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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Sun Apr 25, 2010 12:20 pm Post subject: Simplification |
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ttt recently posted this grid and the elimination r5c6<>6 based on a complex Almost XY-Wing. While examining his logic, I had a feeling that something simpler might be present in the cells he was using.
| Code: | +-----------------------------------------------------------------------+
| 189 13789 378 | 19 4 2 | 3689 5689 35689 |
| 469 349 346 | 59 359 8 | 1 2 7 |
| 189 2 5 | 6 1379 379 | 4 89 389 |
|-----------------------+-----------------------+-----------------------|
| 3 6 478 | 2 789 479 | 789 15 15 |
| 4589 45789 1 | 4789 36789 3479-6 | 2 6789 689 |
| 289 789 278 | 1789 16789 5 | 6789 3 4 |
|-----------------------+-----------------------+-----------------------|
| 268 38 2368 | 789 6789 1 | 5 4 3689 |
| 7 1458 9 | 3 568 46 | 68 168 2 |
| 14568 13458 3468 | 4589 2 469 | 36789 16789 13689 |
+-----------------------------------------------------------------------+
# 138 eliminations remain
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Alternative, Almost Naked Pair in r35c9 leads to:
| Code: | (6) r 5c9 - (6)r5c6
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(3) r3 c9 - (3)r3c6 = (3-6)r5c6
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(89)r35c9 - (9)r79c9 = (9)r9c78 - (9=46)r89c6 - (6)r5c6
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Note: I never would have found this scenario if it hadn't been for ttt's original effort. |
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ttt
Joined: 06 Dec 2008
Posts: 42
Location: vietnam
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| Posted: Sun Apr 25, 2010 1:54 pm Post subject: |
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Excellence, Danny!
Wow..., I was deep involved on ‘Almost” XY-wing pattern based on bi-value (89)r3c8. Nice find.
ttt |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sun Apr 25, 2010 2:56 pm Post subject: Re: Simplification |
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| daj95376 wrote: | Alternative, Almost Naked Pair in r35c9 leads to:
| Code: | (6) r 5c9 - (6)r5c6
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(3) r3 c9 - (3)r3c6 = (3-6)r5c6
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(89)r35c9 - (9)r79c9 = (9)r9c78 - (9=46)r89c6 - (6)r5c6
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Yesterday I considered posting the same POV on Eureka, but planned to call it an AALS.  |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Tue Apr 27, 2010 8:26 am Post subject: |
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Shout out to Mogulmeister:
I though you’d might be interested to see that the first move used on this difficult puzzle by sudoku master Steve Kurzhals was a hidden pair.
| Code: | *--------------------------------------------------------------------*
| 189 13789 378 | 19 4 2 | 3689 5689 35689 |
| 469 349 346 | 59 359 8 | 1 2 7 |
| 189 2 5 | 6 1379 379 | 4 89 389 |
|----------------------+----------------------+----------------------|
| 3 6 478 | 2 789 479 | 789 15 15 |
| 4589 5789 1 | 4789 36789 34679 | 2 6789 689 |
| 289 789 278 | 1789 16789 5 | 6789 3 4 |
|----------------------+----------------------+----------------------|
| 268 38 2368 | 789 6789 1 | 5 4 3689 |
| 7 145 9 | 3 568 46 | 68 168 2 |
| 145 145 368 | 4589 2 469 | 36789 16789 13689 |
*--------------------------------------------------------------------*
hp(36)r5c56 = (6-1)r6c5 = (1-7)r3c5 = (7-3)r3c6 = (3)r5c6 => r5c6<>479 |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Tue Apr 27, 2010 8:31 am Post subject: |
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Shout out to tlanglet:
Ted, don’t feel too bad about stretching your almost legs on easier puzzles. When tackling a puzzle like this, familiarity with those ideas will help one find things like Steve’s grouped almost xy-wing in move two.
| Code: | *--------------------------------------------------------------------*
| 189 13789 378 | 19 4 2 | 3689 5689 35689 |
| 469 349 346 | 59 359 8 | 1 2 7 |
| 189 2 5 | 6 1379 379 | 4 89 *38+9 |
|----------------------+----------------------+----------------------|
| 3 6 478 | 2 789 479 | 789 15 15 |
| 4589 5789 1 | 4789 36789 *36 | 2 6789 *68+9 |
| 289 789 278 | 1789 16789 5 | 6789 3 4 |
|----------------------+----------------------+----------------------|
| 268 38 2368 | 789 6789 1 | 5 4 3689 |
| 7 145 9 | 3 568 46 | 68 168 2 |
| 145 145 368 | 4589 2 469 | 36789 16789 13689 |
*--------------------------------------------------------------------*
(3)r5c6 = NT(649)r589c6 - (9)r7c45 = r7c9 - r35c9 = XYwing(36)r5c6, (68)r5c9, (89)r3c9 => r3c6<>3 |
I always like to follow these chains left to right as well to solidify understanding. Note that Steve’s opening inference in this chain can also be interpreted as an als.
Pretty cool stuff, eh?!
The rest of the solution is here dated April 27,2010. |
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ttt
Joined: 06 Dec 2008
Posts: 42
Location: vietnam
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| Posted: Tue Apr 27, 2010 8:56 am Post subject: |
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| Luke451 wrote: | When tackling a puzzle like this, familiarity with those ideas will help one find things like Steve’s grouped almost xy-wing in move two.
| Code: | *--------------------------------------------------------------------*
| 189 13789 378 | 19 4 2 | 3689 5689 35689 |
| 469 349 346 | 59 359 8 | 1 2 7 |
| 189 2 5 | 6 1379 379 | 4 89 *38+9 |
|----------------------+----------------------+----------------------|
| 3 6 478 | 2 789 479 | 789 15 15 |
| 4589 5789 1 | 4789 36789 *36 | 2 6789 *68+9 |
| 289 789 278 | 1789 16789 5 | 6789 3 4 |
|----------------------+----------------------+----------------------|
| 268 38 2368 | 789 6789 1 | 5 4 3689 |
| 7 145 9 | 3 568 46 | 68 168 2 |
| 145 145 368 | 4589 2 469 | 36789 16789 13689 |
*--------------------------------------------------------------------*
(3)r5c6 = NT(649)r589c6 - (9)r7c45 = r7c9 - r35c9 = XYwing(36)r5c6, (68)r5c9, (89)r3c9 => r3c6<>3 |
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(3)r5c6 = NT(649)r589c6 - (9)r7c45 = r7c9 - r35c9 = XYwing(36)r5c6, (68)r5c9, (83)r3c9 => r3c6<>3
There is typo on Steve's original post (marked with red)
ttt |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Tue Apr 27, 2010 3:15 pm Post subject: |
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| Luke451 wrote: | Shout out to Mogulmeister:
I though you’d might be interested to see that the first move used on this difficult puzzle by sudoku master Steve Kurzhals was a hidden pair.
| Code: | *--------------------------------------------------------------------*
| 189 13789 378 | 19 4 2 | 3689 5689 35689 |
| 469 349 346 | 59 359 8 | 1 2 7 |
| 189 2 5 | 6 1379 379 | 4 89 389 |
|----------------------+----------------------+----------------------|
| 3 6 478 | 2 789 479 | 789 15 15 |
| 4589 5789 1 | 4789 36789 34679 | 2 6789 689 |
| 289 789 278 | 1789 16789 5 | 6789 3 4 |
|----------------------+----------------------+----------------------|
| 268 38 2368 | 789 6789 1 | 5 4 3689 |
| 7 145 9 | 3 568 46 | 68 168 2 |
| 145 145 368 | 4589 2 469 | 36789 16789 13689 |
*--------------------------------------------------------------------*
hp(36)r5c56 = (6-1)r6c5 = (1-7)r3c5 = (7-3)r3c6 = (3)r5c6 => r5c6<>479 |
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Yes - excellent - never really looked at them properly - thanks! |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Tue Apr 27, 2010 5:38 pm Post subject: |
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| Luke451 wrote: | Shout out to tlanglet:
Ted, don’t feel too bad about stretching your almost legs on easier puzzles. When tackling a puzzle like this, familiarity with those ideas will help one find things like Steve’s grouped almost xy-wing in move two.
| Code: | *--------------------------------------------------------------------*
| 189 13789 378 | 19 4 2 | 3689 5689 35689 |
| 469 349 346 | 59 359 8 | 1 2 7 |
| 189 2 5 | 6 1379 379 | 4 89 *38+9 |
|----------------------+----------------------+----------------------|
| 3 6 478 | 2 789 479 | 789 15 15 |
| 4589 5789 1 | 4789 36789 *36 | 2 6789 *68+9 |
| 289 789 278 | 1789 16789 5 | 6789 3 4 |
|----------------------+----------------------+----------------------|
| 268 38 2368 | 789 6789 1 | 5 4 3689 |
| 7 145 9 | 3 568 46 | 68 168 2 |
| 145 145 368 | 4589 2 469 | 36789 16789 13689 |
*--------------------------------------------------------------------*
(3)r5c6 = NT(649)r589c6 - (9)r7c45 = r7c9 - r35c9 = XYwing(36)r5c6, (68)r5c9, (89)r3c9 => r3c6<>3 |
I always like to follow these chains left to right as well to solidify understanding. Note that Steve’s opening inference in this chain can also be interpreted as an als.
Pretty cool stuff, eh?!
The rest of the solution is here dated April 27,2010. |
Luke, thanks for the comments and the puzzle. When I first looked at the code, I "saw" the arrangement as starting with an ALS, not as an "almost" NT. In fact, I do not understand a naked triple such as NT(469) where one of the digits, 9 in this case, has a single occurrence; and then the issue of the using the the single digit 6 in the NT is also not obvious to me. Viewed as an ALS I understand (3)r5c6=(9)r9c6. I need to think on this awhile.
Ted |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Tue Apr 27, 2010 6:15 pm Post subject: |
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Ted, here's a perfunctory way of looking at it.
| Code: | *--------------------------------------------------------------------*
| 189 13789 378 | 19 4 2 | 3689 5689 35689 |
| 469 349 346 | 59 359 8 | 1 2 7 |
| 189 2 5 | 6 1379 379 | 4 89 389 |
|----------------------+----------------------+----------------------|
| 3 6 478 | 2 789 479 | 789 15 15 |
| 4589 5789 1 | 4789 36789 *36 | 2 6789 689 |
| 289 789 278 | 1789 16789 5 | 6789 3 4 |
|----------------------+----------------------+----------------------|
| 268 38 2368 | 789 6789 1 | 5 4 3689 |
| 7 145 9 | 3 568 *46 | 68 168 2 |
| 145 145 368 | 4589 2 *469 | 36789 16789 13689 |
*--------------------------------------------------------------------* |
Move the cursor over the (3) in r5c6 to obscure it. What's left in the high-lighted cells is nt(469). I know this is obvious, but it helps to make the locked set/naked triple stand out. So either the (3)r5c6 is true or the naked triple is true. Both can't be false, the very definition of a strong link.
I include the non-operative values in my als, so I see the als version as (3=469)als:r589c6. Since all strong links are reversible, naturally (469=3)als:r589c6 would also work if you found a way to use it.
That the naked triple part contains only one (9) and the (6) stands alone in r5c6 should be no problem. It's still a naked triple if the (3) is not true. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Apr 27, 2010 8:08 pm Post subject: |
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(3)r5c6 = NT(649)r589c6 - (9)r7c45
... should be ...
(3=46)r58c6 - (46=9)r9c6 - (9)r7c45
Addendum:
Using Ted's ALS is even better.
ALS[(3)r5c6=(9)r9c6] - (9)r7c45
Last edited by daj95376 on Tue Apr 27, 2010 11:01 pm; edited 2 times in total |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Tue Apr 27, 2010 9:46 pm Post subject: |
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| daj95376 wrote: | The problem with allowing anything and everything in chains is that you end up with garbage like this ...
(3)r5c6 = NT(649)r589c6 - (9)r7c45
... where a naked triple in [c6] performs elimination in [b8] that are not in [c6].
What you really have is:
(3=46)r58c6 - (46=9)r9c6 - (9)r7c45 |
Danny, I must be missing something, as I often do.
I have seen this NT move so many times that I certainly didn't blink an eye this time. I've never noticed anyone objecting to that notation before. This is just a notation quibble, right? ...because the logic isn't garbage.
I don't see the NT eliminating anything in box 8. It does provide a link, though. The component of the NT that links to (9)r7c45 only exists in box 8 anyway, so I don't understand that objection. Adding the extra node as you suggest seems superfluous to me. Do you see Steve's notation as an improper shortcut?
I imagine you must object to the als version as well. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Tue Apr 27, 2010 10:49 pm Post subject: |
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| Luke451 wrote: | Danny, I must be missing something, as I often do.
I have seen this NT move so many times that I certainly didn't blink an eye this time. I've never noticed anyone objecting to that notation before. This is just a notation quibble, right? ...because the logic isn't garbage.
I don't see the NT eliminating anything in box 8. It does provide a link, though. The component of the NT that links to (9)r7c45 only exists in box 8 anyway, so I don't understand that objection. Adding the extra node as you suggest seems superfluous to me. Do you see Steve's notation as an improper shortcut?
I imagine you must object to the als version as well. |
I edited my post to remove the objectionable language. That was totally unacceptable on my part, and I apologize!
Yes. The logic is incorrect and I'll stand by my position that a Naked Triple in [c6] can never lead to an elimination in r7c45.
I do not object to Ted's ALS. I would object to your [(3=469)als:r589c6] because of the use of the naked triple. A naked triple implies eliminations in the unit containing it ... never the location of a specific value inside the naked triple.
An acceptable alternative (ala Ted):
[(3)r5c6=(9)r9c6]als:r589c6 |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Wed Apr 28, 2010 7:51 pm Post subject: |
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| daj95376 wrote: | | I would object to your [(3=469)als:r589c6] because of the use of the naked triple. A naked triple implies eliminations in the unit containing it ... never the location of a specific value inside the naked triple. |
I understand why you would prefer to see the (3)r5c6=(9)r9c6 presentation. There is a strong inference btwn any two values within an als, and presenting it the way you suggest clearly identifies the operative values.
I think the reason so many players include all of the values in a locked set is just to make it easier for the reader to identify the set itself. Just guessin, but you have to admit a lot of players do it that way.
I presented the moves in the first place because they were germane to discussions that were going on about hidden pairs and almost xy-wings. It was all about solving to me, not so much about notation.
BTW, I didn't find anything objectionable in your language; it's just a lively discussion. Didn't I once tell you I haven't got thin skin? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Apr 28, 2010 8:43 pm Post subject: |
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What makes it all the more interesting is that Steve used hp() in the proper context in his first chain. Then he slipped in an ALS relationship under the guise of a strong link with an nt(). That's when things went TILT for me.
Still, I shouldn't be the one to criticize. If you look at my suggested replacement chain, I believe it is technically correct but not really proper. RonK showed me the correct way to write it awhile back ... and I forgot.  Then I happened to reread Ted's message and noticed that he had the correct relationship.
It's been awhile since I've tried to unravel some on the solutions presented in Eureka!. I would hope they'd hold such notation to higher scrutiny.
As for ALS and the likes of hp() in this forum, I'm going to take the safe route and ignore solutions with them. |
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