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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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 Posted: Tue Mar 09, 2010 2:51 pm Post subject: Mepham Diabolical 1694 |
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| Code: | +---+---+---+
|4..|5.2|..1|
|...|.1.|..6|
|..6|..8|5..|
+---+---+---+
|..5|...|1.3|
|..1|.4.|7..|
|9.7|...|6..|
+---+---+---+
|..8|3..|2..|
|1..|.7.|...|
|7..|6.9|..5|
+---+---+---+
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Tue Mar 09, 2010 6:19 pm Post subject: |
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Very interesting puzzle ... a "Symphony in Three"
Too bad I don't have time to come here more often and enjoy puzzles like this one.
After basics,
| Code: |
+--------------------------+--------------------------+--------------------------+
| 4 7 39 | 5 6 2 | 89 389 1 |
| 5 8 239 | 79 1 37 | 4 239 6 |
| 23 1 6 | 4 39 8 | 5 2379 279 |
+--------------------------+--------------------------+--------------------------+
| 28 246 5 | 2789 289 67 | 1 2489 3 |
| 238 236 1 | 289 4 356 | 7 2589 289 |
| 9 234 7 | 1 238 35 | 6 2458 248 |
+--------------------------+--------------------------+--------------------------+
| 6 9 8 | 3 5 1 | 2 47 47 |
| 1 5 23 | 28 7 4 | 389 6 89 |
| 7 23 4 | 6 28 9 | 38 1 5 |
+--------------------------+--------------------------+--------------------------+
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there is a skyscraper (3) in cols 1 and 5 (eliminating 3 from r5c6 and r6c2).
But more than that, the strong link (3) r8c3=r8c7 serves as the basis for an m-wing (9)r1c3=r1c7 (r1c8<>9),
which in turn forms a continuous loop and takes out a few more candidates: r8c7<>8, r2c3<>3.
With 3 gone from r2c3, there is now a strong link (3) in box 1 and another m-wing (9)r3c5=r1c7 (r3c89<>9) finishes the puzzle. |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Tue Mar 09, 2010 6:59 pm Post subject: |
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For two steps
(3=2)r8c3 - (2=3)r9c2 - (3=8)r9c7 - (8=9)r1c7 - (9=3)r1c3; r2c3<>3
xy-wing 239 takes out the 9 in r2c4 solving the puzzle
For one step:
(9)r1c7 = (9-3)r8c7 = (3-1)r8c3 = (2)r2c3 - (2=3)r3c1 - (3=9)r3c5; r3c89<>9 |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Wed Mar 10, 2010 2:43 pm Post subject: |
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Well this puzzle lead me on a merry chase for a total of five moves and lots of transports. Each move seemed to use some common cells, which were also generally used in the earlier posts. I just did not seem to find the sweet spot with my deletions.
I had a flightless xy-wing 23-8 plus two transports,
An AIC starting with a potential xy-wing 23-9,
An ALS A & B in box9,
xy-wing -239 plus two transports,
Another AIC starting with a potential xy-wing 38-9 plus two transports.
I had a total of ten deletions!
Ted |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Mar 10, 2010 8:40 pm Post subject: |
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a bit late with this one stepper.
| Code: | +-------------------+-------------------+------------------+
| 4 7 (39) | 5 6 2 | 8(9) 389 1 |
| 5 8 2(9-3) | (79) 1 -7(3) | 4 239 6 |
| 2(3) 1 6 | 4 9(3) 8 | 5 2379 279 |
+-------------------+-------------------+------------------+
| 28 246 5 | 2789 289 67 | 1 2489 3 |
| 238 236 1 | 289 4 356 | 7 2589 289 |
| 9 234 7 | 1 238 35 | 6 2458 248 |
+-------------------+-------------------+------------------+
| 6 9 8 | 3 5 1 | 2 47 47 |
| 1 5 2(3) | 28 7 4 | 8(39) 6 89 |
| 7 23 4 | 6 28 9 | 38 1 5 |
+-------------------+-------------------+------------------+ |
(7=9)r5c6 - (9)r2c3 = (9)r1c3 - (9)r1c7 = (9-3)r8c7 = (3)r8c3 - (3)r12c3 = (3)r3c1 - (3)r3c5 = (3)r2c6; r2c6 <> 7 |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Mar 11, 2010 1:53 am Post subject: |
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I used:
XY-Wing (893) with pincer transport
Multi-coloring (3)
M-Wing (39)
W-Wing (23) with pincer transport |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Mar 11, 2010 9:14 am Post subject: |
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After basics: | Code: | +----------------+----------------+----------------+
| 4 7 39c | 5 6 2 | 89d 38-9 1 |
| 5 8 2-39 | 79 1 37 | 4 239 6 |
| 23 1 6 | 4 39 8 | 5 2379 279 |
+----------------+----------------+----------------+
| 28 246 5 | 2789 289 67 | 1 2489 3 |
| 238 236 1 | 289 4 356 | 7 2589 289 |
| 9 234 7 | 1 238 35 | 6 2458 248 |
+----------------+----------------+----------------+
| 6 9 8 | 3 5 1 | 2 47 47 |
| 1 5 23b | 28 7 4 |3-89 6 89 |
| 7 23a 4 | 6 28 9 | 38e 1 5 |
+----------------+----------------+----------------+ |
abcd is a loop, making the eliminations shown.
An XY-wing 23-9 finishes it off.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Mar 11, 2010 4:52 pm Post subject: |
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| Quote: | | abcd is a loop, making the eliminations shown. |
Did you mean abcde?
Do you make the eliminations based on what you know about loop patterns, or do you have to check each one? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Mar 11, 2010 5:55 pm Post subject: |
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After basics:
| Code: | *** 1x bivalue cells: <39> UR r12c38 cand count = 4/2,3,3,3
(8)r1c8 - (8=9)r1c7 - (9)r3c89
(2)r2c3 - (2=3)r3c1 - (3=9)r3c5 - (9)r3c89
(2)r2c8 - r2c3 = r8c3 - (2=8)r8c4 - r8c79 = r9c7 - (8=9)r1c7 - (9)r3c89
+--------------------------------------------------------------+
| 4 7 *39 | 5 6 2 | 89 *39+8 1 |
| 5 8 *39+2 | 79 1 37 | 4 *39+2 6 |
| 23 1 6 | 4 39 8 | 5 2379 279 |
|--------------------+--------------------+--------------------|
| 28 246 5 | 2789 289 67 | 1 2489 3 |
| 238 236 1 | 289 4 356 | 7 2589 289 |
| 9 234 7 | 1 238 35 | 6 2458 248 |
|--------------------+--------------------+--------------------|
| 6 9 8 | 3 5 1 | 2 47 47 |
| 1 5 23 | 28 7 4 | 389 6 89 |
| 7 23 4 | 6 28 9 | 38 1 5 |
+--------------------------------------------------------------+
# 62 eliminations remain
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Mar 11, 2010 9:19 pm Post subject: |
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| Marty R. wrote: | | Did you mean abcde? |
Yes | Marty R. wrote: | | Do you make the eliminations based on what you know about loop patterns, or do you have to check each one? |
Marty,
If you make an XY-chain where the pincers are in the same house, you have a loop. All the links are strong. Each adjacent pair of cells in the chain are pincers.
I don't know why, it is a rule I learned.
Here is what Sudoku Susser has to say about this example:
| Code: | ...forms a inherently bi-directional loop through the puzzle that permits reductions. On each edge of the loop, one of the two squares must have a particular value, so their common buddies cannot contain that value, as follows:
One of R1C3 and R1C7 must be <9>.
One of R1C7 and R9C7 must be <8>.
One of R9C7 and R9C2 must be <3>.
One of R9C2 and R8C3 must be <2>.
One of R8C3 and R1C3 must be <3>.
Thus we can deduce that:
R1C8 - cannot contain <9> because of R1C3 and R1C7.
R8C7 - cannot contain <8> because of R1C7 and R9C7.
R2C3 - cannot contain <3> because of R8C3 and R1C3. |
Keith |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Fri Mar 12, 2010 2:09 pm Post subject: |
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| storm_norm wrote: | a bit late with this one stepper.
| Code: | +-------------------+-------------------+------------------+
| 4 7 (39) | 5 6 2 | 8(9) 389 1 |
| 5 8 2(9-3) | (79) 1 -7(3) | 4 239 6 |
| 2(3) 1 6 | 4 9(3) 8 | 5 2379 279 |
+-------------------+-------------------+------------------+
| 28 246 5 | 2789 289 67 | 1 2489 3 |
| 238 236 1 | 289 4 356 | 7 2589 289 |
| 9 234 7 | 1 238 35 | 6 2458 248 |
+-------------------+-------------------+------------------+
| 6 9 8 | 3 5 1 | 2 47 47 |
| 1 5 2(3) | 28 7 4 | 8(39) 6 89 |
| 7 23 4 | 6 28 9 | 38 1 5 |
+-------------------+-------------------+------------------+ |
(7=9)r5c6 - (9)r2c3 = (9)r1c3 - (9)r1c7 = (9-3)r8c7 = (3)r8c3 - (3)r12c3 = (3)r3c1 - (3)r3c5 = (3)r2c6; r2c6 <> 7 |
Norm,
Did you mean to start off (7=9)r2c4 instead of r5c6 ? |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Fri Mar 12, 2010 7:11 pm Post subject: |
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| keith wrote: |
If you make an XY-chain where the pincers are in the same house, you have a loop. All the links are strong. Each adjacent pair of cells in the chain are pincers.
I don't know why, it is a rule I learned.
|
Maybe I can help with an explanation.
Consider any chain of alternating strong and weak links.
An xy-chain is such a chain: the strong links are in the bi-value cells, the weak links are between those cells.
Most other types of "wings" use the same basic principle.
Any chain that starts with a strong link and ends in a strong link and has alternating weak and strong links in between is equivalent to one strong link. We usually call these end points "pincers".
Like this: A=B-C=D is equivalent to A=D
also A=B-......-C=D is equivalent to A=D, no matter how many links there are in between.
What happens if the end points of such a chain "see" each other?
"See" is the same as a weak link.
The chain
| Code: |
A=B-x=X.
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D=C-y=Y
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becomes a loop
| Code: |
A=B-x=X.
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D=C-y=Y
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Now, if we look at X and Y, those two are connected by a weak link on the right, but also by a chain:
X=x-B=A-D=C-y=Y
This chain can be shortened to X=Y, which means that at least one of the two must be true (they have become "pincers")
The same is true for any two neighbours, that is why in a loop, any two neighbours are connected by a strong link and additional eliminations can be made.
Edit 2023 GMT+1: corrected some typos
Last edited by nataraj on Fri Mar 12, 2010 7:24 pm; edited 1 time in total |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Fri Mar 12, 2010 7:22 pm Post subject: |
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| Mogulmeister wrote: | | storm_norm wrote: | a bit late with this one stepper.
| Code: | +-------------------+-------------------+------------------+
| 4 7 (39) | 5 6 2 | 8(9) 389 1 |
| 5 8 2(9-3) | (79) 1 -7(3) | 4 239 6 |
| 2(3) 1 6 | 4 9(3) 8 | 5 2379 279 |
+-------------------+-------------------+------------------+
| 28 246 5 | 2789 289 67 | 1 2489 3 |
| 238 236 1 | 289 4 356 | 7 2589 289 |
| 9 234 7 | 1 238 35 | 6 2458 248 |
+-------------------+-------------------+------------------+
| 6 9 8 | 3 5 1 | 2 47 47 |
| 1 5 2(3) | 28 7 4 | 8(39) 6 89 |
| 7 23 4 | 6 28 9 | 38 1 5 |
+-------------------+-------------------+------------------+ |
(7=9)r5c6 - (9)r2c3 = (9)r1c3 - (9)r1c7 = (9-3)r8c7 = (3)r8c3 - (3)r12c3 = (3)r3c1 - (3)r3c5 = (3)r2c6; r2c6 <> 7 |
Norm,
Did you mean to start off (7=9)r2c4 instead of r5c6 ? |
yes, that would be the cell I meant to type. |
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