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Puzzle 10/07/24: A
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Sat Jul 24, 2010 5:12 pm    Post subject: Puzzle 10/07/24: A Reply with quote

Code:
 +-----------------------+
 | 7 . . | . . . | 4 . . |
 | . 9 . | . 4 . | 1 . . |
 | . . . | . . . | . 3 8 |
 |-------+-------+-------|
 | . . . | 4 . . | 9 . . |
 | . 8 5 | . 6 . | . . . |
 | . . . | . 3 7 | . 4 1 |
 |-------+-------+-------|
 | 1 . . | . . . | 6 8 . |
 | 9 . 8 | . . 6 | 3 . . |
 | . . 4 | . . 3 | . 2 . |
 +-----------------------+

Play this puzzle online at the Daily Sudoku site
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Sun Jul 25, 2010 12:22 am    Post subject: Reply with quote

Taking them as they come..........

Quote:
Type 4 UR(28)r14c56 with SL2; r1c6<>8
Type 1 UR (18)r19c45; r1c4<>18
Type 1 UR (56)r24c89; r2c9<>56

xy-wing 2-57 vertex r2c9; r2c8,r3c6<>5

xy-wing -257 vertex (57)r3c7

Ted
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sun Jul 25, 2010 12:57 am    Post subject: Reply with quote

Type 1 UR (56)
XY-Wing (275)
XY-Wing (572)
W-Wing (27) + pincer transport
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peterj



Joined: 26 Mar 2010
Posts: 974
Location: London, UK

PostPosted: Sun Jul 25, 2010 11:25 am    Post subject: Reply with quote

Three VH steps to ease into a Sunday morning..

type 1 UR(56) r24c89; r2c9<>56
xy-wing(27-5) r2c9; r2c8<>5, r3c6<>5
xy-wing(57-2) r3c7; r2c3<>2

[Edit] Didn't seem to need a w-wing...
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Mogulmeister



Joined: 03 May 2007
Posts: 966

PostPosted: Sun Jul 25, 2010 10:24 pm    Post subject: Reply with quote

There's an almost als situation:

Code:
+-------------------+-------------------+-------------------+
| 7     1235  1236  | 1368  128   1258  | 4     9     256   |
| 8     9     236A  | 367A  4     25    | 1     56A   2567* |
| 25    4     126   | 1679* 79*   1259  | 57B   3     8     |
+-------------------+-------------------+-------------------+
| 3     17    17    | 4     28    28    | 9     56    56    |
| 4     8     5     | 19    6     19    | 2     7     3     |
| 26    26    9     | 5     3     7     | 8     4     1     |
+-------------------+-------------------+-------------------+
| 1     2357  237   | 279   579   4     | 6     8     57    |
| 9     257   8     | 27    57    6     | 3     1     4     |
| 56    567   4     | 18    18    3     | 57    2     9     |
+-------------------+-------------------+-------------------+


Two sets A & B

Almost ALS-xz

A={2,3,5,6,7}
B={5,7}
x=5
z=7

This doesn't work off the bat because A has 5 candidates and only 3 cells.
All would be fine if the 2 in r2c3 wasn't there - in that case ALS XY is TRUE and the asterisked 7s would all be eliminated solving the puzzle.

If however the pesky 2 is true then r3c1 is <>2 and puzzle solved.
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ronk



Joined: 07 May 2006
Posts: 398

PostPosted: Sun Jul 25, 2010 11:33 pm    Post subject: Reply with quote

Mogulmeister wrote:
All would be fine if the 2 in r2c3 wasn't there - in that case ALS XY is TRUE and the asterisked 7s would all be eliminated solving the puzzle.

If however the pesky 2 is true then r3c1 is <>2 and puzzle solved.

I know of no one else that presents "the puzzle is solved" as a common outcome. If one case solves the puzzle, why even examine an alternate case?
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Mon Jul 26, 2010 2:20 am    Post subject: Reply with quote

ronk wrote:
I know of no one else that presents "the puzzle is solved" as a common outcome. If one case solves the puzzle, why even examine an alternate case?

You haven't read old oaxen solutions ... have you. They're similar.


Last edited by daj95376 on Mon Jul 26, 2010 4:51 am; edited 3 times in total
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ronk



Joined: 07 May 2006
Posts: 398

PostPosted: Mon Jul 26, 2010 2:38 am    Post subject: Reply with quote

daj95376 wrote:
ronk wrote:
I know of no one else that presents "the puzzle is solved" as a common outcome. If one case solves the puzzle, why even examine an alternate case?

You haven't read old oaxen solutions ... have you. They're similar.

I'll be surprised if Mogulmeister agrees with that. I certainly don't.
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strmckr



Joined: 18 Aug 2009
Posts: 64

PostPosted: Mon Jul 26, 2010 4:00 am    Post subject: Reply with quote

after basics
a fun move just cause i can Smile

Code:

 *-----------------------------------------------------------*
 | 7     1235  1236  | 1368  128   1258  | 4     9     256   |
 | 8     9     236   | 367   4     25    | 1     56    2567  |
 | 25    4     126   | 1679  79    129   | 57    3     8     |
 |-------------------+-------------------+-------------------|
 | 3     1-7   17    | 4     28    28    | 9     56    56    |
 | 4     8     5     | 19    6     19    | 2     7     3     |
 | 26    26@   9     | 5     3     7     | 8     4     1     |
 |-------------------+-------------------+-------------------|
 | 1     235-7 23-7  | 279   579   4     | 6     8     57    |
 | 9     257@  8     | 27    57    6     | 3     1     4     |
 | 56@    67@   4     | 18    18    3     | 57    2     9     |
 *-----------------------------------------------------------*


wxyz wing (2567) R8c2,R9C12 , (26)R6C2 x=2, z =7 => R7C23, R4C1 <> 7
but its not need from this state:

three steps to finish it:

Uniqueness Test 1: 5/6 in r2c89,r4c89 => r2c9<>5, r2c9<>6

XY-Wing: 5/7/2 in r2c9,r3c17 => r2c3<>2
XY-Wing: 2/7/5 in r2c69,r3c7 => r2c8<>5

and singles to the end...
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Mon Jul 26, 2010 4:59 am    Post subject: Reply with quote

ronk wrote:
daj95376 wrote:
ronk wrote:
I know of no one else that presents "the puzzle is solved" as a common outcome. If one case solves the puzzle, why even examine an alternate case?

You haven't read old oaxen solutions ... have you. They're similar.

I'll be surprised if Mogulmeister agrees with that. I certainly don't.

Well, let me rephrase my thoughts.

Mogulmeister presents an either/or scenario where the ALS results in the puzzle being solved. Then he says that r2c3=2 results in r3c1<>2 and this also leads to the puzzle being solved. However, did anyone ever check to see if r2c3=2 leads to the puzzle being solved? It doesn't!

One choice solves the puzzle and an alternate choice doesn't. The first thing I think of is oaxen solutions.
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Mogulmeister



Joined: 03 May 2007
Posts: 966

PostPosted: Tue Jul 27, 2010 4:49 pm    Post subject: Reply with quote

I had a feeling that might set the hares loose before I went to the mountains......

Unfortunately Danny, I, like the majority of those left on this board I suspect, don't remember any of Oaxen's solutions because I never saw one. I do remember his gnomic answers and, as you may recall, I did point out to him that his pronouncements were akin to Fermat's famous note in the margin. You explained that because of the method he uses, an explanation that was postable wasn't possible - or similar. So yes, like Ronk I did wonder about your own gnomic renmark. So glad you went on to explain - at least I exposit my solutions. Smile

I believe that there are possibly many chains out there which employ "false" implications on their way to eliminations or fin based operations. Cells which turn out to have different "actuals" when the solution is made.

In this case with this method we arrive not knowing if there is a 2 in that cell or not. It is a quasi fin situation. My objective was to logically show that the existence or otherwise of the 2 did not affect the outcome.

Ronk - your point about my epexegesis - it must be the anally retentive orthoganalist in me. Like many a murderer I am compelled to explain to my victims. Laughing
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Tue Jul 27, 2010 10:16 pm    Post subject: Reply with quote

from original post wrote:
If however the pesky 2 is true then r3c1 is <>2 and puzzle solved.

Is incorrect because r3c1<>2 will never lead to a solved puzzle where r2c3=2 -- your original premise.

Quote:
I believe that there are possibly many chains out there which employ "false" implications on their way to eliminations or fin based operations. Cells which turn out to have different "actuals" when the solution is made.

In this case with this method we arrive not knowing if there is a 2 in that cell or not. It is a quasi fin situation. My objective was to logically show that the existence or otherwise of the 2 did not affect the outcome.

I hated removing the beautiful prose, but I need to review conjugate logic.

A True implication can only lead to additional True implications. That's half of what's needed to support drawing a conclusion from a conjugate relationship.

Nothing specific can be said about where a False implication will lead. However, it's possible that somewhere along the line it may actually lead to a True implication and subsequent True implications from it.

In a conjugate relationship, it's not necessary to know which parts of the relationship specifically represent the True/False implications. It's only nececessary to confine your conclusions to the common implications.

Regards, Danny
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Wed Jul 28, 2010 1:39 am    Post subject: Reply with quote

<Opening Webster's New Collegiate; rifling pages; finding "epexegesis.">

Ah, yes. I can go on now that I've got that one under my belt Smile.

Hi, Mog. If you'd like to use your almost ALS in a different way, you can. Try out this rule:
At least one of any three values in an AALS must be true.

Code:
 *-----------------------------------------------------------*
 | 7     1235  1236  | 1368  128   1258  | 4     9     256   |
 | 8     9    *236   |*367   4     25    | 1    *56    2567  |
 | 25    4     126   | 1679  79    1259  | 57    3     8     |
 |-------------------+-------------------+-------------------|
 | 3     17    17    | 4     28    28    | 9     56    56    |
 | 4     8     5     | 19    6     19    | 2     7     3     |
 | 26    26    9     | 5     3     7     | 8     4     1     |
 |-------------------+-------------------+-------------------|
 | 1     2357  237   | 279   579   4     | 6     8     57    |
 | 9     257   8     | 27    57    6     | 3     1     4     |
 | 56    567   4     | 18    18    3     | 57    2     9     |
 *-----------------------------------------------------------*

Code:
(23567)aals:r2c348 =>r3c7<>5
 ||
(5)r2c8
 ||
(2)r2c3-(2=5)r3c1
 ||
(7)r2c4-(7)r3c46=(7)r3c7

Circumloquaciously yours,
Luke Wink
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Mogulmeister



Joined: 03 May 2007
Posts: 966

PostPosted: Wed Jul 28, 2010 9:29 am    Post subject: Reply with quote

Danny J wrote:
I hated removing the beautiful prose, but I need to review conjugate logic.


To paraphrase your earlier (now expunged) reply: I would have accepted "negating". Laughing

As a matter of fact I looked for the discontinuous loop first of all because I would have been able to tie it all in a nice(r) bow.

I appreciate the conjugate theory but for me the premise is a lot simpler - whether the 2 is true or not there is a solve path to the puzzle. One of these is false but at that stage I don't know which and it doesn't matter. The fact is that the presence or otherwise of that 2 matters not. Whichever is correct the puzzle is done. There is perhaps more than a little of Schrödinger's cat in this.

I dimly remember this as being "a don't care" scenario when we studied ancient philosophies in the Pleistocene period but I happily defer to those gurus like yourself in this forum who are more versed in this than me.

Luke, your alternative was both elucidational and perfectly pellucid - not at all periphrastic. I thank you. Wink

Cheers,

Mogul
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ronk



Joined: 07 May 2006
Posts: 398

PostPosted: Wed Jul 28, 2010 12:56 pm    Post subject: Reply with quote

Mogulmeister, I didn't see your answer to the below. If you did, would you please rephrase in a style that is more direct and less opaque Question

ronk wrote:
Mogulmeister wrote:
All would be fine if the 2 in r2c3 wasn't there - in that case ALS XY is TRUE and the asterisked 7s would all be eliminated solving the puzzle.

If however the pesky 2 is true then r3c1 is <>2 and puzzle solved.

I know of no one else that presents "the puzzle is solved" as a common outcome. If one case solves the puzzle, why even examine an alternate case?
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ttt



Joined: 06 Dec 2008
Posts: 42
Location: vietnam

PostPosted: Wed Jul 28, 2010 5:02 pm    Post subject: Reply with quote

Luke451 wrote:
Try out this rule:
At least one of any three values in an AALS must be true.

Code:
 *-----------------------------------------------------------*
 | 7     1235  1236  | 1368  128   1258  | 4     9     256   |
 | 8     9    *236   |*367   4     25    | 1    *56    2567  |
 | 25    4     126   | 1679  79    1259  | 57    3     8     |
 |-------------------+-------------------+-------------------|
 | 3     17    17    | 4     28    28    | 9     56    56    |
 | 4     8     5     | 19    6     19    | 2     7     3     |
 | 26    26    9     | 5     3     7     | 8     4     1     |
 |-------------------+-------------------+-------------------|
 | 1     2357  237   | 279   579   4     | 6     8     57    |
 | 9     257   8     | 27    57    6     | 3     1     4     |
 | 56    567   4     | 18    18    3     | 57    2     9     |
 *-----------------------------------------------------------*

Code:
(23567)aals:r2c348 =>r3c7<>5
 ||
(5)r2c8
 ||
(2)r2c3-(2=5)r3c1
 ||
(7)r2c4-(7)r3c46=(7)r3c7



IMO, your AALS was not clear in sometime... So, I present it as AAHS (Almost Almost Hidden Set):

Code:
AAHS(2367)r2c34  => r3c7<>5
 ||
(36)r2c34-(6=5)r2c8
 ||
(2)r2c3-(2=5)r3c1
 ||
(7)r2c4-(7)r2c9=(7)r3c7


ttt
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ronk



Joined: 07 May 2006
Posts: 398

PostPosted: Wed Jul 28, 2010 6:50 pm    Post subject: Reply with quote

ttt wrote:
IMO, your AALS was not clear in sometime... So, I present it as AAHS (Almost Almost Hidden Set):

Code:

AAHS(2367)r2c34  => r3c7<>5
 ||
(36)r2c34-(6=5)r2c8
 ||
(2)r2c3-(2=5)r3c1
 ||
(7)r2c4-(7)r2c9=(7)r3c7

ttt, yours is also an AALS. The AAHS that corresponds to Luke451's AALS would look like ...

Code:

(23567)aals:r2c348 => r3c7<>5                         (257)aahs:r2c34689  => r3c7<>5
 ||                                                    ||
(5)r2c8                                               (5)r2c8
 ||                                                    ||
(2)r2c3-(2=5)r3c1                                     (2)r2c3-(2=5)r3c1
 ||                                                    ||
(7)r2c4-(7)r3c46=(7)r3c7                              (7)r2c4-(7)r3c46=(7)r3c7


... with three candidates in five cells. Graphically, these two are:

__________

Note that the strong inference set is unchanged.
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Luke451



Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California

PostPosted: Thu Jul 29, 2010 6:32 pm    Post subject: Reply with quote

ttt, thanks for the hidden pair perspective. With ronk's graphic, it's become clearer to me the difference btwn AALS and AAHS.

I use the AALS because this is the way I first learned about how to take advantage of "almost almost" sets. Check out this similar move ("April 30, 2009 2:26 am") by ronk. This example is similar to the one I presented in that the three "hidden set" values only appear one time each. It makes finding a useful deduction a little easier, IMO.

I'd like to add that while AALS and AAHS is a pretty big stick with which to beat this puzzle, it's a very powerful weapon to know. ttt, I've seen you frequently use AALS/AAHS in your nets to take down some of the toughest puzzles in the world.

Also, AALS/AAHS nets do not carry the same "assumptivity baggage" associated with moves like kraken cell/row/column/box.
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Mogulmeister



Joined: 03 May 2007
Posts: 966

PostPosted: Thu Jul 29, 2010 11:05 pm    Post subject: Reply with quote

I admit I'm something of a logodaedalus but I have never come across the most marvellous phrase "assumptivity baggage" which I am afraid I will steal at some point Luke because it is so good. Smile

I am enjoying this thread and the resultant discussion from my philosophical trespass. I especially appreciate the xsudo diagram.

Ronk, your earlier answer and repeated question made it clear to me that you had in fact had a glimpse at my response to your original question. Opaque ? Surely not. Smile English is a rich and descriptive language.

However - epexegesis is "by way of further explanation".

I have said elsewhere on this board that when I was a newbie to these and other pages there was sometimes a lot of "assumptivity baggage" when answers are given. I like to think that if someone encountered these pages they should be able to follow very clearly what has been postulated.

We have in these forums already had at least one notation discussion which has recognised the need for better demonstrating certain aspects of the game.

What I am doing in showing two separate solve routes in the way I do is to give a bit more of a narrative and explicitly show what happens. I apologise for being the only person you know who does this or if it appears a tad tautological - but my nonconformity is not purely based on cussedness. Please feel free to show your (undoubtedly better) alternative. I'd like to see others who are ascending the learning curve feel that they could venture here.

This would have been most helpful to me in the early days. Encountering some sudoku boards was sometimes a bit like watching the last eight remaining speakers of Livonian discussing the weather.
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Fri Jul 30, 2010 6:11 am    Post subject: Reply with quote

The various AA* scenarios are interesting, but I find the presence of <3> in most of them unsettling.

To me, <3> is locked in r2c34 with one of four possible truths remaining:

Code:
(2)r2c3   - (2=5)r3c1 - (  5)r3c7
(6)r2c3|4 - (6=5)r2c8 - (  5)r3c7
(7)r2c  4 - (7  )r2c9 = (7-5)r3c7

I find a network for r2c9<>7 interesting because it shows how one value being true forces two values in the same cell to be false -- resulting in a networked discontinuous loop:

Code:
          (5)r2c9 ...........
        /                     \
(7)r2c9 - (7=5)r3c7 - (5)r2c8 = (5-2)r2c6 = (2)r2c3 - (2=5)r3c1 - (5=7)r3c7 - (7)r2c9
        \                                 /
          (2)r2c9 .......................
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