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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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 Posted: Sat Nov 27, 2010 1:28 am Post subject: # 1965 competition |
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370001002000002600090300000400000051000904000520000000000000080005609000010700023
| Code: |
+-------+-------+-------+
| 3 7 . | . . 1 | . . 2 |
| . . . | . . 2 | 6 . . |
| . 9 . | 3 . . | . . . |
+-------+-------+-------+
| 4 . . | . . . | . 5 1 |
| . . . | 9 . 4 | . . . |
| 5 2 . | . . . | . . . |
+-------+-------+-------+
| . . . | . . . | . 8 . |
| . . 5 | 6 . 9 | . . . |
| . 1 . | 7 . . | . 2 3 |
+-------+-------+-------+
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Nov 27, 2010 3:52 pm Post subject: |
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[code]*-----------------------------------------------------------*
| 3 7 46 | 5 689 1 | 48 49 2 |
|*18 5 1-8 | 4 79 2 | 6 3 79 |
| 26 9 246 | 3 678 678 | 1478 147 5 |
|-------------------+-------------------+-------------------|
| 4 68 9 | 28 2367 367 | 37 5 1 |
|*178 368 1378 | 9 5 4 | 2 67 78 |
| 5 2 *78 | 18 1367 367 | 347 4679 4789 |
|-------------------+-------------------+-------------------|
| 279 4 237 | 12 123 35 | 59 8 6 |
| 28 38 5 | 6 238 9 | 147 147 47 |
| 689 1 68 | 7 4 58 | 59 2 3 |
*-----------------------------------------------------------*[/code]
AXY-wing 17-8 vertex (17)r5c1, pincers (18)r2c1 & (78)r6c3 with fin (8)r5c1
xy-wing (17-8)=(8)r5c1-(8=7)r5c9-(7=9)r2c9-(9=4)r1c8-(4=6)r1c3-(6=2)r3c1-(2=8)r8c1; contradiction => r2c3<>8=1
Ted |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Sat Nov 27, 2010 5:57 pm Post subject: |
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I played the two xy-wings first time through...
| Code: | xy-wing(28-6) r8c1 ; r9c1<>6, r13c3<>6
xy-wing(17-8) r5c1 ; r2c3<>8 |
The second one being Ted's almost one. Ted, just btw you could finish your fin (4=6)r1c3-(6=8)r9c3 to make the same elimination rather than the contradiction - if preferred.
Here's a nice one-stepper using a strong link from a UR...
| Code: | *-----------------------------------------------------------------*
| 3 7 46 | 5 689 1 | 48 49 2 |
| (18) 5 1-8 | 4 79 2 | 6 3 79 |
| 26 9 246 | 3 678 678 | 1478 147 5 |
|-------------------------+-------------------+-------------------|
| 4 68 9 | 28 2367 367 | 37 5 1 |
| (1)8+(7) 368 (1)8+(37)| 9 5 4 | 2 67 78 |
| 5 2 (78) | 18 1367 367 | 347 4679 4789 |
|-------------------------+-------------------+-------------------|
| 279 4 237 | 12 123 35 | 59 8 6 |
| 28 38 5 | 6 238 9 | 147 147 47 |
| 689 1 68 | 7 4 58 | 59 2 3 |
*-----------------------------------------------------------------*
(8=7)r6c3 - UR(18)r25c13[(7)r5c13=(3)r5c3] - (1)r5c3=r5c1 - (1=8)r2c1 ; r2c3<>8 |
[Edit.Tom should be Ted. It was a long day...]
Last edited by peterj on Sun Nov 28, 2010 9:37 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: Sat Nov 27, 2010 6:29 pm Post subject: |
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I had three XY-wings: -479, 2-68, 17-8.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Nov 27, 2010 11:04 pm Post subject: |
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I played the 286 and 673 XY-Wings.
Then the DP 14-17-47 created pincers on 3; r6c5<>3, after which the grid was reduced to a BUG+2. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Nov 27, 2010 11:07 pm Post subject: |
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This is just to format Ted's grid.
| tlanglet wrote: | | Code: | *-----------------------------------------------------------*
| 3 7 46 | 5 689 1 | 48 49 2 |
|*18 5 1-8 | 4 79 2 | 6 3 79 |
| 26 9 246 | 3 678 678 | 1478 147 5 |
|-------------------+-------------------+-------------------|
| 4 68 9 | 28 2367 367 | 37 5 1 |
|*178 368 1378 | 9 5 4 | 2 67 78 |
| 5 2 *78 | 18 1367 367 | 347 4679 4789 |
|-------------------+-------------------+-------------------|
| 279 4 237 | 12 123 35 | 59 8 6 |
| 28 38 5 | 6 238 9 | 147 147 47 |
| 689 1 68 | 7 4 58 | 59 2 3 |
*-----------------------------------------------------------* |
AXY-wing 17-8 vertex (17)r5c1, pincers (18)r2c1 & (78)r6c3 with fin (8)r5c1
xy-wing (17-8)=(8)r5c1-(8=7)r5c9-(7=9)r2c9-(9=4)r1c8-(4=6)r1c3-(6=2)r3c1-(2=8)r8c1; contradiction => r2c3<>8=1
Ted |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Nov 28, 2010 2:32 am Post subject: |
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This puzzle combines three strong links in a way that always amazes me at its simplicity (and difficulty to find).
| Code: | (1)r5c1 = (1 )r5c3
( -3)r5c3 = (3 )r7c3
( -7)r7c3 = (7)r7c1 => r5c1<>7
+--------------------------------------------------------------+
| 3 7 46 | 5 689 1 | 48 49 2 |
| 18 5 18 | 4 79 2 | 6 3 79 |
| 26 9 246 | 3 678 678 | 1478 147 5 |
|--------------------+--------------------+--------------------|
| 4 68 9 | 28 2367 367 | 37 5 1 |
| 178 368 1378 | 9 5 4 | 2 67 78 |
| 5 2 78 | 18 1367 367 | 347 4679 4789 |
|--------------------+--------------------+--------------------|
| 279 4 237 | 12 123 35 | 59 8 6 |
| 28 38 5 | 6 238 9 | 147 147 47 |
| 689 1 68 | 7 4 58 | 59 2 3 |
+--------------------------------------------------------------+
# 76 eliminations remain
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Nov 28, 2010 3:42 am Post subject: |
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Danny, a different way to look at it:
If R7C1 <>7, R7C3 <>23, R5C3 <3>;
If R7C1 <>7, R5C1 <>18, R5C3 <1>;
Thus R7C1 <7>.
There may be a recipe here. I'll have to think about it. Something like a rectangle:
| Code: | aX - {X} - bXY
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{X} {Y}
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cXZ - {Z} - dYZ |
a, b, c, d are any values, and also the cell labels.
{X} is a strong link in X, etc.
Not X in a implies Y in d, via b.
Not X in a implies Z in d, via c.
Thus, a is X. (Because, if a is not X, there is a contradiction in d.)
Seems to me it is a Medusa reverse skyscraper, or some other backward (inverse) logic.
We have noted a few times that there are a number of unnamed four-link chains, unnamed because they are not recognizable and therefore not useful. This may be one that becomes useful!
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Nov 28, 2010 3:57 pm Post subject: |
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| keith wrote: | There may be a recipe here. I'll have to think about it. Something like a rectangle:
| Code: | aX - {X} - bXY
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{X} {Y}
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cXZ - {Z} - dYZ
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... This may be one that becomes useful!
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Thanks Keith for the analysis. Unfortuntately, you have one more strong link than mandated by the conditions of the chain.
| Code: | aX - {X} - bXY
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{Y}
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cZ - {Z} - dYZ
"a" can not contain "Z"
"c" can not contain "X"
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This is an example of using three strong links in an unnamed pattern. (No, I don't want to name it.)
I've encountered this pattern often -- especially as a single-stepper in puzzles that would normally use several conventional steps.
Regards, Danny
[Edit: added last line in code block.]
Last edited by daj95376 on Sun Nov 28, 2010 5:59 pm; edited 1 time in total |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sun Nov 28, 2010 4:43 pm Post subject: |
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Looks like two overlapping L-Wings.
[edit: add link]
Last edited by ronk on Sun Nov 28, 2010 7:03 pm; edited 1 time in total |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Nov 28, 2010 5:18 pm Post subject: |
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Danny,
I think we are both correct. The patterns (and conclusions) are slightly different.
I'll keep an eye out for this kind of thing. I guess the usual questions apply: Is it common? Is it useful? Is it easy to spot?
(I guess I'll have to find out what an L-wing is.)
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Nov 28, 2010 5:48 pm Post subject: |
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| ronk wrote: | Looks like two overlapping L-Wings.
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Okay, I checked your updated post and its reference link. I confess to failing to include the L3-Wing in my notes file. Thanks for keeping me honest.
Regards, Danny
[Edit: acknowledged ronk's reference link.]
Last edited by daj95376 on Sun Nov 28, 2010 9:39 pm; edited 1 time in total |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Nov 28, 2010 6:06 pm Post subject: |
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| keith wrote: | I think we are both correct. The patterns (and conclusions) are slightly different.
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I'm not so sure. I went back and appended "c" is not "X" as an additional conclusion to my scenario. That ruins your scenario.
| keith wrote: | I'll keep an eye out for this kind of thing. I guess the usual questions apply: Is it common? Is it useful? Is it easy to spot?
(I guess I'll have to find out what an L-wing is.)
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I think the pattern is common. It's often useful. And I think it probably qualifies as difficult to spot. A search option is to find a strong link, "Y", and look for two strong links radiating from it and having endpoints in the same house.
The definition of L2/L3-Wing are in ronk's post above.
[Edit: corrected L-Wing comment.]
Last edited by daj95376 on Sun Nov 28, 2010 10:04 pm; 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: Sun Nov 28, 2010 7:26 pm Post subject: |
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Danny,
My scenario is: a is X.
Your scenario is: a is not Z.
In your scenario, I see the logic as:
i) a may be X, in which case it is not Z.
ii) Or: a is not X, in which case c is Z, and a is not Z.
In both cases, of course, c is not X.
My scenario can be argued a couple of ways. Here is one:
i) a is not X implies c is X via the strong link between a and c.
ii) And: a is not X implies c is Z, as in your scenario.
This is a contradiction: a must therefore be X. (And, of course, c is not X.)
I will take a look at the L-wing
Best wishes,
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Nov 28, 2010 10:00 pm Post subject: |
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| keith wrote: | My conclusion is: a is X.
Your conclusion is: a is not Z, c is not X.
In your scenario, I see the logic as:
i) a may be X, in which case it is not Z and c is not X.
ii) Or: a is not X, in which case c is Z and not X, and a is not Z.
In both cases, of course, c is not X.
My scenario can be argued a couple of ways. Here is one:
i) a is not X implies c is X via the strong link between a and c.
ii) And: a is not X implies c is Z, as in your scenario.
This is a contradiction: a must therefore be X. (And, of course, c is not X.)
I will take a look at the L-wing
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Your scenario requires an additonal strong link, (i), on X between a and c. This is an extraneous constraint that isn't present in this puzzle and is probably less likely to be present in other puzzles as well. Basically, you've over-constrained the situation.
Regards, Danny
Ron: I forgot all about your L3-Wing scenario. I updated my post above. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Nov 29, 2010 12:19 am Post subject: |
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| daj95376 wrote: | | Your scenario requires an additonal strong link, (i), on X between a and c. This is an extraneous constraint that isn't present in this puzzle and is probably less likely to be present in other puzzles as well. Basically, you've over-constrained the situation. |
Danny,
If you can show how your scenario concludes that a is X, I will concede that my scenario is over constrained.
Otherwise, my scenario, with an additional constraint (compared to yours), reaches a different conclusion (compared to yours).
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Nov 29, 2010 1:46 am Post subject: |
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| Quote: | | This is an extraneous constraint that isn't present in this puzzle and is probably less likely to be present in other puzzles as well. |
On the contrary: | Code: | +----------------+----------------+----------------+
| 3 7 46 | 5 689 1 | 48 49 2 |
| 18 5 18 | 4 79 2 | 6 3 79 |
| 26 9 246 | 3 678 678 | 1478 147 5 |
+----------------+----------------+----------------+
| 4 68 9 | 28 2367 367 | 37 5 1 |
| 178d 368 1378c| 9 5 4 | 2 67 78 |
| 5 2 78 | 18 1367 367 | 347 4679 4789 |
+----------------+----------------+----------------+
| 279a 4 237b | 12 123 35 | 59 8 6 |
| 28 38 5 | 6 238 9 | 147 147 47 |
| 689 1 68 | 7 4 58 | 59 2 3 |
+----------------+----------------+----------------+ |
If a is not 7, b is 7 not 3, c is 3 not 1, d is 1 not 7, a is 7.
Exactly the pattern I spelled out in my scenario.
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Mon Nov 29, 2010 6:03 am Post subject: |
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| keith wrote: | | Quote: | | This is an extraneous constraint that isn't present in this puzzle and is probably less likely to be present in other puzzles as well. |
On the contrary: | Code: | +----------------+----------------+----------------+
| 3 7 46 | 5 689 1 | 48 49 2 |
| 18 5 18 | 4 79 2 | 6 3 79 |
| 26 9 246 | 3 678 678 | 1478 147 5 |
+----------------+----------------+----------------+
| 4 68 9 | 28 2367 367 | 37 5 1 |
| 178d 368 1378c| 9 5 4 | 2 67 78 |
| 5 2 78 | 18 1367 367 | 347 4679 4789 |
+----------------+----------------+----------------+
| 279a 4 237b | 12 123 35 | 59 8 6 |
| 28 38 5 | 6 238 9 | 147 147 47 |
| 689 1 68 | 7 4 58 | 59 2 3 |
+----------------+----------------+----------------+ |
If a is not 7, b is 7 not 3, c is 3 not 1, d is 1 not 7, a is 7.
Exactly the pattern I spelled out in my scenario.
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I acknowledge that the part in red is incorrect.
If you stop after the logic in blue, then you have my scenario and can deduce a<>1 & d<>7 -- independent of a fourth strong link being present. With my scenario, a conclusion can be reached whether we start with the strong link on <1> or the strong link on <7>. Your scenario only reaches a conclusion if we start with the strong link on <7>.
In a puzzle where the fourth strong link doesn't exist, then your scenario doesn't exist but my scenario and eliminations would still exist. In a puzzle where the fourth strong link does exist, then your conclusion would follow as a Hidden Single after applying my scenario. This is why I think your fourth strong link is an extraneous constraint.
Regards, Danny
| Code: | example where 4th strong link is not present (in [r4])
(1)r4c4 = (1-3)r7c4 = (3-5)r7c2 = (5)r4c2 => r4c4<>5 (and r4c2<>1)
r6c4=5 follows independently
+--------------------------------------------------------------+
| 5 2 1 | 6 9 7 | 3 4 8 |
| 6 7 4 | 2 8 3 | 59 1 59 |
| 8 9 3 | 4 1 5 | 6 7 2 |
|--------------------+--------------------+--------------------|
| 7 d58 2589 | a19-5 3 129 | 4 6 159 |
| 4 6 259 | 8 7 129 | 1259 59 3 |
| 3 1 259 | 59 4 6 | 2589 589 7 |
|--------------------+--------------------+--------------------|
| 9 c358 58 | b13 6 18 | 7 2 4 |
| 2 4 6 | 7 5 89 | 189 3 19 |
| 1 38 7 | 39 2 4 | 589 589 6 |
+--------------------------------------------------------------+
# 43 eliminations remain
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Nov 29, 2010 12:47 pm Post subject: |
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Whatever.
Keith |
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