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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Sun Jun 20, 2010 8:12 pm Post subject: A four-cell contradiction chain |
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A four-cell contradiction chain.
Sudoku Susser keeps on pointing these out. For example:
| Code: |
+----------------+----------------+----------------+
| 1 379 79 | 57 4 6 | 2 8 357 |
| 378 5 4 | 2 1 789 | 39 6 379 |
| 78 6 2 | 589a 3 5789d| 1 4 579 |
+----------------+----------------+----------------+
| 579 1 79 | 3 58 89 | 4 2 6 |
| 2 4 3 | 59 6 1 | 59 7 8 |
| 6 89 58 | 4 7 2 | 359 1 39 |
+----------------+----------------+----------------+
| 35 38 1 | 6 58 4 | 7 9 2 |
| 4 2 58 | 578b 9 578c | 6 3 1 |
| 79 79 6 | 1 2 3 | 8 5 4 |
+----------------+----------------+----------------+
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5 in a forces 5 in d; a is not 5.
The stencil is something like:
| Code: |
589a (-5) 5789d
(=8) (=5)
578b (=7) 578c
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If X, Y, Z are particular candidates, and t, u, v, w are any candidates:
| Code: |
tXY (-X) wX
(=Y) (=X)
uYZ (=Z) vXZ
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The cell tXY cannot be X.
Are these worth looking for? Can we construct a recipe for the pencil & paper crowd to find them?
Keith
PS: Sports on TV this afternoon is golf, soccer, and NASCAR. The question for many must be: "Which is less boring?" |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Jun 20, 2010 10:35 pm Post subject: |
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| Code: | +--------------------------------------------------------------+
| 1 379 79 | 57 4 6 | 2 8 357 |
| 378 5 4 | 2 1 789 | 39 6 379 |
| 78 6 2 | *589 3 #5789 | 1 4 579 |
|--------------------+--------------------+--------------------|
| 579 1 79 | 3 58 89 | 4 2 6 |
| 2 4 3 | 59 6 1 | 59 7 8 |
| 6 89 58 | 4 7 2 | 359 1 39 |
|--------------------+--------------------+--------------------|
| 35 38 1 | 6 58 4 | 7 9 2 |
| 4 2 58 | *578@ 9 #578@ | 6 3 1 |
| 79 79 6 | 1 2 3 | 8 5 4 |
+--------------------------------------------------------------+
(*) strong link on <8>
(@) strong link on <7>
(#) strong link on <5>
(8)r3c4 = (8-7)r8c4 = (7-5)r8c6 = (5)r3c6 => r3c4<>5, r3c6<>8
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The AIC is three strong links that reside in four cells that form a "U" pattern. It starts and ends with two cells that see each other. Eliminations are possible in both the starting and ending cells.
I have no idea how difficult this would be for P&P people to emulate.
===== ===== ===== ===== Puzzle Specific Note
If you wish to reduce the number of different candidate values used, then you can take advantage of r7c5=58 in this puzzle.
| Code: | (8)r3c4 = r8c4 - (8=5)r7c5 - r8c6 = (5)r3c6 => r3c4<>5, r3c6<>8
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Jun 20, 2010 11:13 pm Post subject: |
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| Quote: | Eliminations are possible in both the starting and ending cells.
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Really? In general, or just in this example?
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Jun 20, 2010 11:51 pm Post subject: |
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| keith wrote: | | Quote: | Eliminations are possible in both the starting and ending cells.
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Really? In general, or just in this example?
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I'm not sure what you mean by "in general". Here's what I mean.
If a starting cell is assumed false for candidate <X> and an (ending) peer cell is derived as true for candidate <Y>, then <Y> can be deleted from the starting cell and <X> can be deleted from the ending cell. <X> can not be equal to <Y>.
Regards, Danny |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Jun 21, 2010 4:12 am Post subject: |
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| daj95376 wrote: | | keith wrote: | | Quote: | Eliminations are possible in both the starting and ending cells.
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Really? In general, or just in this example?
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I'm not sure what you mean by "in general". Here's what I mean.
If a starting cell is assumed false for candidate <X> and an (ending) peer cell is derived as true for candidate <Y>, then <Y> can be deleted from the starting cell and <X> can be deleted from the ending cell. <X> can not be equal to <Y>.
Regards, Danny |
Danny,
What if the ending cell does not contain X (in your notation, which is not the same as mine)? The implication of your statement is that the starting and ending cells each need to contain both X and Y.
Here's what I mean:
If a starting cell is assumed true for candidate <Y> and an (ending) peer cell is derived as true for candidate <Y>, then <Y> can be deleted from the starting cell.
Keith |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Mon Jun 21, 2010 10:22 am Post subject: |
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| keith wrote: | What if the ending cell does not contain X (in your notation, which is not the same as mine)? The implication of your statement is that the starting and ending cells each need to contain both X and Y.
Here's what I mean:
If a starting cell is assumed true for candidate <Y> and an (ending) peer cell is derived as true for candidate <Y>, then <Y> can be deleted from the starting cell. |
I think most would agree with daj95376. If cells A and B are peer cells and you have the AIC ...
(x)A = ... = (z)B
... where x and z are unlike digits, then the two potential exclusions are A<>z and B<>x. Some Eureka folks called this a 'Type 2 AIC.' |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Jun 21, 2010 3:44 pm Post subject: |
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Okay, here's the longer version of my explanation.
If a starting cell is assumed false for candidate <X> and an (ending) peer cell is derived as true for candidate <Y>, then <Y> can be deleted from the starting cell and <X> can be deleted from the ending cell. Of course, if <Y> does not exist in the starting cell and/or <X> does not exist in the ending cell, then the missing candidate(s) can be considered pre-eliminated!
| Quote: | Here's what I mean:
If a starting cell is assumed true for candidate <Y> and an (ending) peer cell is derived as true for candidate <Y>, then <Y> can be deleted from the starting cell.
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<X> can not be equal to <Y>.
The explanation goes back to the forcing chains that I use to derive the relationships. If you'd like, I'll include them.
Regards, Danny |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Jun 21, 2010 4:35 pm Post subject: |
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Ronk and Danny,
Thank you.
Keith |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Tue Jun 22, 2010 11:18 pm Post subject: Re: A four-cell contradiction chain |
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| keith wrote: | A four-cell contradiction chain.
Sudoku Susser keeps on pointing these out. For example:
| Code: |
+----------------+----------------+----------------+
| 1 379 79 | 57 4 6 | 2 8 357 |
| 378 5 4 | 2 1 789 | 39 6 379 |
| 78 6 2 | 589a 3 5789d| 1 4 579 |
+----------------+----------------+----------------+
| 579 1 79 | 3 58 89 | 4 2 6 |
| 2 4 3 | 59 6 1 | 59 7 8 |
| 6 89 58 | 4 7 2 | 359 1 39 |
+----------------+----------------+----------------+
| 35 38 1 | 6 58 4 | 7 9 2 |
| 4 2 58 | 578b 9 578c | 6 3 1 |
| 79 79 6 | 1 2 3 | 8 5 4 |
+----------------+----------------+----------------+
|
5 in a forces 5 in d; a is not 5.
The stencil is something like:
| Code: |
589a (-5) 5789d
(=8) (=5)
578b (=7) 578c
|
If X, Y, Z are particular candidates, and t, u, v, w are any candidates:
| Code: |
tXY (-X) wX
(=Y) (=X)
uYZ (=Z) vXZ
|
The cell tXY cannot be X.
Are these worth looking for? Can we construct a recipe for the pencil & paper crowd to find them?
|
My pet name for these is "strong rectangles." Udosuk categorized them among what he called "Hybrid Wings," although they are not often referred to as such.
I see all wings as AICs, but this particular one will stand out for us P&P types if all conjugate pairs are somehow delineated (I mark mine in bold.)
| Keith wrote: | | Sports on TV this afternoon is golf, soccer, and NASCAR. The question for many must be: "Which is less boring?" |
Surprised no one jumped you for that one? Maybe they all agree, or are just too swept up in the heart-stopping excitement of sudoku to respond....
NASCAR: I call it NECKCAR but acknowledge that it's hugely popular.
GOLF: The U.S. Open at Pebble Beach! Say no more.
"SOCCER": The World Cup!! The greatest tournament of them all!
I'd bet the "many" to whom you refer are outnumbered by the billions worldwide who can't get enough. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Tue Jun 22, 2010 11:24 pm Post subject: |
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Keith wrote:
Sports on TV this afternoon is golf, soccer, and NASCAR. The question for many must be: "Which is less boring?"
Or, I perhaps missed the Canadian curling championships?
Keith |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Tue Jun 22, 2010 11:43 pm Post subject: |
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| Hey, the gf watches home-improvement TV all Sunday afternoon. Now, that's literally watching paint dry! |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Wed Jun 23, 2010 2:29 am Post subject: |
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| keith wrote: |
Or, I perhaps missed the Canadian curling championships?
Keith |
Tried to slide that past me, did 'ya. Wrong time of year. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Jun 23, 2010 3:17 am Post subject: |
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| wapati wrote: | | keith wrote: |
Or, I perhaps missed the Canadian curling championships?
Keith |
Tried to slide that past me, did 'ya. Wrong time of year. |
Sorry, I meant the reruns of the curling competitions. We all know how compelling the originals are! 
Eh!
Keith |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Wed Jun 23, 2010 4:16 am Post subject: |
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| Hurry HARD, eh? |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Wed Jun 23, 2010 4:25 am Post subject: |
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I like curling. It is slow to watch but that gives you time to figure what shot you prefer. Strategy.
Soccer, I do like it, much like hockey. Hockey is my sport of choice.
Baseball, I can watch a close game.
American football? 4 seconds of action between minutes of doldrums.
The last 3 minutes take 20 minutes. Awesome?
Worst TV sport for me is darts. I have never lasted more than a moment. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Wed Jun 23, 2010 4:27 am Post subject: |
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Eh
Rugby |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Thu Jun 24, 2010 4:02 am Post subject: |
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***WOW!*** U.S v. Algeria
There's a reason it's called "The Beautiful Game."
(Video link zapped by FIFA )
Last edited by Luke451 on Thu Jun 24, 2010 1:44 pm; edited 1 time in total |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Jun 24, 2010 5:54 am Post subject: |
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Absolutely Luke!
Thrilling finale and as a special reward you get the Ghanaians and we get the Germans!  |
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