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ravel
Joined: 21 Apr 2006
Posts: 536
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 Posted: Tue Apr 15, 2008 1:43 pm Post subject: VH+ by gsf |
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Same pattern, needs a bit more than VH methods, e.g. UR + coloring (or a nice deadly pattern) on a long way.
| Code: | +-------+-------+-------+
| . . . | . . . | . . . |
| . . 4 | 3 . 5 | 8 . . |
| . 2 . | 1 . 6 | . 7 . |
+-------+-------+-------+
| . 4 8 | . . . | 9 5 . |
| . . . | . . . | . . . |
| . 6 1 | . . . | 4 3 . |
+-------+-------+-------+
| . 7 . | 6 . 2 | . 4 . |
| . . 9 | 8 . 1 | 7 . . |
| . . . | . . . | . . . |
+-------+-------+-------+
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>>> play online |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Apr 15, 2008 6:26 pm Post subject: |
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| There was probably stuff there, like potential DPs, W-Wings, and the like, but I couldn't do anything with them. Things started off with an XY-Wing, three ERs, an M-Wing and Type 1 UR. I'm not particularly proud of the way I finished it off. I'm sure Medusa could have solved it, but I used the flightless XYZ-Wing on 457. One of the three cells had to be = 4 and any of the three would result in r1c5 = 4, which solved it. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Apr 15, 2008 8:34 pm Post subject: |
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| It took me 3 steps: that initial XY Wing, then a nice and easy to spot 8-cell DP, and finally a Type 1 UR. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue Apr 15, 2008 8:52 pm Post subject: |
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type 1 UR {1,6} removes 1 and 6 from r5c9
the m-wing on {2,7} removes 2 from r9c9
coloring removes 7 from r6c5
xy-wing {1,8,9} removes 8 from box 1 and 7
xyz-wing removes 6 in r1c8
this all leaves you with this...
| Code: | 8 #35 67 | 247 247 9 | 126 12 #35
67 1 4 | 3 27 5 | 8 269 69
9 2 #35 | 1 8 6 |#35 7 4
------------------------------------------------------------------
23 4 8 | 27 16 37 | 9 5 16
35 9 27 | 45 16 34 | 16 8 27
257 6 1 | 9 25 8 | 4 3 27
------------------------------------------------------------------
1 7 #35 | 6 9 2 |#35 4 8
246 #35 9 | 8 345 1 | 7 26 (35)6
246 8 26 | 457 3457 47 | 126 1269 13569 |
then chose your xy-chain.
Asellus, I would love to see the DP.
edit:
ok, I see it, its on the {3,5} loop the 35 in r8c9 would form the deadly pattern. I marked the cells in the grid above.
Last edited by storm_norm on Tue Apr 15, 2008 9:10 pm; edited 3 times in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Apr 15, 2008 9:05 pm Post subject: |
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| Quote: | | then a nice and easy to spot 8-cell DP |
Easy for you, an oxymoron for me.  |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Wed Apr 16, 2008 6:40 pm Post subject: |
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| Marty R. wrote: |
| Quote: | | ex falso quodlibet |
Q: How many dictionaries does it take to understand a Sudoku forum?
A: Indeterminate |
| Marty R. wrote: | | Quote: | | then a nice and easy to spot 8-cell DP |
Easy for you, an oxymoron for me. |
And now we need a Greek dictionary as well ...  |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Apr 16, 2008 8:13 pm Post subject: |
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Well... perhaps it might become a little less of an oxymoron if one notes the following patterns:
The smallest Deadly Pattern (DP) is 4 matching bivalues cells that are contained in 2 rows, 2 columns and 2 boxes, with 2 of the cells in each of these. In other words, a "Unique Rectangle" (UR).
A DP of 6 matching bivalue cells will be contained in 3 rows, 3 columns and 3 boxes, again with 2 of the cells in each of these. For example:
| Code: | +--------+-------+---------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+--------+-------+---------+
| . . 35 | . . . | 35 . . |
| . . 35 | . . . | . . 35 |
| . . . | . . . | . . . |
+--------+-------+---------+
| . . . | . . . | 35 . 35 |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+--------+-------+---------+ |
And, a DP of 8 matching bivalue cells (in must always be an even number of cells) will occur in 4 rows, 4 column and 4 boxes, each with 2 of the cells... as in ravel's puzzle above.
I'm pretty sure it's not possible to form a DP of matching bivalues containing more than 8 cells.
And, of course, if the bivalue cells don't all have to match, then there are many more possibilities and the DP is better camouflaged. And, if trivalue, etc., cells are involved, then we're definitely talking hard to spot! |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Apr 16, 2008 9:57 pm Post subject: |
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| Code: | +--------+-------+---------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+--------+-------+---------+
| . . 35 | . . . | 35 . . |
| . . 35 | . . . | . . 35 |
| . . . | . . . | . . . |
+--------+-------+---------+
| . . . | . . . | 35 . 35 |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+--------+-------+---------+ |
How would you explain the theory? We know that URs are predicated on the fact that the four corners must lie in two boxes, or one "chute", if you will. So the four cells in the second band are not a DP, but apparently become one with the added two cells in box 9. What is there about that addition that turns it into a DP?
(I have done one or two 6-cell DPs, but all six were in the same chute). |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Apr 17, 2008 9:02 am Post subject: |
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| Marty wrote: | | How would you explain the theory? |
Each unsolved house (row, column, box) in the DP contains two unsolved matching bivalues. The other cells in each of those houses don't "care" which is <3> and which is <5>. So, assuming the pattern has a valid solution, you can xx the order and the solution would still be valid. Thus there would necessarily be two valid solutions, which is not allowed. It is "deadly."
The "colinear" cells in b4 and b9 act as "walls" that prevent the DP from spreading further. (A UR is two such walls staring at each other.) The offset cells in b4 allow the DP to "bend around a corner."
Of course, now I see that 8 cells is not the limit. For 10 cells, one way to do it is:
| Code: | +----------+-------+---------+
| . . . | . . . | . . . |
| 35 . 35 | . . . | . . . |
| . . . | . . . | . . . |
+----------+-------+---------+
| . 35 . | . . . | 35 . . |
| . . 35 | . . . | . . 35 |
| . . . | . . . | . . . |
+----------+-------+---------+
| . . . | . . . | 35 . 35 |
| . . . | . . . | . . . |
| 35 35 . | . . . | . . . |
+----------+-------+---------+ |
(Note that if you consider only the leftmost Tower and placed the two {35} bivalues in b6 together on the same row, you would have your 6-cell identical bivalue DP in a single "chute," as you mentioned.)
I suppose that an 18-cell DP of this sort is possible. Whether or not it would occur in the real world, I don't know.
By the way, if you stick with bivalues but let go of the requirement they all be identical, then you can form DPs by inserting one or more "converting pairs" in the midst of such patterns. For instance:
| Code: | +----------+--------+---------+
| . . . | . . . | . . . |
| 35 . 35 | . . . | . . . |
| . . . | . . . | . . . |
+----------+--------+---------+
| . 35 . | 34 . . | 45 . . |
| . . 35 | 34 . . | . . 45 |
| . . . | . . . | . . . |
+----------+--------+---------+
| . . . | . . . | 45 . 45 |
| . . . | . . . | . . . |
| 35 35 . | . . . | . . . |
+----------+--------+---------+ |
The {34}s in b5 "convert" the {35}s in b4 to the {45}s in b6. Note that we now have 3 DP cells in those two rows, paired into 3 boxes. While a bit trickier to spot than the cases with all identical bivalues, these aren't really so hard to spot either. And, they occur much more often.
In actual experience, I've very rarely encountered a DP of more than 8 cells... at least not ones I've recognized as such or that appear to be of any use in finding a solution. So, you don't really need to worry much about checking for such widespread patterns.
[Edit to clarify the 6-cell Tower DP statement.] |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Apr 17, 2008 3:33 pm Post subject: |
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| As always, thank you for the explanation. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Thu Apr 17, 2008 5:46 pm Post subject: |
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Look here for some nice samples for such deadly patterns with 10 and 12 cells (note that they also can be of type 2).
Nicolas Juillerat mentions there, that the theoretical maximum length is 16. Dont know why, now.
Whats wrong with this one ?
| Code: | +----------+---------+----------+
| . . . | 35 . . | 35 . . |
| 35 . 35 | . . . | . . . |
| . . . | . . 35| . 35 . |
+----------+---------+----------+
| . 35 . | . . . | . 35 . |
| . . 35 | . . . | . . 35 |
| . . . | 35 . 35| . . . |
+----------+---------+----------+
| . . . | . . . | 35 . 35 |
| 34 . . | . 35 . | . . . |
| . 35 . | . 35 . | . . . |
+----------+---------+----------+
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Apr 17, 2008 7:02 pm Post subject: |
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| ravel wrote: | | Whats wrong with this one ? |
Now that you mention it, I can see the reason: Were would the extra <3> or <5> go in b7 to kill the DP? Every possible place is prevented by a naked pair. So, an 18-cell DP cannot be resolved into a valid puzzle. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Fri Apr 18, 2008 7:27 am Post subject: |
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| Yes, of course, we are only talking about single solution puzzles. |
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