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abnormally difficult

 
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Wed Feb 27, 2008 9:54 am    Post subject: abnormally difficult Reply with quote
Code:
+-------+-------+-------+
| . 5 . | 8 . 1 | . . . |
| 6 1 . | . . 2 | 9 . . |
| . . . | . 7 . | . . . |
+-------+-------+-------+
| 3 6 . | . . . | 7 . . |
| 8 . . | . . . | . . 3 |
| . . 2 | . . . | . 4 1 |
+-------+-------+-------+
| . . . | . 9 . | . . . |
| . . 9 | 5 . . | . 1 2 |
| . . . | 4 . 6 | . 8 . |
+-------+-------+-------+


this from sudokupuzz.com,

anyways, I was randomly selecting fiendish puzzles having no problem, some didn't require any advanced moves and some did, but nothing more than xy-wing or x-wing...

until this one, this is by far the hardest I seen on that site.

this is after an x-wing on 3 and an xy-chain that removed three 4's... then I got bug-eyed and had enough.

Code:
   |---c1--|---c2--|---c3--||---c4--|---c5--|---c6--||---c7--|---c8--|---c9--
-----------------------------------------------------------------------------
r1 |     9 |     5 |   347 ||     8 |    46 |     1 ||    34 |     2 |   467
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r2 |     6 |     1 |   478 ||     3 |    45 |     2 ||     9 |    57 |   478
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r3 |     2 |    34 |    48 ||    69 |     7 |   59  ||     1 |    35 |   468
===========================||=======================||=======================
r4 |     3 |     6 |    14 ||    12 |  128  |    48 ||     7 |     9 |     5
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r5 |     8 |   479 |   145 ||    79 |   15  |   459 ||     2 |     6 |     3
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r6 |    57 |    79 |     2 ||   679 |   356 |   359 ||     8 |     4 |     1
===========================||=======================||=======================
r7 |    15 |   238 |     6 ||    12 |     9 |    38 ||    45 |    37 |    47
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r8 |     4 |    38 |     9 ||     5 |    38 |     7 ||     6 |     1 |     2
---+-------+-------+-------||-------+-------+-------||-------+-------+-------
r9 |    17 |    27 |    35 ||     4 |    12 |     6 ||    35 |     8 |     9
.............................................................................


then I shoved it in SE and analyzed it and it spit out 3 more xy-chains which I am still scratching my head over.
oh and it not only spit out those bidirectional y cycles A.K.A. xy-chains...but also just a bidirectional cycle without the y Question lol

and not to mention the turbot fish and a forcing chain Rolling Eyes

not to sound obvious, this was a big surprise. good luck, break out the heavy weapons on this one.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
PostPosted: Wed Feb 27, 2008 11:06 am    Post subject: Reply with quote
I didn't need any forcing chains... or even a Turbot Fish:

(1) X Wing on <3> in r19
(2) Finned X Wing c26 removes <4> r5c5
(3) Type "6" {48} UR r23c39 removes <4> r2c9
(4) {79} UR with <7> strong links in r5 and c4 and <9> strong link in c2 removes <9> r6c4 and <7> r5c2
(5) XY Loop: ...r4c34, r7c4, r9c52, r965c2,... removes <1> r4c5 and <4> r5c3
(6) X Wing c35 removes <4> r4c6
and solves the puzzle.
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ravel



Joined: 21 Apr 2006
Posts: 536
PostPosted: Wed Feb 27, 2008 12:14 pm    Post subject: Reply with quote
Code:
 *------------------------------------------------*
 | 9   5    347  | 8   *46    1    | 34  2   34-67|
 | 6   1   #478  | 3   *45    2    | 9  *57 #478  |
 | 2   34  #48   |-69   7     459  | 1   35 #468  |
 |---------------+-----------------+--------------|
 | 3   6    14   | 12   1248  48   | 7   9   5    |
 | 8   479  145  | 79   15    459  | 2   6   3    |
 | 57  79   2    | 679  356   359  | 8   4   1    |
 |---------------+-----------------+--------------|
 | 15  238  6    | 12   9     38   | 45  37  47   |
 | 4   38   9    | 5    38    7    | 6   1   2    |
 | 17  27   35   | 4    12    6    | 35  8   9    |
 *------------------------------------------------*

More from the UR 48: r3c39=7 or r3c9=6
r3c39=7 => r2c8=5 => r2c5=4 => r1c5=6
=> r1c9<>6, r3c4<>6
Code:
 *----------------------------------------------*
 | 9   5    37   | 8   6     1    | 34  2   47  |
 | 6   1   -47   | 3  #45    2    | 9   57  8   |
 | 2  #34   8    | 9   7    -45   | 1   35  6   |
 |---------------+----------------+-------------|
 | 3   6    14   | 12  1248  48   | 7   9   5   |
 | 8   49   145  | 7   15    459  | 2   6   3   |
 | 57  79   2    | 6  #35    359  | 8   4   1   |
 |---------------+----------------+-------------|
 | 15  238  6    | 12  9     38   | 45  37  47  |
 | 4  @38   9    | 5  @38    7    | 6   1   2   |
 | 17  27   35   | 4   12    6    | 35  8   9   |
 *----------------------------------------------*

w-wing variant 35/54 instead of 34, connected by the strong link for 3 in r8.
r8c2=3 => r3c2=4 or r8c5=3 => r6c5=5 => r2c5=4
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
PostPosted: Wed Feb 27, 2008 2:17 pm    Post subject: Reply with quote
The first step for me was a Finned X-Wing@, the fin(F) is in R4C6 and takes out <4> in R5C5

Code:
+--------------------------+--------------------------+--------------------------+
| 9         5        347   | 8         46        1    | 34         2        467  |
| 6         1        478   | 3         45        2    | 9          57       478  |
| 2       @ 34       348   | 69        7       @ 459  | 1          35       468  |
+--------------------------+--------------------------+--------------------------+
| 3         6        14    | 12       1248     F 48   | 7          9        5    |
| 8       @ 479      145   | 79       1-[4]5   @ 459  | 2          6        3    |
| 57        79       2     | 679      356        359  | 8          4        1    |
+--------------------------+--------------------------+--------------------------+
| 15        238      6     | 12       9          38   | 345        37       47   |
| 4         38       9     | 5        38         7    | 6          1        2    |
| 17        27       35    | 4        12         6    | 35         8        9    |
+--------------------------+--------------------------+--------------------------+


Then the type 6 [79] UR* in R56C24 pins <6> in R6C4
either R5C2=4 or/both R6C4=6 to avoid the DP
When R5C2=|4| => R5C6=|9| => R5C4=|7| => R6C4=|6| => R6C4=6

Code:
+--------------------------+--------------------------+--------------------------+
| 9         5        347   | 8         46        1    | 34         2        467  |
| 6         1        478   | 3         45        2    | 9          57       478  |
| 2         34       348   | 69        7         459  | 1          35       468  |
+--------------------------+--------------------------+--------------------------+
| 3         6        14    | 12       1248       48   | 7          9        5    |
| 8        *|4|79    145   |*|7|9     15         45|9|| 2          6        3    |
| 57       *79       2     |*|6|79    356        359  | 8          4        1    |
+--------------------------+--------------------------+--------------------------+
| 15        238      6     | 12       9          38   | 345        37       47   |
| 4         38       9     | 5        38         7    | 6          1        2    |
| 17        27       35    | 4        12         6    | 35         8        9    |
+--------------------------+--------------------------+--------------------------+

A four cell xy-chain with pincer ends in R7C6(A) and R3C8(D) that takes out <3> in R7C8 completes the puzzle


Code:
+--------------------------+--------------------------+--------------------------+
| 9         5        37    | 8         6         1    | 34         2        47   |
| 6         1        47    | 3         45        2    | 9          57       8    |
| 2         34       8     | 9         7       C 45   | 1        D 35       6    |
+--------------------------+--------------------------+--------------------------+
| 3         6        14    | 12       1248     B 48   | 7          9        5    |
| 8         49       145   | 7        15         459  | 2          6        3    |
| 57        79       2     | 6        35         359  | 8          4        1    |
+--------------------------+--------------------------+--------------------------+
| 15        238      6     | 12       9        A 38   | 345      -[3]7      47   |
| 4         38       9     | 5        38         7    | 6          1        2    |
| 17        27       35    | 4        12         6    | 35         8        9    |
+--------------------------+--------------------------+--------------------------+
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ravel



Joined: 21 Apr 2006
Posts: 536
PostPosted: Wed Feb 27, 2008 4:16 pm    Post subject: Reply with quote
Nice.

What i just saw now in your grid - but is in all of them - is this constellation.
Code:
 *------------------------------------------------*
 | 9   5    347  | 8    46    1    | 34  2   467  |
 | 6   1    478  | 3    45    2    | 9   57  478  |
 | 2  @34   48   | 69   7    -459  | 1   35  468  |
 |---------------+-----------------+--------------|
 | 3   6    14   | 12   1248 @48   | 7   9   5    |
 | 8   479  145  | 79   145   459  | 2   6   3    |
 | 57  79   2    | 679  356   359  | 8   4   1    |
 |---------------+-----------------+--------------|
 | 15  238  6    | 12   9    #38   | 45  37  47   |
 | 4  #38   9    | 5   #38    7    | 6   1   2    |
 | 17  27   35   | 4    12    6    | 35  8   9    |
 *------------------------------------------------*
The pairs 38 in r7c6 and r8c2 can be used like the pivot cell of an xy-wing, because they always must have the same value.
I.e. either r8c2=3 => r3c2=4 or r7c6=8 => r4c6=4.

Of course this would not solve the puzzle, but e.g. could replace Asellus' last 2 steps.
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
PostPosted: Wed Feb 27, 2008 6:11 pm    Post subject: Reply with quote
Ravel,

Great stuff observing this constellation with the naked eye, it would take me to Mount Palomar to see this Laughing
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storm_norm



Joined: 18 Oct 2007
Posts: 1741
PostPosted: Thu Feb 28, 2008 12:26 am    Post subject: Reply with quote
all I have to say is wow.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Thu Feb 28, 2008 2:22 am    Post subject: Reply with quote
Good spotting ravel, but that is what I learned as an XY-Wing Chain and Keith calls, I think, an extended XY-Wing. Now we have another name, "Constellation." Haven't heard that one since David Bryant left. Laughing
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