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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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 Posted: Fri Aug 10, 2007 2:30 pm Post subject: Alternate VH for 8/10 |
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Since today's VH went too easily, I found another.
After basic elimination, I came to this. Enjoy.
Earl
| Code: |
+--------------+---------+----------------+
| 89 15 1359 | 7 4 18 | 12359 6 1239 |
| 68 145 13456 | 9 2 18 | 1345 45 7 |
| 7 2 149 | 3 6 5 | 149 8 149 |
+--------------+---------+----------------+
| 5 6 8 | 2 7 9 | 34 1 34 |
| 4 9 7 | 6 1 3 | 8 2 5 |
| 1 3 2 | 5 8 4 | 79 79 6 |
+--------------+---------+----------------+
| 2 8 469 | 1 5 7 | 469 3 49 |
| 3 145 145 | 48 9 6 | 12457 457 1248 |
| 69 7 14569 | 48 3 2 | 14569 459 1489 |
+--------------+---------+----------------+
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Play this puzzle online at the Daily Sudoku site |
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Fri Aug 10, 2007 4:02 pm Post subject: |
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| Hey Earl, could there be a mistake somewhere? Simple Sudoku says this puzzle has 6 solutions. |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Fri Aug 10, 2007 4:59 pm Post subject: alternate VH |
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Tracy,
Oops! I must have made a mistake in applying the first basic steps.
I will post the original completely unsolved.
Thanks
Earl |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Sat Aug 11, 2007 12:13 am Post subject: Alernate VH |
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Here is the original puzzle, untouched by my mistakes.
Sorry. Thanks for the Patience.
Earl
| Code: |
+-------+-------+-------+
| . . . | . . . | . 6 . |
| . . . | 9 2 . | . . 7 |
| . 2 . | 3 . 5 | . 8 1 |
+-------+-------+-------+
| 5 . . | 2 . 9 | . 1 . |
| 4 . 7 | . 1 . | 8 . 5 |
| . 3 . | 5 . 4 | . . 6 |
+-------+-------+-------+
| 2 8 . | 1 . 7 | . 3 . |
| 3 . . | . 9 6 | . . . |
| . 7 . | . . . | . . . |
+-------+-------+-------+
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Play this puzzle online at the Daily Sudoku site |
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Sat Aug 11, 2007 1:43 am Post subject: |
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Thanks for posting the corrected puzzle, Earl. I know some people think a puzzle like that is 6 times the fun, but to me it's 6 times the work.
Not as hard as some that you've posted, but fun nonetheless. A little less fun once I realized that the two finned X-wings on 4 that I used were really just part of a swordfish. Kinda burst my bubble.
Did run across this coloring situation, which wasn't technically necessary to solve the puzzle, but it's something that I don't ever remember seeing before.
| Code: |
*-----------------------------------------------------------*
| 89a 15 1359 | 7 4 18 | 2359 6 239 |
| 68 145 1356 | 9 2 18 | 35 45 7 |
| 7 2 49B | 3 6 5 | 49b 8 1 |
|-------------------+-------------------+-------------------|
| 5 6 8 | 2 7 9 | 34 1 34 |
| 4 9 7 | 6 1 3 | 8 2 5 |
| 1 3 2 | 5 8 4 | 79c 79C 6 |
|-------------------+-------------------+-------------------|
| 2 8 469 | 1 5 7 | 469 3 49 |
| 3 145 15 | 48 9 6 | 1257 457 28 |
| 69A 7 1569 | 48 3 2 | 156 459c 89 |
*-----------------------------------------------------------*
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A-a, B-b & C-c mark three separate strongly linked chains. The B-b chain links the A-a & C-c chains (the bridge, as Asellus would call it). If both a & c were true, then neither B-b could be true, so one of A or C must be true. And where do A & C intersect? At r9c8, which is part of the C-c chain. That's the first time that I know of where an exclusion from a coloring chain/chains occurred in a cell that was part of one of the chains. Maybe it's because it wasn't really necessary to include that cell in the chain for the exclusion to occur. Unusual nonetheless. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Aug 11, 2007 11:20 pm Post subject: |
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Tracy,
First, just a point to avoid some confusion...
While your B-b link does "bridge" your other chains together, I only use the term to indentify a weak link that serves as the basis for a Color Wing. Your B-b is a strong link and the logic here is different from that of a Color Wing.
As for your chains...
Normally, simple Coloring is restricted to strong link connections. However, implication logic allows weak links to be included provided they only occur at alternate positions.
Here is a way of writing your combined chain:
R9C1-s*-R1C1-w-R3C3-s*-R3C7-w-R6C7-s*-R6C8
The chain has alternate strong links, marked *, so is valid. (One or both of the "w" positions could be "s" and all is still valid.)
More formally, the chain would be written in Eureka notation as:
[9]R9C8-[9=9]R91C1-[9=9]R3C37-[9=9]R6C78-[9]R9C8; R9C8<>9
Note that if you include R2C1, this is just a 7-cell XY-Chain. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Aug 11, 2007 11:26 pm Post subject: |
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P.S.
This might be a good time to point out that XY-Chains alternate links within bivalue cells and links between bivalue cells. The links within the bivalue cells are always strong links. The links between cells can be either strong or weak. One needn't pay attention to that since the technique assures alternating strong links. |
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Sun Aug 12, 2007 11:08 pm Post subject: |
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| Asellus wrote: | | Normally, simple Coloring is restricted to strong link connections. |
That's true but this is not simple coloring, it is multi-coloring. If all the cells were strongly linked it would be considered one chain. Since they aren't, the linking chain B-b allows the other two to basically function as one chain. My apologies for incorrectly using the bridge term. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Aug 13, 2007 12:07 am Post subject: |
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Ach! This terminology stuff!
I confusingly said "Simple Coloring" when I meant something more like "basic single-digit coloring." My point was only to show that you had constructed a single standard implication chain.
From a "Color Wing" perspective, there are two Color Wing Bridges in your example: a-B and b-c. With two bridges and three chains, it is not so helpful, it seems to me, for folks to try to consider it as a Color Wing since the logic gets more involved. But, a Color Wing type logic exists:
The a-B Bridge means: A and/or b
The b-c Bridge means: B and/or C
The B-b strong link means: B or b
This has a necessary implication: A and/or C
Hence the elimination.
I find it easier to see and follow the implication chain logic.
I don't recommend that folks try using multiple bridges in Color Wings unless they really know what they are doing. |
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Mon Aug 13, 2007 4:15 pm Post subject: |
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| Asellus wrote: | | Ach! This terminology stuff! |
Could not agree more! Hence my confusion with the 'bridge' term. Upon re-reading the link you provided to explain the 'color wing' and looking at your post in the "A Challenge" topic, where you explained your steps to solving that puzzle, I realized from where my confusion came.
| Quote: | | While your B-b link does "bridge" your other chains together, I only use the term to indentify a weak link that serves as the basis for a Color Wing. |
Your 'color wing' can be the same as my multi-coloring. Each involve separate chains of strongly linked cells. Those chains must be connected in some way. There can be three different connections between the cells of the separate chains. Strong links, weak links or no links. If there is no link, then the chains are worthless for exclusions. If the link is strong, then there is only one chain and it is simple coloring. So it must be a weak link that connects them. It seems superfluous to give that weak link a separate name, when there are already terms to describe it. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Aug 13, 2007 7:20 pm Post subject: |
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| TKiel wrote: | | It seems superfluous to give that weak link a separate name, when there are already terms to describe it. |
Well, perhaps yes. But, if superfluousness were the criterion, we'd have to throw out most of the terms in common use. When I first started reading this board, I was excited to see references to "Skyscrapers" and "Kites," among others. "Wow! Great new techniques to learn!" I thought. But, as I figured out what they were, I was disappointed. "Why, those are nothing but simple applications of Coloring or Color Wings! What useless unnecessary terminology." And, maybe it was for me.
People learn by different routes that use different terminology along the way. I don't have a problem with learning synonyms. What I try to do is understand the terminology used by others, even if it seems unnecessary for me, and then try to use it accurately when I attempt to communicate with them. It can be awkward when words such as "Bridge" or "Multi-Coloring" have specific established meanings that aren't inherently obvious in the words themselves.
Every now and then, we step on a communication land mine. But, that's just part of life. |
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TKiel
Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
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| Posted: Mon Aug 13, 2007 9:15 pm Post subject: |
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| Quote: | | Every now and then, we step on a communication land mine. |
Or we trip and fall off a bridge. |
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