... at least in the grid above. |
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re'born
Joined: 28 Oct 2007
Posts: 80
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| Posted: Sat Nov 10, 2007 9:43 am Post subject: |
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| Asellus wrote: | | I hate to spoil things after all that discussion but... re'born's grid is not fully reduced: there's a {248} Locked Set in R9. |
That was by design. The first time I solved the puzzle, I spotted the naked triple and used it, but in the post mortem realized I could apply the skyscraper much earlier making the naked triple superfluous. That is why I was careful to list exactly what techniques I used before the skyscraper (instead of my usual "after basics"). You'll notice I couldn't apply it before the naked pair. |
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