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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Wed Nov 18, 2009 11:24 am Post subject: Puzzle NR 09/11/18 (XYZ) |
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Alert: XYZ-Wing present in my solver's solution.
| Code: | +-----------------------+
| . . . | 9 . . | . 7 6 |
| . . 9 | 8 6 . | . 2 . |
| . 6 . | . 2 . | . . . |
|-------+-------+-------|
| 1 8 . | 6 3 . | 7 . . |
| . 9 7 | 5 . . | . . 8 |
| . . . | . . . | . . 1 |
|-------+-------+-------|
| . . . | 2 . . | 8 . . |
| 9 2 . | . . . | . 5 7 |
| 8 . . | . 5 6 | . 3 9 |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Nov 18, 2009 4:48 pm Post subject: |
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| What is the significance of mentioning the presence of the XYZ? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Wed Nov 18, 2009 5:19 pm Post subject: |
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| Marty R. wrote: | | What is the significance of mentioning the presence of the XYZ? |
All too often, without the alert, the presence of an XYZ-Wing is missed by those solving the puzzle and they go through all sorts of gyrations coming up with an alternative -- like Medusa coloring. I wanted to reduce the discomfort by letting everyone know that finding the XYZ-Wing might help them in getting past a bottleneck. You're certainly free to ignore the alert!
Also, it supports my claim that I created an NR puzzle and not a more complex puzzle!!!
The good news is that I only have five more puzzles with XYZ-Wing present in my solver's solutions.
Regards, Danny |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Nov 18, 2009 6:06 pm Post subject: |
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Thanks for the response, even though I don't understand.
| Quote: | | All too often, without the alert, the presence of an XYZ-Wing is missed by those solving the puzzle and they go through all sorts of gyrations coming up with an alternative -- like Medusa coloring. I wanted to reduce the discomfort by letting everyone know that finding the XYZ-Wing might help them in getting past a bottleneck. |
What's different about an XYZ-Wing from XY, W, Kite UR, etc?
| Quote: | | The good news is that I only have five more puzzles with XYZ-Wing present in my solver's solutions. |
I don't know why that's "good" news. I like XYZ-Wings. But that's OK, no need to respond further, you've got better uses for your time. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Nov 18, 2009 8:04 pm Post subject: |
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| Code: | +-------------------+-----------------+-------------+
| 2 35 8 | 9 4 35 | 1 7 6 |
| 357 1357 9 | 8 6 1357 | 4 2 35 |
| 3457 6 134 | 13-7 2 1357 | 9 8 35 |
+-------------------+-----------------+-------------+
| 1 8 5 | 6 3 49 | 7 49 2 |
| 46 9 7 | 5 1 2 | 3 46 8 |
| 36-4 3(4) 2 | (47) 79 8 | 5 69-4 1 |
+-------------------+-----------------+-------------+
| 357 357 6 | 2 79 379 | 8 1 4 |
| 9 2 134 | 134 8 134 | 6 5 7 |
| 8 -1(47) 14 | 14(7) 5 6 | 2 3 9 |
+-------------------+-----------------+-------------+ |
Step #1...m-wing loop: (4=7)r6c4 - (7)r9c4 = (7-4)r9c2 = (4)r6c2; r6c1 and r6c8 <> 4,
r3c4 <> 7
| Code: | +-----------------+---------------+-----------+
| 2 5(3) 8 | 9 4 5(3) | 1 7 6 |
| 357 1 9 | 8 6 357 | 4 2 35 |
| 3457 6 34 | 13 2 1357 | 9 8 35 |
+-----------------+---------------+-----------+
| 1 8 5 | 6 3 (49) | 7 49 2 |
| 46 9 7 | 5 1 2 | 3 46 8 |
| 36 (34) 2 | 7-4 79 8 | 5 69 1 |
+-----------------+---------------+-----------+
| 35 357 6 | 2 79 (39) | 8 1 4 |
| 9 2 134 | 134 8 134 | 6 5 7 |
| 8 47 14 | 147 5 6 | 2 3 9 |
+-----------------+---------------+-----------+ |
Step #2...(4=3)r6c2 - (3)r1c2 = (3)r1c6 - (3=9)r7c6 - (9=4)r4c6; r6c4 <> 4
----
or you can combine the two for a one stepper if you notice this string of inferences from step #1...
(7)r9c4 = (7-4)r9c2 = (4)r6c2
| Code: | +------------------+-----------------+------------+
| 2 35 8 | 9 4 35 | 1 7 6 |
| 357 1357 9 | 8 6 1357 | 4 2 35 |
| 3457 6 134 | 137 2 1357 | 9 8 35 |
+------------------+-----------------+------------+
| 1 8 5 | 6 3 49 | 7 49 2 |
| 46 9 7 | 5 1 2 | 3 46 8 |
| 346 3(4) 2 | 47 79 8 | 5 469 1 |
+------------------+-----------------+------------+
| 357 357 6 | 2 79 379 | 8 1 4 |
| 9 2 134 | 134 8 134 | 6 5 7 |
| 8 1(47) 14 | 14(7) 5 6 | 2 3 9 |
+------------------+-----------------+------------+ |
notice how this string of inferences is weakly linked to the 7 in r7c6.
IOW, if the chain in step #2 is false...
[(4=3)r6c2 - (3)r1c2 = (3)r1c6 - (3=9)r7c6 - (9=4)r4c6]
then the 7 in r7c6 is true... leads too...
(7)r7c6 - (7)r9c4 = (7-4)r9c2 = (4)r6c2
and either way, the 4 in r6c4 is eliminated.
| Code: | +------------------+------------------+------------+
| 2 5(3) 8 | 9 4 5(3) | 1 7 6 |
| 357 1357 9 | 8 6 1357 | 4 2 35 |
| 3457 6 134 | 137 2 1357 | 9 8 35 |
+------------------+------------------+------------+
| 1 8 5 | 6 3 (49) | 7 49 2 |
| 46 9 7 | 5 1 2 | 3 46 8 |
| 346 (34) 2 | 7-4 79 8 | 5 469 1 |
+------------------+------------------+------------+
| 357 357 6 | 2 79 (379) | 8 1 4 |
| 9 2 134 | 134 8 134 | 6 5 7 |
| 8 1(47) 14 | 14(7) 5 6 | 2 3 9 |
+------------------+------------------+------------+ |
so we get this branched chain
[(4=3)r6c2 - (3)r1c2 = (3)r1c6 - (3=9)r7c6 - (9=4)r4c6] = (7)r7c6 - (7)r9c4 = (7-4)r9c2 = (4)r6c2; r6c4 <> 4 |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Wed Nov 18, 2009 10:43 pm Post subject: |
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I found a couple of different solutions for this puzzle; both were five steps. The one without the xyz-wing is:
x-wing 3,
UR 46,
w-wing 47,
useless xy-wing 1-47 with pincer transports
w-wing 35
I tried for some time to take advantage of the potential 6-cell DP 35 in boxes 1, 2 & 3 but could not find a deletion. Did anyone else pursue this possibility?
Ted |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Nov 19, 2009 12:20 am Post subject: |
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| tlanglet wrote: | I found a couple of different solutions for this puzzle; both were five steps. The one without the xyz-wing is:
x-wing 3,
UR 46,
w-wing 47,
useless xy-wing 1-47 with pincer transports
w-wing 35
I tried for some time to take advantage of the potential 6-cell DP 35 in boxes 1, 2 & 3 but could not find a deletion. Did anyone else pursue this possibility?
Ted |
do you mean in boxes 1,2,3 and columns 1, 6 and 9? |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Thu Nov 19, 2009 2:19 am Post subject: |
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| storm_norm wrote: | | tlanglet wrote: |
I tried for some time to take advantage of the potential 6-cell DP 35 in boxes 1, 2 & 3 but could not find a deletion. Did anyone else pursue this possibility?
Ted |
do you mean in boxes 1,2,3 and columns 1, 6 and 9? |
No, I mean columns 2, 6 and 9
Ted |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Nov 19, 2009 2:37 am Post subject: |
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| Code: | +-------------------+-----------------+--------------+
| 2 (35) 8 | 9 4 (35) | 1 7 6 |
| 357 (35)17 9 | 8 6 1357 | 4 2 (35) |
| 3457 6 134 | 137 2 (35)17 | 9 8 (35) |
+-------------------+-----------------+--------------+
| 1 8 5 | 6 3 49 | 7 49 2 |
| 46 9 7 | 5 1 2 | 3 46 8 |
| 346 34 2 | 47 79 8 | 5 469 1 |
+-------------------+-----------------+--------------+
| 357 357 6 | 2 79 379 | 8 1 4 |
| 9 2 134 | 134 8 134 | 6 5 7 |
| 8 147 14 | 147 5 6 | 2 3 9 |
+-------------------+-----------------+--------------+
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Nov 19, 2009 3:14 am Post subject: |
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| Code: | .------------------.------------------.------------------.
| 2 35 8 | 9 4 35 | 1 7 6 |
| 357 1357 9 | 8 6 1357 | 4 2 35 |
| 3457 6 134 | 137 2 1357 | 9 8 35 |
:------------------+------------------+------------------:
| 1 8 5 | 6 3 49 | 7 49 2 |
| 46 9 7 | 5 1 2 | 3 46 8 |
| 346 34 2 | 47 79 8 | 5 469 1 |
:------------------+------------------+------------------:
| 357 357 6 | 2 79 379 | 8 1 4 |
| 9 2 134 | 134 8 134 | 6 5 7 |
| 8 147 14 | 147 5 6 | 2 3 9 |
'------------------'------------------'------------------' |
found it, but I have to use a diagram.
in the DP on {3,5} in r123c269 we see that there are 4 candidates total within the DP cells that can destroy the deadly pattern.
{1,7} in r2c2 and {1,7} in r3c6
| Code: | (1)r2c2
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(7)r2c2 - (7)r79c2 = (7)r7c1 - (7)r7c5 = (7)r6c5 - (7=4)r6c4 - (4)r6c2 = (4)r9c2
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(1)r3c6 - (1)r3c3 = (1)r2c2
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(7)r6c3 - (7)r7c6
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(3)r7c6 - (3)r1c6 = (3)r2c6 - (3=4)r6c2 - (4=7)r6c4 - (7)r9c4 = (7)r9c2
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(9)r7c6 - (9=7)r7c5 - (7)r9c4 = (7)r9c2
all that to prove that r9c2 <> 1
which doesn't do very much. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Nov 19, 2009 4:20 am Post subject: |
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ok, I had my head in this for a while.
here is the one stepper off the DP 35 pattern
I wrote it all out as a diagram.
all this does is eliminate 4 from r9c2 and solves the puzzle.
from the same {1,7} candidates in r2c2 and r3c6.
 |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Nov 19, 2009 5:49 am Post subject: |
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ERs (3,3)
XYZ-Wing (147)
Type 4 UR (46)
Multi-coloring (4)
M-Wing (34) |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Thu Nov 19, 2009 1:17 pm Post subject: |
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Norm, that is the most impressive example of brute force, intelligent analysis of Sudoku I have ever seen or even imagined 
Congratulation...................
Ted |
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oaxen
Joined: 10 Jul 2006
Posts: 96
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| Posted: Thu Nov 19, 2009 6:13 pm Post subject: |
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| a "9" in r4c8 makes it a one stepper |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Nov 19, 2009 6:33 pm Post subject: |
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| Well, it looks like everyone had fun ... either with or without the XYZ-Wing. |
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