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Puzzle 11/06/25: ~ XY

 
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Sat Jun 25, 2011 9:25 pm    Post subject: Puzzle 11/06/25: ~ XY Reply with quote

Code:
 +-----------------------+
 | 7 9 . | . . . | . . . |
 | 8 . . | 3 . 5 | . . . |
 | . . 1 | 6 7 . | . 4 . |
 |-------+-------+-------|
 | . 6 7 | 9 1 . | 4 8 . |
 | . . 9 | 2 . 4 | . . . |
 | . 8 . | . 5 6 | . . . |
 |-------+-------+-------|
 | . . . | 8 . . | 9 . 7 |
 | . . 8 | 5 . . | . 6 4 |
 | . . . | . . . | 8 5 2 |
 +-----------------------+

Play this puzzle online at the Daily Sudoku site
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sun Jun 26, 2011 12:32 pm    Post subject: Reply with quote

An uncomplicated one stepper...............

Quote:
anp(29=3)r28c5-r8c7=r7c8-(3=2)r1c8; r1c5<>2=4

Ted
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Sun Jun 26, 2011 1:37 pm    Post subject: Reply with quote

Here is a loop that makes 11 deletions but does not solve the puzzle.

Code:
*--------------------------------------------------------------------*
 | 7      9      256    |e14    d24     128    | 2356  c23     368    |
 | 8      4      26     | 3      29     5      | 1267   1279   169    |
 | 35     235    1      | 6      7      89     | 25     4      89     |
 |----------------------+----------------------+----------------------|
 | 2      6      7      | 9      1      3      | 4      8      5      |
 | 135    135    9      | 2      8      4      | 1367   137    136    |
 | 134    8      34     | 7      5      6      | 123    1239   139    |
 |----------------------+----------------------+----------------------|
 | 46    a1235   25     | 8      46     12     | 9     b13     7      |
 | 139    1237   8      | 5      239    1279   | 13     6      4      |
 | 13469  137   g34     |f14     3469   179    | 8      5      2      |
 *--------------------------------------------------------------------*


(3)r7c2=(3)r7c8-(3=2)r1c8-(2=4)r1c5-r1c4=r9c4-(4=3)r9c3-Loop; r56c8<>3, r1c367<>2, r9c15<>4, r89c12<>3

Sometimes it pays to be lucky............

Ted
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Marty R.



Joined: 12 Feb 2006
Posts: 5159
Location: Rochester, NY, USA

PostPosted: Sun Jun 26, 2011 4:00 pm    Post subject: Reply with quote

I managed to stagger to the finish line with seven steps. Couple of XY-Wings, a DP and two Finned X-Wings. Then a key step was a Fin Transport (r2c5<>4) which opened up a short XY-Chain (r1c5, r2c78<>2).
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PIsaacson



Joined: 13 Jun 2011
Posts: 11
Location: Campbell, CA

PostPosted: Sun Jun 26, 2011 10:31 pm    Post subject: Reply with quote

After basics and an XY-Wing 123 pivot at r7c8 + r1c8 & r7c6 => r1c6 <> 2 I arrived at:
Code:
 *--------------------------------------------------------------------*
 | 7      9      256    | 14     4-2    18     | 2356  *23     368    |
 | 8      4      26     | 3     *29     5      | 167-2  179-2  169    |
 | 35     235    1      | 6      7      89     | 25     4      89     |
 |----------------------+----------------------+----------------------|
 | 2      6      7      | 9      1      3      | 4      8      5      |
 | 135    135    9      | 2      8      4      | 1367   137    136    |
 | 134    8      34     | 7      5      6      | 123    1239   139    |
 |----------------------+----------------------+----------------------|
 | 46     1235   25     | 8      46     12     | 9     *13     7      |
 | 139    27     8      | 5     *39     27     |*13     6      4      |
 | 13469  137    34     | 14     3469   179    | 8      5      2      |
 *--------------------------------------------------------------------*

This first struck me as a DB with the stem cells bi-local 3 in box 9 tied to ALS r28c5 and ALS r1c8 with the common end-point 2s producing the 3 eliminations indicated. Then I looked at it again and thought it looked more like an ALS-XY Wing with ALSs r28c5 -3- r8c7 -1- r17c8 (other combinations are possible). But upon further examination, it looked like a simple XY-chain starting from either end r2c5 or r1c8, but again providing the same 3 eliminations. Regardless of POV, it's singles from there on.

Cheers,
Paul

That which we call a rose, by any other name...
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dejsmith



Joined: 23 Oct 2005
Posts: 40

PostPosted: Sun Jun 26, 2011 11:12 pm    Post subject: Reply with quote

I started with the same XY Wing as Paul; but, of course, my XY Chain was less efficient & lots longer! From Paul's grid, starting at r8c5: 93-31-13-32-24-41-18-89; r2c5<>9. I spend lots of time looking for those type chains when I cannot solve puzzles otherwise.

Dave
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Mon Jun 27, 2011 1:17 pm    Post subject: Reply with quote

Hi Paul, nice to have you joining our "Dailysudoku" activities.

I have been looking at "almost" conditions recently and noticed that your five cell pattern immediately after basic is an "almost xy-chain" with fin (2)r8c5. This pattern only deletes r1c5<>2 but completes the puzzle in one step.

Ted
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PIsaacson



Joined: 13 Jun 2011
Posts: 11
Location: Campbell, CA

PostPosted: Mon Jun 27, 2011 5:35 pm    Post subject: Reply with quote

Ted,

Nice! If I reproduced this correctly, the following PM appears fairly early in basics prior to any XY wing or coloring etc.:
Code:
 *--------------------------------------------------------------------*
 | 7      9      256    | 14     4-2    128    | 2356  b23     368    |
 | 8      4      26     | 3     a29     5      | 1267   1279   169    |
 | 35     235    1      | 6      7      289    | 235    4      389    |
 |----------------------+----------------------+----------------------|
 | 2      6      7      | 9      1      3      | 4      8      5      |
 | 135    135    9      | 2      8      4      | 1367   137    136    |
 | 134    8      34     | 7      5      6      | 123    1239   139    |
 |----------------------+----------------------+----------------------|
 | 13456  1235   25     | 8      2346   12     | 9     *13     7      |
 | 139    1237   8      | 5     a239    1279   |*13     6      4      |
 | 13469  137    34     | 14     3469   179    | 8      5      2      |
 *--------------------------------------------------------------------*

The 5 cells still define either a DB or an XY-Wing, but this time the mutual peers of both ALSs on the candidate 2 are restricted to the single r1c5 <> 2 elimination.

Denis Berthier would call this pattern an nrczt whip using 2r1c5 as the z-target start point. Prior to his implementation of the full nrczt logic, I think he would have called it an XY(z) chain. A very abridged version of his logic would be to consider a chain of logic starting from some z-target truth, and then extending the chain via AIC steps, but with the truths being applied as the chain is developed so that "promotions" (converting weak links to stong links) and "collisions" (impossible grid positions) are detected and applied on the fly. This is easy to emulate using SS by turning off "Block Invalid Moves" and then setting the truths. Allan Barker's XSudo allows you to easily enter nrczt chains as well.

Cheers,
Paul
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Jun 27, 2011 5:47 pm    Post subject: Reply with quote

Or simply:

Code:
(2=3)r1c8 - (3=1)r7c8 - (1=3)r8c7 - (3=29)r82c5  =>  r1c5<>2
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tlanglet



Joined: 17 Oct 2007
Posts: 2461
Location: Northern California Foothills

PostPosted: Mon Jun 27, 2011 7:58 pm    Post subject: Reply with quote

daj95376 wrote:
Or simply:

Code:
(2=3)r1c8 - (3=1)r7c8 - (1=3)r8c7 - (3=29)r82c5  =>  r1c5<>2


... which is the reverse of my original post. It is wonderful how AICs work that way.

Ted
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daj95376



Joined: 23 Aug 2008
Posts: 3855

PostPosted: Mon Jun 27, 2011 9:39 pm    Post subject: Reply with quote

tlanglet wrote:
... which is the reverse of my original post. It is wonderful how AICs work that way.

Well, now I'm completely disheveled. I'd forgotten your original (whitened-out) solution, and thought you were commenting on a "new" observation related to Paul's post. Oh Well !!!

Regards, Danny
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