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andras
Joined: 31 Oct 2007
Posts: 56
Location: Mid Wales
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 Posted: Mon May 19, 2008 8:14 am Post subject: VH May 19 - contains spoilers! |
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An interesting one today - I used four different xy-wings (three of them on 1,3,8 and the other on 1,4,7), but I suspect that there are quicker ways of getting there.
Any offers? 
John |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon May 19, 2008 10:15 am Post subject: |
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I accept the offer, John.
this xy-wing shown below is a little more powerful than just killing off the 3 in r5c8
because either 3 on each end of the xy-wing is true, the coloring can be extended...
medusa says that if we color the 3's in r4c3 and r1c8 both green, then we can extend the coloring so that the 1 and 3 in r1c5 can see both green and blue and can be eliminated. solving the puzzle.
Last edited by storm_norm on Mon May 19, 2008 8:09 pm; edited 1 time in total |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Mon May 19, 2008 10:30 am Post subject: |
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I used the 27 UR* in R79C28, which pins <5> in R7C3 collapsing the whole puzzle. Notice when R7C3=3, digit <1> must be in R7C8 otherwise we have a 27 Deadly Pattern in R79C28. But when R7C3=3 => R9C5=3 => R7C5=4 => R7C7=1 which results in a 27 DP so R7C3 must be <5>.
| Code: | +-------------------------+-------------------------+-------------------------+
| 6 18 2 | 5 138 4 | 7 13 9 |
| 7 5 189 | 1238 1389 239 | 1348 6 148 |
| 3 4 189 | 168 16789 79 | 18 5 2 |
+-------------------------+-------------------------+-------------------------+
| 2 9 37 | 13 5 8 | 6 4 17 |
| 15 38 4 | 7 139 6 | 2 139 158 |
| 15 6 378 | 4 2 39 | 138 1379 1578 |
+-------------------------+-------------------------+-------------------------+
| 9 * 237 [=3]5 | 238 3[=4]78 2357 |[=1]4 * 127 6 |
| 4 127 15 | 26 67 257 | 9 8 3 |
| 8 * 237 6 | 9 [=3]47 1 | 5 * 27 47 |
+-------------------------+-------------------------+-------------------------+ |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon May 19, 2008 10:36 am Post subject: |
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| Johan wrote: | I used the 27 UR* in R79C28, which pins <5> in R7C3 collapsing the whole puzzle. Notice when R7C3=3, digit <1> must be in R7C8 otherwise we have a 27 Deadly Pattern in R79C28. But when R7C3=3 => R9C5=3 => R7C5=4 => R7C7=1 which results in a 27 DP so R7C3 must be <5>.
| Code: | +-------------------------+-------------------------+-------------------------+
| 6 18 2 | 5 138 4 | 7 13 9 |
| 7 5 189 | 1238 1389 239 | 1348 6 148 |
| 3 4 189 | 168 16789 79 | 18 5 2 |
+-------------------------+-------------------------+-------------------------+
| 2 9 37 | 13 5 8 | 6 4 17 |
| 15 38 4 | 7 139 6 | 2 139 158 |
| 15 6 378 | 4 2 39 | 138 1379 1578 |
+-------------------------+-------------------------+-------------------------+
| 9 * 237 [=3]5 | 238 3[=4]78 2357 |[=1]4 * 127 6 |
| 4 127 15 | 26 67 257 | 9 8 3 |
| 8 * 237 6 | 9 [=3]47 1 | 5 * 27 47 |
+-------------------------+-------------------------+-------------------------+ |
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nice!!! |
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andras
Joined: 31 Oct 2007
Posts: 56
Location: Mid Wales
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| Posted: Mon May 19, 2008 12:35 pm Post subject: |
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Nice one, Norm!
John |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Mon May 19, 2008 1:58 pm Post subject: |
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Thought this was a VH VH. Seemed to be an awful lot of clutter still remaining after basics.
I could only find wings:
<147> xy wing to remove <1> in R6C7
<138> xy wing to remove <3> in R56C8 (leaves a single <3> Box 6)
x wing for <3>
<138> xy wing |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon May 19, 2008 3:19 pm Post subject: |
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For me, this was one of the longest, most difficult VH for a very long time. (Obviously I did not see any of the killer solutions already reported.)
After basics, I found a Swordfish on 3s that cleared several cells. Then I addressed the potential <15> UR in r56c19 and using an xy chain, determined that r6c9 could not be <7> which resulted in a basic Type 2 UR allowing the <8> in r2c9 to be removed. Then coloring on 1s, xy-wing on <138>, coloring on 1s again and finally another xy-wing on <138> broke it open. I need a nap! 
Ted |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon May 19, 2008 3:37 pm Post subject: |
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| I used two XY-Wings, the 15 UR in rows 56 and another XY-Wing to finish it off. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon May 19, 2008 3:39 pm Post subject: |
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Norm,
I have never tried medusa so I was not able to follow your explanation but will, in fact, read up on it this afternoon.
However, pursuing your line of thought, I used normal coloring to extend the two pincers on 3s from r1c8 to r1c5 and from r5c2 to r5c5 so that all other 3s in c5 can be removed which also solves the puzzle
Ted |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Mon May 19, 2008 10:39 pm Post subject: |
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| storm_norm wrote: | I accept the offer, John.
this xy-wing shown below is a little more powerful than just killing off the 3 in r5c8
because either 3 on each end of the xy-wing is true, the coloring can be extended...
medusa says that if we color the 3's in r4c3 and r1c8 both green, then we can extend the coloring so that the 1 and 3 in r1c5 can see both green and blue and can be eliminated. solving the puzzle. |
Norm, I am having a problem understanding your medusa extended coloring. You start with the 3s in r4c3 and r1c8 both green. I assume that you colored the pincers in the original xy-wing with green in r1c8 and blue in r5c2 followed by an extension on 3 get the green 3 at r4c3. In your diagram, you seem to show the green 3 in the original xy-wing pincer location, r5c2. At his point I am confused.
Given the green 3 in r5c2, I understand the <13> eliminations in r1c5.
Overall, I am lost on my first venture into medusa. Gory details would be much appreciated.
Ted  |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon May 19, 2008 11:18 pm Post subject: |
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Ted, very good, you are right.
this is what the coloring should look like, and I apologize for the mistake. and you are also right that the 3's in col 5 are eliminated by the 3 in r1c5 and r5c5 being colored green and blue. as follows.
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon May 19, 2008 11:27 pm Post subject: |
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Norm,
I'm not following your Medusa Multi-coloring logic. First, it appears you colored the <3> in r5c2 (not r4c3) green (they can't both be green). Your elimination is valid only if those pincers are conjugate (which they turn out to be in this case ... you were lucky).
In Medusa multi-coloring, it is dangerous to use the same color (in this case, green) for the strong pair in two different clusters. If I use "A" and "B" instead, the coloring looks like this (after fixing the hidden single <9> in r5c8):
| Code: | +------------------+------------------+------------------+
| 6 18 2 | 5 13a8 4 | 7 1a3A 9 |
| 7 5 189 | 1238 1389 23 | 1348 6 148 |
| 3 4 189 | 168 1689 7 | 18 5 2 |
+------------------+------------------+------------------+
| 2 9 3b7B | 1b3B 5 8 | 6 4 17 |
| 15 3B8b 4 | 7 1B3b 6 | 2 9 158 |
| 15 6 78 | 4 2 9 | 138 137 1578 |
+------------------+------------------+------------------+
| 9 1237 35 | 238 3478 235 | 14 127 6 |
| 4 127 15 | 26 67 25 | 9 8 3 |
| 8 237 6 | 9 347 1 | 5 27 47 |
+------------------+------------------+------------------+ |
"AB" is the strong pair and "ab" is the weak pair. Notice that the <1> in r1c8 is colored "a" and the <3> in r5c5 is colored "b". You colored both of these "blue." However, they aren't actually the same color. (However, if AB is conjugate, then ab is also conjugate and the two clusters merge, allowing your elimination. But you have not demonstrated that AB is conjugate.)
Meanwhile, we CAN use those XY-Wing pincers to eliminate the <3> in r1c5 via the ERs in b78: r1c5 sees the r1c8 <3> directly and the r5c2 <3> via the two ERs. (You could also see this as "transporting" the <3> in r5c2 to r7c3 and then to r9c5.) And, the <1> is eliminated by the XY-Wing with r5c2 pivot, determining r1c5 as <8>. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon May 19, 2008 11:37 pm Post subject: |
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Ted/Norm,
I just want to emphasize: Wing pincers cannot be assumed to be conjugate. We can only assume the strong inference. Therefore, coloring from from wing pincers must be done with multi-coloring with a separate cluster colored from each pincer. The two pincer colors form the strong pair. Those <3> eliminations in c5 are not valid (even though they turn out to be correct in this case). |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue May 20, 2008 5:22 am Post subject: |
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Ted,
very sorry, I hope I didn't mislead you. that was bad logic on my part. the overkill tactic was probably uncalled for. however, I find it a challenge to find moves, as Johan did, to kill it as fast as possible. I need to be more careful along the way.
Asellus,
thanx, as always. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Tue May 20, 2008 12:42 pm Post subject: |
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Norm and All,
I am immensely in awe of all you folks who contribute to this forum with a multitude of ingenuous solutions; I struggle to just find the mechanical patterns. Frankly, my ego gets just a little boost when one you gurus has a problem, so no apology is necessary.
The bottom line is that as a result of this exchange, I now (hopefully) understand more that I did before it occurred.
Thanks again for all the help from everyone.
Ted |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Tue May 20, 2008 4:40 pm Post subject: |
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| Asellus wrote: | Norm,
I'm not following your Medusa Multi-coloring logic. First, it appears you colored the <3> in r5c2 (not r4c3) green (they can't both be green). Your elimination is valid only if those pincers are conjugate (which they turn out to be in this case ... you were lucky).
In Medusa multi-coloring, it is dangerous to use the same color (in this case, green) for the strong pair in two different clusters. If I use "A" and "B" instead, the coloring looks like this (after fixing the hidden single <9> in r5c8):
| Code: | +------------------+------------------+------------------+
| 6 18 2 | 5 13a8 4 | 7 1a3A 9 |
| 7 5 189 | 1238 1389 23 | 1348 6 148 |
| 3 4 189 | 168 1689 7 | 18 5 2 |
+------------------+------------------+------------------+
| 2 9 3b7B | 1b3B 5 8 | 6 4 17 |
| 15 3B8b 4 | 7 1B3b 6 | 2 9 158 |
| 15 6 78 | 4 2 9 | 138 137 1578 |
+------------------+------------------+------------------+
| 9 1237 35 | 238 3478 235 | 14 127 6 |
| 4 127 15 | 26 67 25 | 9 8 3 |
| 8 237 6 | 9 347 1 | 5 27 47 |
+------------------+------------------+------------------+ |
"AB" is the strong pair and "ab" is the weak pair. Notice that the <1> in r1c8 is colored "a" and the <3> in r5c5 is colored "b". You colored both of these "blue." However, they aren't actually the same color. (However, if AB is conjugate, then ab is also conjugate and the two clusters merge, allowing your elimination. But you have not demonstrated that AB is conjugate.)
Meanwhile, we CAN use those XY-Wing pincers to eliminate the <3> in r1c5 via the ERs in b78: r1c5 sees the r1c8 <3> directly and the r5c2 <3> via the two ERs. (You could also see this as "transporting" the <3> in r5c2 to r7c3 and then to r9c5.) And, the <1> is eliminated by the XY-Wing with r5c2 pivot, determining r1c5 as <8>. |
Asellus,
I believe that I understand your point about conjugate pincers, but I have one more question on this topic please. Specifically, you indicate that the xy-wing pincers AB are in fact conjugate, but that fact was not demonstrated. How do you demonstrate it?
Ted (Still trying to learn  ) |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue May 20, 2008 9:22 pm Post subject: |
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| Ted wrote: | | I believe that I understand your point about conjugate pincers, but I have one more question on this topic please. Specifically, you indicate that the xy-wing pincers AB are in fact conjugate, but that fact was not demonstrated. How do you demonstrate it? |
Well, one way is to extend that Bb coloring on the <8>s in c2 and r1:
| Code: | +------------------+------------------+------------------+
| 6 18B 2 | 5 13a8b 4 | 7 1a3A 9 |
| 7 5 189 | 1238 1389 23 | 1348 6 148 |
| 3 4 189 | 168 1689 7 | 18 5 2 |
+------------------+------------------+------------------+
| 2 9 3b7B | 1b3B 5 8 | 6 4 17 |
| 15 3B8b 4 | 7 1B3b 6 | 2 9 158 |
| 15 6 78 | 4 2 9 | 138 137 1578 |
+------------------+------------------+------------------+
| 9 1237 35 | 238 3478 235 | 14 127 6 |
| 4 127 15 | 26 67 25 | 9 8 3 |
| 8 237 6 | 9 347 1 | 5 27 47 |
+------------------+------------------+------------------+ |
Now, apply that 18-83-31 XY Wing in c2 and r5 to remove <1> from r1c5. We are left with the 3a8b bivalue in r1c5. This makes the ab weak pair conjugate, which in turn makes the strong AB pair conjugate (and merges the Aa and Bb clusters into a single cluster, as it happens ... so Aa, Bb, AB and ab are all conjugate pairs).
How's that? |
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