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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Fri May 29, 2009 5:42 pm Post subject: Unchained! |
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Here are lots of chains in this one, but there is another way ...
| Code: | Puzzle: M4844513sh(15)
+-------+-------+-------+
| . . . | 6 . . | 8 . . |
| 4 . 6 | . . . | . 3 . |
| . 2 . | 8 3 1 | . 9 . |
+-------+-------+-------+
| . . 7 | . . . | . . 5 |
| 6 . . | . . . | . . 9 |
| 1 3 2 | . 7 . | . . . |
+-------+-------+-------+
| . . . | . . 9 | . . . |
| . . . | . 4 3 | 7 . . |
| . . . | 5 . . | . . 4 |
+-------+-------+-------+ |
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat May 30, 2009 6:09 pm Post subject: |
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Dang!!! I bet Keith made the <268> DP work, but I (and my solver) had to plow through rocky terrain to make any headway. Fortunately, I recently updated the UR logic in my solver to identify possible URs that it can't currently handle.
1) possible UR [r79c58] => manually finding [r9c5]<>6
2) UR Type 4 [r78c18] => [r7c18]<>8
3) Skyscraper r57\c3 => [r4c5],[r9c6]<>8
4) possible UR [r49c56] => manually finding [r4c6]<>2
5) BUG+3 => manually finding [r7c4]<>2
Personally, I don't have anything against a single-step 6-cell XY-Chain.  |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat May 30, 2009 7:40 pm Post subject: |
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Danny,
This was kind of inspired by one of your recent posts! | Code: | +----------------+----------------+----------------+
| 39 19 13 | 6 5 4 | 8 2 7 |
| 4 8 6 | 27 9 27 | 5 3 1 |
| 7 2 5 | 8 3 1 | 4 9 6 |
+----------------+----------------+----------------+
| 89 49 7 | 34 268 268 | 23 1 5 |
| 6 5 48 | 34 1 28 | 23 7 9 |
| 1 3 2 | 9 7 5 | 6 4 8 |
+----------------+----------------+----------------+
|25-8 47 48 | 27 +268 9 | 1 +56-8 3 |
| 58 6 9 | 1 4 3 | 7 58 2 |
| 238 17 13 | 5 +268 2678 | 9 68 4 |
+----------------+----------------+----------------+ |
There is a Type 4 <58> UR, taking out <8> in R7C18.
But, wait! There is a Type ? <68> UR: Either there is a <2> in B8C5, or R7C8 is <5>. Either way, R7C4 is <7>.
The problem is, an elimination made by the <58> UR hides the <68> UR.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat May 30, 2009 8:54 pm Post subject: |
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| keith wrote: | Danny,
This was kind of inspired by one of your recent posts! | Code: | +----------------+----------------+----------------+
| 39 19 13 | 6 5 4 | 8 2 7 |
| 4 8 6 | 27 9 27 | 5 3 1 |
| 7 2 5 | 8 3 1 | 4 9 6 |
+----------------+----------------+----------------+
| 89 49 7 | 34 268 268 | 23 1 5 |
| 6 5 48 | 34 1 28 | 23 7 9 |
| 1 3 2 | 9 7 5 | 6 4 8 |
+----------------+----------------+----------------+
|25-8 47 48 | 27 +268 9 | 1 +56-8 3 |
| 58 6 9 | 1 4 3 | 7 58 2 |
| 238 17 13 | 5 +268 2678 | 9 68 4 |
+----------------+----------------+----------------+ |
There is a Type 4 <58> UR, taking out <8> in R7C18.
But, wait! There is a Type ? <68> UR: Either there is a <2> in B8C5, or R7C8 is <5>. Either way, R7C4 is <7>.
The problem is, an elimination made by the <58> UR hides the <68> UR.
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Interesting. I can't get the second UR to work cleanly unless I first perform half of the UR Type 4.
(Yes, I know that an eliminated candidate can still be considered present in a UR, but I don't have to like it.)
1) UR Type 4 => [r7c1]<>8 but not [r7c8]<>8
2) UR Type ? => [r7c4]<>2
If I didn't already drink, this would drive me to it.
Congrats Keith!
Danny |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat May 30, 2009 9:14 pm Post subject: |
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Danny,
I was probably lucky with this example, since there are no easy detours.
At the point I posted, these are all true:
| Quote: | There is a Type 4 <58> UR, taking out <8> in R7C18.
But, wait! There is a Type ? <68> UR: Either there is a <2> in B8C5, or R7C8 is <5>. |
The lesson is, consider ALL the UR implications before making any eliminations.
By the way, I have no idea how to write code to solve this puzzle. Perhaps, collect UR implications. If they do not make any progress, keep them and re-test them after making further eliminations?
I'll drink to that!
Keith |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat May 30, 2009 9:58 pm Post subject: |
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| Code: | .------------------.------------------.------------------.
| 39 19 13 | 6 5 4 | 8 2 7 |
| 4 8 6 |*27 9 *27 | 5 3 1 |
| 7 2 5 | 8 3 1 | 4 9 6 |
:------------------+------------------+------------------:
| 89 49 7 | 34 268 268 | 23 1 5 |
| 6 5 *48 | 34 1 *28 | 23 7 9 |
| 1 3 2 | 9 7 5 | 6 4 8 |
:------------------+------------------+------------------:
|U258 47 *48 |-27 *268 9 | 1 U568 3 |
|U58 6 9 | 1 4 3 | 7 U58 2 |
| 238 17 13 | 5 *268 *678 | 9 *68 4 |
'------------------'------------------'------------------' |
Ironically, 
you can perform a strong link on the {5,8} UR to prove r7c4 is 7.
the UR {5,8} says that either the 2 in r7c1 is true or the 6 in r7c8 is true.
UR58[(2)r7c1 = (6)r7c8] - (6=8)r9c8 - (8)r9c56 = (8)r7c5 - (8)r7c3 = (8)r5c3 - (8=2)r5c6 - (2)r2c6 = (2)r2c4; r7c4 <> 2
means r7c4 = 7
-----
edited because for some reason the 2's in r79c5 were missing in my grid. I have now added them.
Last edited by storm_norm on Sat May 30, 2009 11:06 pm; edited 1 time in total |
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