There Was a Time: 04/04/13

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There Was a Time: 04/04/13

Postby daj95376 » Thu Apr 04, 2013 3:48 pm

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

Play this puzzle online at the Daily Sudoku site

Q: I have puzzles that are less/more difficult than those I've been posting. Anyone interested? Which type?
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Re: There Was a Time: 04/04/13

Postby ArkieTech » Thu Apr 04, 2013 4:30 pm

Code: Select all
 *--------------------------------------------------------------------*
 | 2      6      1      | 347    34     347    | 8      5      9      |
 | 8      4      59     | 2      6      59     | 7      3      1      |
 | 3      59     7      | 59     18     18     | 26     24    b46     |
 |----------------------+----------------------+----------------------|
 | 49     1     a23     | 8      2349   6      | 5      7     a34     |
 |c459    8-2    368-2  |c34     7     c3459   | 1     c249   c346    |
 | 459    7      236    | 1      23459  3459   | 26     249    8      |
 |----------------------+----------------------+----------------------|
 | 7      289    2489   | 6      1489   1489   | 3      18     5      |
 | 1      58     458    | 347    3458   34578  | 9      6      2      |
 | 6      3      589    | 59     1589   2      | 4      18     7      |
 *--------------------------------------------------------------------*
als xy-wing
(2=4)r4c39-(4=6)r3c9-(6=2)r5c14689 => -2r5c23; ste


Danny,
Yes! I like your puzzles. Prefer ones with complexity > w-wing
Last edited by ArkieTech on Fri Apr 05, 2013 1:07 am, edited 1 time in total.
dan
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Re: There Was a Time: 04/04/13

Postby Leren » Thu Apr 04, 2013 9:32 pm

Code: Select all
*--------------------------------------------------------------*
| 2     6     1      | 347   34    347    | 8     5     9      |
| 8     4     59     | 2     6     59     | 7     3     1      |
| 3     59    7      | 59    18    18     | 26    24    46     |
|--------------------+--------------------+--------------------|
| 49    1    a23A    | 8     2349  6      | 5     7    b34     |
| 459   28B  d36-28C | 34    7     3459   | 1     249  c346    |
| 459   7     236    | 1     23459 3459   | 26    249   8      |
|--------------------+--------------------+--------------------|
| 7     289   2489   | 6     1489  1489   | 3     18    5      |
| 1     58    458    | 347   3458  34578  | 9     6     2      |
| 6     3     589    | 59    1589  2      | 4     18    7      |
*--------------------------------------------------------------*
h2-wing + bi-value extension cell:

-2 r4c3 = 3 r4c3 - r4c9 = (3-6) r5c9 = r5c3 => -2 r5c3;
 2 r4c3 - (2=8) r5c2 - r5c3                 => -8 r5c3; stte

Yes I definitely like your puzzles - you could vary the complexity with a "hint" as to the minimum number
of (non forcing net) moves for a "good " solution. You could also change the thread name to Danny's Daily Demon
or a similar humorous and challenging name. The solution to your previous puzzle was so cool I've generalised it and
included it in my solver.

Leren
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Re: There Was a Time: 04/04/13

Postby Marty R. » Thu Apr 04, 2013 11:30 pm

I don't think it's necessary to supply details.

Remote Pairs (59)
XYZ-Wing (249), flightless with transport
XY-Wing (362), flightless with transport
XY-Chain
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Re: There Was a Time: 04/04/13

Postby JC Van Hay » Thu Apr 04, 2013 11:35 pm

#1. UP38;LC(4)
Code: Select all
+--------------------+---------------------+--------------+
| 2    6     1       | 347    34     347   | 8   5    9   |
| 8    4     (59)    | 2      6      (59)  | 7   3    1   |
| 3    59    7       | (59)   18-59  18-59 | 26  24   46  |
+--------------------+---------------------+--------------+
| 49   1     2349    | 8      2349   6     | 5   7    34  |
| 459  2589  2345689 | 34-59  7      3459  | 1   249  346 |
| 459  7     234569  | 1      23459  3459  | 26  249  8   |
+--------------------+---------------------+--------------+
| 7    289   2489    | 6      1489   1489  | 3   18   5   |
| 1    58    458     | 347-5  3458   34578 | 9   6    2   |
| 6    3     8-59    | (59)   1589   2     | 4   18   7   |
+--------------------+---------------------+--------------+
#2. Chain[4] : RemotePairs(59r2c36.r39c4) :=> -59r9c3[.r58c4.r3c56]; UP52[; HP(29)r46c5]
Code: Select all
+--------------+----------------+-------------------+
| 2    6  1    | 347  34    347 | 8      5    9     |
| 8    4  5    | 2    6     9   | 7      3    1     |
| 3    9  7    | 5    18    18  | 26     24   46    |
+--------------+----------------+-------------------+
| 49   1  (23) | 8    9(2)  6   | 5      7    4(3)  |
| 459  8  236  | 34   7     345 | 1      249  4(36) |
| 459  7  236  | 1    9(2)  345 | -2(6)  249  8     |
+--------------+----------------+-------------------+
| 7    2  9    | 6    14    14  | 3      8    5     |
| 1    5  4    | 37   38    378 | 9      6    2     |
| 6    3  8    | 9    5     2   | 4      1    7     |
+--------------+----------------+-------------------+
#3. Chain[4] : 6r6c7=(6-3)r5c9=3r4c9-(3=2)r3c3-2r4c5=2r6c5 :=> -2r6c7; UP81
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Re: There Was a Time: 04/04/13

Postby Luke » Thu Apr 04, 2013 11:50 pm

For kicks, here's a deadly pattern that's easily overlooked. It does a lot of damage, but no one-stepper.

Code: Select all
 *--------------------------------------------------------------------*
 | 2      6      1      | 347    34     347    | 8      5      9      |
 | 8      4      59     | 2      6      59     | 7      3      1      |
 | 3      59     7      | 59    *18    *18     | 26     24     46     |
 |----------------------+----------------------+----------------------|
 | 49     1      23     | 8      2349   6      | 5      7      34     |
 | 459    28     2368   | 34     7      3459   | 1      249    346    |
 | 459    7      236    | 1      23459  3459   | 26     249    8      |
 |----------------------+----------------------+----------------------|
 | 7      289    2489   | 6     *18+49 *18+49  | 3     *18     5      |
 | 1      5-8    4-8    | 347    3458   34578  | 9      6      2      |
 | 6      3      589    | 59    *18+59  2      | 4     *18     7      |
 *--------------------------------------------------------------------*


(18)Bug-Lite (overlapping AURs) ==> r8c23<>8
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Re: There Was a Time: 04/04/13

Postby daj95376 » Fri Apr 05, 2013 6:37 am

I sometimes need to use actual assignments to see that a DP exists.

Code: Select all
 +-----------------------------------------------------------------------+
 |  2      6      1      |  347    34     347    |  8      5      9      |
 |  8      4      59     |  2      6      59     |  7      3      1      |
 |  3      59     7      |  59     18     18     |  26     24     46     |
 |-----------------------+-----------------------+-----------------------|
 |  49     1      23     |  8      2349   6      |  5      7      34     |
 |  459    28     2368   |  34     7      3459   |  1      249    346    |
 |  459    7      236    |  1      23459  3459   |  26     249    8      |
 |-----------------------+-----------------------+-----------------------|
 |  7      289    2489   |  6      1489   1489   |  3      18     5      |
 |  1      58     458    |  347    3458   34578  |  9      6      2      |
 |  6      3      589    |  59     1589   2      |  4      18     7      |
 +-----------------------------------------------------------------------+
 # 79 eliminations remain

Code: Select all
 Scenario: r8c56<>8 and r3c5=1 forces (#) cells for <1,8>.
 *--------------------------------------------------------------------*
 | 2      6      1      | 347    34     347    | 8      5      9      |
 | 8      4      59     | 2      6      59     | 7      3      1      |
 | 3      59     7      | 59    #1     #8      | 26     24     46     |
 |----------------------+----------------------+----------------------|
 | 49     1      23     | 8      2349   6      | 5      7      34     |
 | 459    28     2368   | 34     7      3459   | 1      249    346    |
 | 459    7      236    | 1      23459  3459   | 26     249    8      |
 |----------------------+----------------------+----------------------|
 | 7      29     249    | 6      49    #1      | 3     #8      5      |
 | 1      58     458    | 347    345    3457   | 9      6      2      |
 | 6      3      59     | 59    #8      2      | 4     #1      7      |
 *--------------------------------------------------------------------*

Code: Select all
 Scenario: r8c56<>8 and r3c5=8 forces (#) cells for <1,8>.
 *--------------------------------------------------------------------*
 | 2      6      1      | 347    34     347    | 8      5      9      |
 | 8      4      59     | 2      6      59     | 7      3      1      |
 | 3      59     7      | 59    #8     #1      | 26     24     46     |
 |----------------------+----------------------+----------------------|
 | 49     1      23     | 8      2349   6      | 5      7      34     |
 | 459    28     2368   | 34     7      3459   | 1      249    346    |
 | 459    7      236    | 1      23459  3459   | 26     249    8      |
 |----------------------+----------------------+----------------------|
 | 7      29     249    | 6      49    #8      | 3     #1      5      |
 | 1      58     458    | 347    345    3457   | 9      6      2      |
 | 6      3      59     | 59    #1      2      | 4     #8      7      |
 *--------------------------------------------------------------------*

I see a 6-cell DP that results when r8c56<>8 ... and so Luke451's conclusion of r8c23<>8 follows.
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Re: There Was a Time: 04/04/13

Postby daj95376 » Fri Apr 05, 2013 6:57 am

These two steps are a solution to this puzzle:

Code: Select all
 W-Wing:  (9=5)r2c3 - r2c6 = r3c4 - (5=9)r9c4  =>  r9c3<>9

 (6=2)r6c7 - r6c5 = r4c5 - (2=3)r4c3 - r4c9 = (3)r5c9  =>  r5c9<>6

But I find the following just as effective: (ala Marty's and JC's use of the Remote Pair)

Code: Select all
 RP: (5=9)r2c3 - (9=5)r2c6 - (5=9)r3c4 - (9=5)r9c4  =>  r9c3<>5
 RP: (9=5)r2c3 - (5=9)r2c6 - (9=5)r3c4 - (5=9)r9c4  =>  r9c3<>9

 XY-Chain: (2=6)r3c7 =4r3c9 =3r4c9 =2r4c3 =9r4c5 - (9=2)r6c5  =>  r6c7<>2
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Re: There Was a Time: 04/04/13

Postby JC Van Hay » Fri Apr 05, 2013 7:29 am

daj95376 wrote:These two steps are a solution to this puzzle:

Code: Select all
 W-Wing:  (9=5)r2c3 - r2c6 = r3c4 - (5=9)r9c4  =>  r9c3<>9

 (6=2)r6c7 - r6c5 = r4c5 - (2=3)r4c3 - r4c9 = (3)r5c9  =>  r5c9<>6

Just one observation : If basics=Locked Subsets+Locked Candidates, then the W-Wing or the RP(59) or even the Skyscrapers(59C24) is not required.
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Re: There Was a Time: 04/04/13

Postby daj95376 » Fri Apr 05, 2013 4:11 pm

JC Van Hay wrote:Just one observation : If basics=Locked Subsets+Locked Candidates, then the W-Wing or the RP(59) or even the Skyscrapers(59C24) is not required.

JC,

I'm confused by your comment. Please elaborate. As for basics ...

Basics = Singles + Subsets + Locked Candidates
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Re: There Was a Time: 04/04/13

Postby Leren » Sat Apr 06, 2013 1:01 am

My POV on the DP aspects of this puzzle was:

Code: Select all
*-----------------------------------------------------------------------*
| 2      6      1       |a347   a34    a347     | 8      5      9       |
| 8      4      59      | 2      6      59      | 7      3      1       |
| 3      59     7       | 59     18     18      | 26     24     46      |
|-----------------------+-----------------------+-----------------------|
| 49     1      23      | 8      2349   6       | 5      7      34      |
| 459    28     2368    | 34     7      3459    | 1      249    346     |
| 459    7      236     | 1      23459  3459    | 26     249    8       |
|-----------------------+-----------------------+-----------------------|
| 7      289    2489    | 6      1489   1489    | 3      18     5       |
| 1     c58    d4-58    |b347   b34+58 b347+58  | 9      6      2       |
| 6      3      589     | 59     1589   2       | 4      18     7       |
*-----------------------------------------------------------------------*

6 cell DP (347+58) r18c456 + bi-value helper cell r8c2 => -58 r8c3;

Code: Select all
*-------------------------------------------------------------------------*
| 2      6      1       | 347    34       347     | 8      5      9       |
| 8      4      59      | 2      6        59      | 7      3      1       |
| 3      59     7       | 59   @*18     @*18      | 26     24     46      |
|-----------------------+-------------------------+-----------------------|
| 49     1      23      | 8      2349     6       | 5      7      34      |
| 459    28     2368    | 34     7        3459    | 1      249    346     |
| 459    7      236     | 1      23459    3459    | 26     249    8       |
|-----------------------+-------------------------+-----------------------|
| 7      289    289     | 6    #@149-8  @*149-8   | 3    #*18     5       |
| 1      58     4       | 37     358      3578    | 9      6      2       |
| 6      3      589     | 59   #*159-8    2       | 4    #*18     7       |
*-------------------------------------------------------------------------*

Overlapping potential 6/4/4 cell DPs in cells marked *, @ and #

8 r7c6 => 6 cell DP in cells * if there are Strong links on 1 in Row 9 or Col 5
8 r9c5 => 6 cell DP in cells * if there are Strong links on 1 in Row 7 or Col 6
8 r7c5 => 4 cell DP in cells @ if there is a Strong link on 1 in Col 6
8 r7c5 => 4 cell DP in cells # if there is a Strong link on 1 in Row 9

As there are, in fact, Strong links on 1 in Row 9 and Col 6 => -8 r7c56, r9c5

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Re: There Was a Time: 04/04/13

Postby eleven » Sat Apr 06, 2013 11:48 am

Often it is useful to work with external candidates.
If you have a potentially deadly pattern, one of the candidates must be outside in all unit pairs (or triples etc) to prevent it (otherwise the candidates are restricted to the DP cells).

In the 347 DP there must be a 3, 4 or 7 in the rest of rows 1 or 9. The only possible digit there is the 4 in r8c3. (Alternatively one of the digits has to be outside in one of the boxes, leading to r7c56=4)

Concerning the overlapping DP's:
Code: Select all
----------------
*  *  .|ab .  .|
*  *  .|ab .  .|
.  .  .|.  .  .|
----------------
ab ab .|
.  .  .|
.  .  .|
--------

In such a constellation any pair ab in the starred cells leads to a deadly pattern.
So if 2 or more of the cells contain both ab, then only one of these cells can be ab, and at least one of a or b must be in the rest of the cells in this box (they cant be elsewhere in the other 2 boxes).

In the sample above this means, that 1 or 8 has to be outside the 3 cells in box 8 => r8c45=8.
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Re: There Was a Time: 04/04/13

Postby JC Van Hay » Sat Apr 06, 2013 1:06 pm

daj95376 wrote:
JC Van Hay wrote:Just one observation : If basics=Locked Subsets+Locked Candidates, then the W-Wing or the RP(59) or even the Skyscrapers(59C24) is not required.

JC,

I'm confused by your comment. Please elaborate. As for basics ...

Basics = Singles + Subsets + Locked Candidates
After Singles, LC(4,9) in B4 :=> -49r4c3 and Chain[4] -> 6r6c7=3r5c9 :=> -6r5c9 crack the puzzle.
Other Subsets and Locked Candidates are therefore optional.

On the other hand, "basics"+SS(59C34)[my "basics" include any kind of "Fish"] or RP(59) :=> r9c3=8 helps to understand why the puzzle is solved by the chain[4] and its equivalents : that is, R4 ends up containing only bivalues which is a stronger indication than B3 contains only bivalues. Without such indications, the solution of the puzzle would seem a desperate random hacking away of candidates by hopping from one chain to another.

Note : Locked Subests=N-tuple, N=1,2, ...

JC
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Re: There Was a Time: 04/04/13

Postby daj95376 » Sat Apr 06, 2013 4:15 pm

eleven wrote:Concerning the overlapping DP's:
Code: Select all
----------------
*  *  .|ab .  .|
*  *  .|ab .  .|
.  .  .|.  .  .|
----------------
ab ab .|
.  .  .|
.  .  .|
--------

In such a constellation any pair ab in the starred cells leads to a deadly pattern.
So if 2 or more of the cells contain both ab, then only one of these cells can be ab, and at least one of a or b must be in the rest of the cells in this box (they cant be elsewhere in the other 2 boxes).

In the sample above this means, that 1 or 8 has to be outside the 3 cells in box 8 => r8c45=8.

eleven, thanks for the details!
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Re: There Was a Time: 04/04/13

Postby daj95376 » Sat Apr 06, 2013 4:36 pm

JC Van Hay wrote:Note : Locked Subsets=N-tuple, N=1,2, ...

JC, we're working from different definitions. Your definition seems identical to what Sudopedia calls a Locked Set. FYI, here's the definitions (from Sudopedia) that I use:

Code: Select all
       Singles: Naked/Hidden; N=1      (in a cell or house/unit)

       Subsets: Naked/Hidden; N=2..4   (in a house/unit)

Locked Subsets: Naked       ; N=2..3   (in the intersection of a line and box)

Where Locked Subsets is part of Intersections.
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