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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Wed Jun 23, 2010 8:17 pm Post subject: Puzzle 10/06/23: (C) XY |
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| Code: | +-----------------------+
| . 4 . | 2 . 6 | . . 9 |
| 1 6 . | . 9 7 | . . . |
| . . . | . 1 4 | . . 7 |
|-------+-------+-------|
| 5 . . | . . . | . . . |
| . 3 4 | . 5 . | . . . |
| 9 . 1 | . . 3 | 5 . . |
|-------+-------+-------|
| . . . | . . 9 | 6 . . |
| 3 . 5 | . . . | . 2 . |
| . 9 2 | . . . | . . 4 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site
| Code: | after basics
+-----------------------------------------------------------------------+
| 8 4 7 | 2 3 6 | 1 5 9 |
| 1 6 3 | 5 9 7 | 248 48 28 |
| 2 5 9 | 8 1 4 | 3 6 7 |
|-----------------------+-----------------------+-----------------------|
| 5 28 6 | 1479 478 128 | 2478 14789 3 |
| 7 3 4 | 169 5 128 | 28 189 1268 |
| 9 28 1 | 467 4678 3 | 5 478 268 |
|-----------------------+-----------------------+-----------------------|
| 4 1 8 | 37 2 9 | 6 37 5 |
| 3 7 5 | 46 46 18 | 9 2 18 |
| 6 9 2 | 13 78 5 | 78 13 4 |
+-----------------------------------------------------------------------+
# 49 eliminations remain
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Jun 24, 2010 6:48 am Post subject: |
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A couple of XY wings do it in two steps or:
ALS XZ
A = {1,2,4,6,7,8} (Pink)
B = {1,2,6,8} (Green)
Restricted Common x = 6 in row 6
Common Candidate z = 1 (Blue) so r8c6<>1
[Edit to reinsert image after demise of Tinypic]
Last edited by Mogulmeister on Thu Jul 15, 2021 2:44 pm; edited 4 times in total |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Jun 24, 2010 9:26 am Post subject: |
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Looking at those ALS you can also see an ANP
(1) ANP (6=28)r26c9-(8=1)r8c9-(1)r8c6 so r8c6<>1 (If NP True)
(2)ANP (28=6)r26c9-(6=478)r6c4|r46c5-(8=12)r45c6-(1)r8c6; r8c6<>1(IF NP False)
Tidier (!) is to show the complement to the ALS XZ elimination which is that r8c9<>8 by extending (2)
ANP (28=6)r26c9-(6=478)r6c4|r46c5-(8=12)r45c6-(1=8)r8c6 ie r8c9<>8
Last edited by Mogulmeister on Thu Jul 15, 2021 3:07 pm; edited 5 times in total |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Thu Jun 24, 2010 4:16 pm Post subject: |
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Blimey! I would never spot an ALS as complex as that in the proverbial month of sundays!! I did fiddle with the ANPs though but never quite got there..
My three steps more conventional...
| Quote: | w-wing(28); r2c7<>2, r56c9<>2
xy-chain (2=8)r5c7 - (8=7)r9c6 - (7=8)r9c5 - (8=1)r8c6 - (1=2)r4c6 ; r4c7<>2, r5c6<>2
kite(8); r8c9<>8 |
Perhaps I missed something because there were no xy-wings the path I took? |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Jun 24, 2010 4:24 pm Post subject: |
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Peter,
I used to think that also, but if you start with the same mindset that you might do anyway -looking at strongly linked bivalues- it is amazing how can spot these - especially if we remember how many of our well known patterns are "subsumed" by ALS.
It is true to say though that they aren't always productive and it can be frustrating but I find it -er- therapeutic. You have to "anchor" from a likely spot to look for qualifying conditions building outwards from the simplest XZs (ie shortest XY chain/ XY Wing). I often start by looking for the restricted common as a pivot to other things.
I like them because they feel more "spatial" to me and looking for them makes a welcome change from the usual suspects. Trying to construct them also helps assemble some of the "almost" gang. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Jun 24, 2010 4:32 pm Post subject: |
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I have no doubt that Danny could construct an algorithm that bags them (if he hasn't already!!).  |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Jun 24, 2010 4:42 pm Post subject: |
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Mogulmeister: That is one interesting ALS 
I might have noticed the green cells, but I agree with peterj about catching the pink cells. The only way I'd "bag" something like this is if I examined the SIN (forcing network) implication chains listed by my solver. Otherwise, I just review what others find.
| Code: | ALS [ (1)r45c6 = (6)r6c45 ] - ALS [ (6)r6c9 = (1)r8c9 ] => r8c6<>1
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Note #1: I don't handle ALS in my solver because I really don't know how to implement it. There are too many combinations of "almost" for me to negotiate. The only way I know to examine them all is to implement a brute-force DFS approach. Here's how your ALS would be viewed using this approach:
| Code: | Assume r8c6=1 =>
<28> Naked Pair [b5]
<467> Naked Triple [b5]
<6> Locked Candidate 1 [r6]
<28> Naked Pair [c9]
<1> Naked Single [r8c9]
-<1> r8c6 ... contradiction to assumption
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Note #2: The first version of my solver accidentally implemented this approach for chains. It finds most ALS eliminations. However, I can't reconstruct an ALS from its intermediate results.
| Quote: | A couple of XY wings do it in two steps ...
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You might want to review this claim. |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Thu Jun 24, 2010 6:05 pm Post subject: |
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| Mogulmeister wrote: | Peter,
I used to think that also, but if you start with the same mindset that you might do anyway -looking at strongly linked bivalues- it is amazing how can spot these - especially if we remember how many of our well known patterns are "subsumed" by ALS.
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My mindset seems more receptive to strong links in cells i.e. xy-chain sort of patterns, and so I often find chains with simple almost-pairs in them and then once I have concluded them I often see they are actual an AlS-XZ move - particularly if the chain goes up and down two columns. But they usually are triples/pair with a bivalue or possibly a pair, nothing as big as this. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Jun 24, 2010 6:43 pm Post subject: |
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| daj95376 wrote: |
| Quote: | A couple of XY wings do it in two steps ...
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You might want to review this claim. |
Thanks Danny - yes, I meant to say "a couple of xy wings and another 2 steps"  Thats what happens when you try to talk on the phone, watch the tennis and work on two separate screens.
Last edited by Mogulmeister on Fri Jun 25, 2010 9:04 am; edited 1 time in total |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Fri Jun 25, 2010 6:34 am Post subject: |
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| peterj wrote: | | Mogulmeister wrote: | Peter,
I used to think that also, but if you start with the same mindset that you might do anyway -looking at strongly linked bivalues- it is amazing how can spot these - especially if we remember how many of our well known patterns are "subsumed" by ALS.
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My mindset seems more receptive to strong links in cells i.e. xy-chain sort of patterns, and so I often find chains with simple almost-pairs in them and then once I have concluded them I often see they are actual an AlS-XZ move - particularly if the chain goes up and down two columns. But they usually are triples/pair with a bivalue or possibly a pair, nothing as big as this. |
I had exhausted my repertoire of moves that might secure an elimination in the <18> pair of cells, so I began with an ALS XZ in mind - not knowing if it were possible. So the reverse of what you just described Peter.
Looking for a common candidate (z) it soon becomes apparent that the <18> in b9 has no way (that I could find) of establishing a usable connection with the two sets A and B - its position means it must see 8s in two sets and can only see into b8 and b3 and b6. Any set formation with b8 means that the formed set would contains 8s that could no longer be seen by the 8 in b9. So out.
This leaves us with the 1 in b8 as the potential common candidate. There is a promising start when you see that the 1 in b8 sees a column of 1s in b5 AND the 1 in b9. So far so good.
However, there is still no bridge between the column of 1s in b5 and the single 1 in b9. To make a connection we need to extend out from b9. The ONLY place a connection can be made is in b6. It will not be enough to make a connection - that connection must also house the restricted common (x) (and this is often the place that this building process fails). This can only be done with the <268> in r6c9 and presents a problem as there are now 4 candidates and only 2 cells which means we have N+2 and so are one cell short (remember for an ALS, candidates must equal N+1 where number of cells = N) so we must also include the <28> in r2c9 to retain the N+1 for set A.
We now have two connected sets and a common candidate and a restricted common identified. We have a total of 3 cells in b5 but 6 candidates in all. We must either drop candidates or find another 2 cells to satisy ALS+1 AND not compromise the newly discovered restricted common. When I did this originally I thought I had narrowly failed and would be stuck with an almost ALS XZ (as I did in another thread*) but saw that I could add r6c4 and r4c5.
It sounds tortuous when I write it out but can be, (for me anyway) absorbing - especially when other lines of attack have failed.
*http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=4682&start=6
Ed - for N+1 and typos
Last edited by Mogulmeister on Fri Jun 25, 2010 11:49 am; edited 4 times in total |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Fri Jun 25, 2010 6:43 am Post subject: |
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| Bit like working with clay. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Fri Jun 25, 2010 8:41 am Post subject: |
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Forgive me, what's a DFS Danny ? Over here they're a sofa warehouse.  |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Fri Jun 25, 2010 1:37 pm Post subject: |
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Given the problems with my first XY puzzle, I was expecting the worst, but it was not a BBDBer.
1. Flightless w-wing 28 r2c9 & r4c2 with GSL 2 r245c7: (2)r2c9 - r8c9 = r9c7* - r9c5 = r8c6**; r4c67<>8
2. kite 8 with hinge box8; r5c7<>8
3. AUR19[(6)r5c4 = (8)r5c8]r45c48 - (8=6)r6c9; r6c45<>6
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Jun 25, 2010 2:58 pm Post subject: |
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| Mogulmeister wrote: | | Forgive me, what's a DFS Danny ? Over here they're a sofa warehouse. |
Depth-First Search: A search methodology. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Fri Jun 25, 2010 5:58 pm Post subject: |
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| Thanks. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Jun 26, 2010 12:13 pm Post subject: |
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W-Wing (28)
ER (8)
X-Wing (8) |
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