| View previous topic :: View next topic |
| Author |
Message |
storm_norm
Joined: 18 Oct 2007
Posts: 1741
|
 Posted: Fri Mar 07, 2008 9:59 pm Post subject: competition #971 |
 |
|
| Code: | +-------+-------+-------+
| 6 . . | . . . | . . 4 |
| . . . | . . . | . 1 . |
| . 3 1 | . . 9 | 7 . . |
+-------+-------+-------+
| . . . | 7 . 1 | . 2 . |
| . . 4 | . 9 . | 5 . 8 |
| . 9 . | 5 . 6 | . . . |
+-------+-------+-------+
| . . 5 | 2 . . | 1 4 . |
| . 8 . | . . . | . . . |
| 7 . . | . . . | . . 6 |
+-------+-------+-------+ |
this puzzle isn't rated any higher than previous diabolical competitions... try telling that to my eyes  |
|
| Back to top |
|
 |
Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
|
| Posted: Sat Mar 08, 2008 2:01 am Post subject: |
|
|
Believe it or not, it is solved in two steps. The first one is an AIC Loop, which is an interesting occurrence. It works exactly the same as an XY Loop. The grid after basics:
| Code: |
+------------+-------------+-----------------+
| 6 2 789 | 1 357 357 | 389 3589 4 |
|e59 4 79 | 8 2 357 | 6 1 f359 |
| 58 3 1 | 4 6 9 | 7 58 2 |
+------------+-------------+-----------------+
| 38 5 6 | 7 48 1 | 349 2 39 |
| 1 7 4 | 3 9 2 | 5 6 8 |
| 2 9 38 | 5 48 6 | 34 7 1 |
+------------+-------------+-----------------+
|d39 6 5 | 2 c37 8 | 1 4 379 |
| 4 8 239 | 6 1 b357 | 239 359 a3579 |
| 7 1 23 | 9 35 4 | 238 358 6 |
+------------+-------------+-----------------+
|
The AIC loop is marked "a" to "f" (and back to "a"). "c-d-e" are an XY Chain. "a-b-c" are linked by conjugate <7>s. "e-f is a weak link on <5>. And, "f-a" are conjugate <5>s.
"a" is <7> or it is not <7>. "a" not 7 --> b=7 --> c=3 --> d=9 --> e=5 --> f is not 5 --> a=5. So, "a" is either <7> or it is <5>. This completes the AIC Loop and all the intervening links become conjugate, resulting in these eliminations:
<3> and <9> are removed from r8c9, <3> is removed from r7c9, and <5> is removed from r2c6.
In Eureka, the Loop is:
(5-7)r8c9=(7)r8c6-(7=3)r7c5-(3=9)r7c1-(9=5)r2c1-(5)r2c9=(5-7)r8c9...
(By the way, there is a Type "6a" {23} UR based elimination of <3> in r8c7, but it doesn't advance the solution.)
The second step:
| Code: |
+------------+-------------+----------------+
| 6 2 789 | 1 357 357 | 389 3589 4 |
| 59 4 79 | 8 2 a37 | 6 1 359 |
| 58 3 1 | 4 6 9 | 7 58 2 |
+------------+-------------+----------------+
| 38 5 6 | 7 48 1 | 349 2 39 |
| 1 7 4 | 3 9 2 | 5 6 8 |
| 2 9 38 | 5 48 6 | 34 7 1 |
+------------+-------------+----------------+
|A39 6 5 | 2 #-37 8 | 1 4 79 |
| 4 8 239 | 6 1 b357 | 239 359 57 |
| 7 1 23 | 9 c35 4 | 238 358 6 |
+------------+-------------+----------------+
|
There is now an otherwise useless XYZ Wing "abc". The <3> in "a" can be transported to "A" (via c9, r4, c1), eliminating <3> from r7c5 and solving the puzzle.
_______
Edit sometime later:
I just realized that my second step is also a {37} W-Wing that eliminates <7>s with the same effect. The external strong link is provided by the color wing (multicoloring) on <3> in c9-r4-c1. |
|
| Back to top |
|
|
nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
|
| Posted: Sat Mar 08, 2008 12:07 pm Post subject: |
|
|
I got as far as this position using a short xy-chain ('59' in r2c1...r3c1,r4c1...'39' in r4c9)
and an xy-wing (39-59-35, pivot r2c1):
| Code: |
+--------------------------+--------------------------+--------------------------+
| 6 2 78 | 1 357 357 | 389 3589 4 |
| 59 4 79 | 8 2 357 | 6 1 35 |
| 58 3 1 | 4 6 9 | 7 58 2 |
+--------------------------+--------------------------+--------------------------+
| 38 5 6 | 7 48 1 | 349 2 39 |
| 1 7 4 | 3 9 2 | 5 6 8 |
| 2 9 38 | 5 48 6 | 34 7 1 |
+--------------------------+--------------------------+--------------------------+
| 39 6 5 | 2 37 8 | 1 4 79 |
| 4 8 239 | 6 1 357 | 239 359 3579 |
| 7 1 23 | 9 35 4 | 238 358 6 |
+--------------------------+--------------------------+--------------------------+
|
Another xy-chain '78' in r1c3 ... r3c1,r2c1,r7c1...'37' in r7c5, which makes r1c5<>7, solves the puzzle |
|
| Back to top |
|
|
keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
|
| Posted: Sat Mar 08, 2008 8:35 pm Post subject: |
|
|
After basics:
| Code: | +----------------+----------------+----------------+
| 6 2 789 | 1 357 357 | 389 3589 4 |
| 59e 4 79 | 8 2 357 | 6 1 35-9 |
| 58 3 1 | 4 6 9 | 7 58 2 |
+----------------+----------------+----------------+
| 38d 5 6 | 7 48 1 |-349 2 39a |
| 1 7 4 | 3 9 2 | 5 6 8 |
| 2 9 38 | 5 48 6 | 34 7 1 |
+----------------+----------------+----------------+
| 39c 6 5 | 2 37 8 | 1 4 379b |
| 4 8 239f | 6 1 357 | 239 359 357-9|
| 7 1 23 | 9 35 4 | 238 358 6 |
+----------------+----------------+----------------+
|
A half M-wing: If a is <9>, so is c, and d is <3>, taking out <3> in R4C7.
An M-wing: a and c are now connected via d by strong links on <3>. Extending with <9> in C1 to e takes out <9> in R2C9, and thus in R1C3.
Extending with <9> in B7 to f takes out <9> in R8C9.
An XY-wing <39> takes out <3> in R7C9. Bringing us to here:
| Code: | +----------------+----------------+----------------+
| 6 2 78 | 1 357 357 | 389 3589 4 |
| 59 4 79 | 8 2 357B | 6 1 35b |
| 58 3 1 | 4 6 9 | 7 58 2 |
+----------------+----------------+----------------+
| 38A 5 6 | 7 48 1 | 49 2 39a |
| 1 7 4 | 3 9 2 | 5 6 8 |
| 2 9 38 | 5 48 6 | 34 7 1 |
+----------------+----------------+----------------+
| 39a 6 5 | 2 37A 8 | 1 4 79 |
| 4 8 239 | 6 1 -357 | 239 359 357 |
| 7 1 23 | 9 35 4 | 238 358 6 |
+----------------+----------------+----------------+ |
Multicoloring on <3> a-A and b-B takes out <3> in R8C6. In C9, one of a and b is false; one of A and B is true.
Extending a-A by the new strong link in B8 takes out <3> in R1C5 and R9C7. Leaving us here:
| Code: | +----------------+----------------+----------------+
| 6 2 78 | 1 57d 357 | 389 3589 4 |
| 59# 4 79a | 8 2 35-7 | 6 1 35 |
| 58 3 1 | 4 6 9 | 7 58 2 |
+----------------+----------------+----------------+
| 38 5 6 | 7 48 1 | 49 2 39 |
| 1 7 4 | 3 9 2 | 5 6 8 |
| 2 9 38 | 5 48 6 | 34 7 1 |
+----------------+----------------+----------------+
| 39# 6 5 | 2 37c 8 | 1 4 79b |
| 4 8 239 | 6 1 57 | 239 359 357 |
| 7 1 23 | 9 35 4 | 28 358 6 |
+----------------+----------------+----------------+
|
a and b are a W-wing connected by the stong link <9> in C1. Coloring on <7> to c and d takes out <7> in R2C6, solving the puzzle.
Whew!
(I am not sure how much of this is necessary, but it's how I solved it.)
Keith |
|
| Back to top |
|
|
|
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
Powered by phpBB © 2001, 2005 phpBB Group
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
