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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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 Posted: Tue Sep 01, 2009 9:01 pm Post subject: Vanhegan Insane for Sept 1 |
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Today's Vanhegan Insame was a fun VH+ type of puzzle and also had what I thought was an interesting circumstance. At least I don't remember seeing the event before.
| Code: |
+-------+-------+-------+
| 4 . 3 | 8 . 2 | 5 . 9 |
| . . 2 | . 9 . | 4 . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . 5 4 | 3 8 7 | 9 1 . |
| 6 . . | . . . | . . 5 |
| . 7 1 | 4 6 5 | 3 2 . |
+-------+-------+-------+
| . . . | . . . | . . . |
| . . 9 | . 5 . | 2 . . |
| 7 . 6 | 9 . 8 | 1 . 3 |
+-------+-------+-------+
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Play this puzzle online at the Daily Sudoku site
Enjoy ..........
Ted |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Sep 03, 2009 2:39 am Post subject: |
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at each grid, I didn't see any x-wings, xy-wings or xyz-wings. I didn't see any useful URs either. so this might be a longish path.
| Code: | .---------------------.---------------------.---------------------.
| 4 *16 3 | 8 17 2 | 5 *67 9 |
| 58 AB68 2 | 567 9 36 | 4 367-8 1 |
|15-8 9 7 | 156 134 1346 |A68 368 2 |
:---------------------+---------------------+---------------------:
| 2 5 4 | 3 8 7 | 9 1 6 |
| 6 3 8 | 12 12 9 | 7 4 5 |
| 9 7 1 | 4 6 5 | 3 2 8 |
:---------------------+---------------------+---------------------:
| 138 1248 5 | 1267 12347 1346 | 68 9 47 |
| 138 14-8 9 | 167 5 1346 | 2 B68 47 |
| 7 24 6 | 9 24 8 | 1 5 3 |
'---------------------'---------------------'---------------------' |
the two cool looking w-wings on 68, marked A and B both connected by the strong links on 6 in row 1 eliminate the 8's in r3c1, r2c8, r8c2.
| Code: | .---------------------.---------------------.---------------------.
| 4 16 3 | 8 17 2 | 5 67 9 |
|*58 68 2 | 567 9 36 | 4 367 1 |
|*15 9 7 | 156 *134 *-1346 | 68 368 2 |
:---------------------+---------------------+---------------------:
| 2 5 4 | 3 8 7 | 9 1 6 |
| 6 3 8 | 12 12 9 | 7 4 5 |
| 9 7 1 | 4 6 5 | 3 2 8 |
:---------------------+---------------------+---------------------:
|*138 *1248 5 | 1267 12347 1346 | 68 9 47 |
|*138 14 9 | 167 5 1346 | 2 68 47 |
| 7 *24 6 | 9 *24 8 | 1 5 3 |
'---------------------'---------------------'---------------------' |
(1=5)r3c1 - (5=8)r2c1 - (8)r78c1 = (8-2)r7c2 = (2-4)r9c2 = (4)r9c5 - (4)r3c5 = (4)r3c6; r3c6 <> 1
| Code: | .------------------.------------------.------------------.
| 4 16 3 | 8 17 2 | 5 67 9 |
|*58 *68 2 | 567 9 36 | 4 367 1 |
|*15 9 7 |*156 134 346 | 68 368 2 |
:------------------+------------------+------------------:
| 2 5 4 | 3 8 7 | 9 1 6 |
| 6 3 8 |*12 *12 9 | 7 4 5 |
| 9 7 1 | 4 6 5 | 3 2 8 |
:------------------+------------------+------------------:
| 138 *1-248 5 | 267 2347 1346 | 68 9 47 |
| 138 14 9 | 67 5 1346 | 2 68 47 |
| 7 *24 6 | 9 *24 8 | 1 5 3 |
'------------------'------------------'------------------' |
(2)r9c2 = (2)r9c5 - (2)r5c5 = (2-1)r6c4 = (1)r3c4 - (1=5)r3c1 - (5=8)r2c1 - (8)r2c2 = (8)r7c2; r7c2 <> 2
| Code: | .---------------.---------------.---------------.
| 4 *16 3 | 8 *17 2 | 5 *67 9 |
| 58 *68 2 | 567 9 36 | 4 367 1 |
| 15 9 7 | 156 13 4 | 68 368 2 |
:---------------+---------------+---------------:
| 2 5 4 | 3 8 7 | 9 1 6 |
| 6 3 8 | 12 12 9 | 7 4 5 |
| 9 7 1 | 4 6 5 | 3 2 8 |
:---------------+---------------+---------------:
| 138 *148 5 | 267 *237 136 | 68 9 *4-7 |
| 138 14 9 | 67 5 136 | 2 68 47 |
| 7 2 6 | 9 4 8 | 1 5 3 |
'---------------'---------------'---------------' |
(7)r7c5 = (7)r1c5 - (7=6)r1c2 - (6)r1c2 = (6-8)r2c2 = (8-4)r7c2 = (4)r7c9; r7c9 <> 7 |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Sep 03, 2009 3:56 am Post subject: |
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| I don't see anything labeled Insane on their home page. Where are they found and how do they compare with Fiendish? |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Sep 03, 2009 4:00 am Post subject: |
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As Norm says, there is a neat 68 W-wing pattern that makes at least two eliminations. I looked long and hard, but I could not find a use for the remaining 68 pattern. We are here: | Code: | +-------------------+-------------------+-------------------+
| 4 16c 3 | 8 17b 2 | 5 67 9 |
| 58 68d 2 | 567a 9 36 | 4 367 1 |
| 15 9 7 | 156 134 1346 | 68 368 2 |
+-------------------+-------------------+-------------------+
| 2 5 4 | 3 8 7 | 9 1 6 |
| 6 3 8 | 12 12 9 | 7 4 5 |
| 9 7 1 | 4 6 5 | 3 2 8 |
+-------------------+-------------------+-------------------+
| 138 1248 5 | 1267 12347 1346 | 68 9 47 |
| 138 14 9 | 167 5 1346 | 2 68 47 |
| 7 24 6 | 9 24 8 | 1 5 3 |
+-------------------+-------------------+-------------------+ |
What is this?
In the chain abcd, a is not 6. Try it!
An unnamed three-variable, four cell chain? I don't believe it! (This is the same size as an XY-wing.)
Keith
Last edited by keith on Thu Sep 03, 2009 4:06 am; edited 2 times in total |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Sep 03, 2009 4:02 am Post subject: |
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| Marty R. wrote: | | I don't see anything labeled Insane on their home page. Where are they found and how do they compare with Fiendish? |
Marty,
Ever the Sudoku masochist!  |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Sep 03, 2009 4:24 am Post subject: |
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| Quote: | What is this?
In the chain abcd, a is not 6. Try it!
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what keith saw is the inverse of a xy-wing. the normal xy-wing exploits the strong inferences within the bi-value cells.
Keith's example exploits the weak inferences within the bi-value cells.
(6)r2c2 = (6-1)r1c2 = (1-7)r1c5 = (7)r2c4
in order to see that the chain does in fact have a weak inference node at each cell I am going to add the weakly inferenced 6 on the end in red.
(6)r2c2 = (6-1)r1c2 = (1-7)r1c5 = (7-6)r2c4
| Code: | xy-wing: (A=B) - (B=C) - (C=A)
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strong strong strong
keith's: A = (A-B) = (B-C) = (C-A)
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weak weak weak
in grid: 6 = (6-1) = (1-7) = (7-6) |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Sep 03, 2009 6:25 am Post subject: |
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Keith's chain could also be viewed as exploiting the strong (bilocation) inferences/links for {6,1,7} ... and the fact that the SI/SL for <7> ends in a peer cell of the starting cell.
| Code: | Keith: (6) = (6-1) = (1-7) = (7)
|*****| |*****| |*****|
SI/SL SI/SL SI/SL
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In which case, it's just another un-named short chain pattern (to my knowledge). |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Sep 03, 2009 9:05 am Post subject: |
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| daj95376 wrote: | Keith's chain could also be viewed as exploiting the strong (bilocation) inferences/links for {6,1,7} ... and the fact that the SI/SL for <7> ends in a peer cell of the starting cell.
| Code: | Keith: (6) = (6-1) = (1-7) = (7)
|*****| |*****| |*****|
SI/SL SI/SL SI/SL
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In which case, it's just another un-named short chain pattern (to my knowledge). |
you are more right than you give yourself credit for.
lets examine the inferences involved only
=-=-=
strong, weak, strong, weak, strong
guess what? all bi-value named wings fall into this inference set.
| Code: | this inference set encompasses all the wings we love to see in a grid.
the inferences don't change down the list. its how the values are arranged that give us our patterns.
three strong, two weak, inference set
= - = - =
xy-wing: (A=B) - (B=C) - (C=A)
w-wing: (A=B) - B = B - (B=A)
*GM-wing: (A=B) - B = (B-A) = A
inv/xy: A = (A-B) = (B-C) = C {1st A and last C are in the same house}
fishy: A = A - A = A - A = A {1st and last A in the same house} loop
Cycle {includes swordfish}
x-cycle: A = A - A = A - A = A {first and last A not in the same house}
Danny's
skyscraper: A = A - A = (A-B) = B {1st A and last B in the same house}
extension
*generalized m-wing in this case because the "(B-A)" cell doesn't need to be bi-value.
--------------------------------------
two strong, one weak, inference set...
= - =
naked pair: (A=B) - (B=A) {both cells in same row/col/box} loop
Hidden Pair:A = (A-B) = B {the first A and the last B are in the same cell
all in the same row/col/box} loop
X-wing: A = A - A = A {First A and last A in the same house} loop
includes
skyscraper
kite
turbot fish:A = A - A = A {First A and last A not in the same house}
xyz-wing would go here too. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Thu Sep 03, 2009 2:39 pm Post subject: |
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| Marty R. wrote: | | I don't see anything labeled Insane on their home page. Where are they found and how do they compare with Fiendish? |
Marty (and everyone else),
Very sorry about the title for this thread; obviously it is not correct. However, Vanhegan does not provide a way to retrieve old puzzles and the Decabit site, which does have "Insane" puzzles, is down presently so I can't verify where I found this puzzle. I will try again later. Also, I find the Vanhegan Fiednish similar to the Decabit Insane.
Keith found the point of interest that I noted when I posted the puzzle; I found it interesting.
To solve the puzzle, I used the two w-wings 68, which opened up a
xy-wing 1-24 with pivot 14 in r8c2 and pincer 12 extended: (1)r8c2 - (1) r1c2 = (1)r1c5 - (1=2)r5c5 - (2)r5c4 = (2)r7c4; r7c2<>2, and finally a
xy-wing 14-7 with pivot 14 in r8c2 and pincer 17 extended: (1)r8c2 - (1)r1c2 = (1-7)r1c5 = (7)r2c4; r8c4<>7
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Sep 03, 2009 5:04 pm Post subject: |
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| storm_norm wrote: | | Code: | includes
skyscraper
kite
turbot fish:A = A - A = A {First A and last A not in the same house}
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Nice reference table Norm.
A grouped 2-String Kite occurs (sometimes*) when a grouped strong link is used for the weak inference "A - A". If you allow the grouped strong inference in an ERI for the last "A = A", then you can add Empty Rectangle to this list of techniques.
BTW: I believe that my extended Skyscraper should be shown as ...
| Code: | Danny's
skyscraper: A = (A - B) = B - B = B {1st A and last B in the same house}
extension
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*sometimes: not every grouped strong link will work. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Sep 03, 2009 6:50 pm Post subject: |
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| Quote: | If you allow the grouped strong inference in an ERI for the last "A = A", then you can add Empty Rectangle to this list of techniques.
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yes, the empty rectangle goes in the two strong, one weak list.
| Quote: | BTW: I believe that my extended Skyscraper should be shown as ...
| Code: | Danny's
skyscraper: A = (A - B) = B - B = B {1st A and last B in the same house}
extension |
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AHA, another great point.
and I was thinking about this after I made the inference tables. I believe Keith is one of the most active posters on the forum who try and find other permutations of the same inference set. this three strong, two weak inference set has other permutations not named.
here is what we have so far. notice that the pattern Keith saw in the puzzle is also called a strong wing. I saw it called that in the players forum a couple times.
| Code: | xy-wing: (A=B) - (B=C) - (C=A)
w-wing: (A=B) - B = B - (B=A)
Gm-wing: (A=B) - B = (B-A) = A
inv/xy: A = (A-B) = (B-C) = C {or strong wing}
Cycle: A = A - A = A - A = A
skyscraper
extension: A = A - A = (A-B) = B |
not every permuation is accounted for. Danny brought up the point that the skyscraper extension can also be written with two A's and four B's.
what might interest Keith and anyone looking to name a pattern is that not all the permutations are accounted for in the table.
here are some...
| Code: | not named three strong, two weak, two candidate permutations
= - = - =
A = A - (A=B) - B = B {1st A and last B in same house}
eliminates candidate A from the cell of the last B
notice the cyclops bi-value cell in the middle, ha!
A = (A-B) = B - B = B {1st A and last B in same house
{skyscraper extension}
eliminates candidate A from last B cell
same as
A = A - A = (A-B) = B {eliminates B from first A cell}
---------------------
the xy-wing is a "named" three strong, two weak, three candidate chain
(A=B) - (B=C) - (C=A)
not named permutations including three candidates
(A=B) - (B=C) - C = C {A and last C in same house}
eliminates candidate A from the cell of the last C
A = (A-B) = B - (B=C) {1st A and C in same house}
this one eliminates candidate C from the 1st A cell
same as
(A=B) - B = (B-C) = C {A and last C in same house}
this eliminates candidate A from the last C cell
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Sep 03, 2009 9:43 pm Post subject: |
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| Quote: | | what might interest Keith and anyone looking to name a pattern |
Not quite correct. I am trying to establish patterns that human solvers can readily recognize, and recipes for recognizing them.
Thank you, norm and danny, for the interesting posts. I will have to study them.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Sep 04, 2009 5:37 pm Post subject: |
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Ted: I tried everything I could to get this puzzle to crack easily. It wouldn't, but probably because I can't find DPs worth a darn.
I even ran the puzzle through HoDoKu and didn't see any sign that it could do any better. But, it doesn't do DPs, either.
The best solution I could get from my solver uses three XY-Chains for the advanced steps. (The first XY-Chain is equivalent to one of the W-Wings already presented.) I'm including them because they are far from friendly.
| Code: | after basics
+-----------------------------------------------------------------------+
| 4 16 3 | 8 17 2 | 5 67 9 |
| 58 68 2 | 567 9 36 | 4 3678 1 |
| 158 9 7 | 156 134 1346 | 68 368 2 |
|-----------------------+-----------------------+-----------------------|
| 2 5 4 | 3 8 7 | 9 1 6 |
| 6 3 8 | 12 12 9 | 7 4 5 |
| 9 7 1 | 4 6 5 | 3 2 8 |
|-----------------------+-----------------------+-----------------------|
| 138 1248 5 | 1267 12347 1346 | 68 9 47 |
| 138 148 9 | 167 5 1346 | 2 68 47 |
| 7 24 6 | 9 24 8 | 1 5 3 |
+-----------------------------------------------------------------------+
# 55 eliminations remain
(8=6)r2c2-(6=1)r1c2-(1=7)r1c5-(7=6)r1c8-(6=8)r8c8; r2c8,r8c2 <>8
(2=1)r5c5-(1=7)r1c5-(7=6)r1c8-(6=1)r1c2-(1=4)r8c2-(4=2)r9c2; r9c5 <>2
(6=7)r8c4-(7=4)r8c9-(4=1)r8c2-(1=6)r1c2-(6=7)r1c8-(7=1)r1c5-(1=3)r3c5-(3=6)r2c6; r23c4,r78c6<>6
_________________________________________________________________________________________________
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Note: the last eliminations for <6> in [b8] are interesting to me because they are part of the possible <134> DP in [band 3] present from the beginning. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Sep 05, 2009 9:50 pm Post subject: |
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The Decabit site still seems to be offline so I remain unsure where I got this puzzle, but I "believe" that it was a Decabit Insane puzzle.
In any case, it stimulated a good discussion which is always a positive.
Ted |
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