Suggest A Move (SAM#1)

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Suggest A Move (SAM#1)

Postby DonM » Mon Feb 16, 2009 12:42 pm

People seem to take a particular interest in looking at a given puzzle state and coming up with different patterns/chains. It can be rewarding & instructive seeing the different approaches various solvers take at the same given point in a puzzle. So, let's see how this flies: This is the 'Suggest A Move' series (SAM:) ), occurring periodically or more likely sporadically and consisting of of a puzzle at a point where there are some interesting patterns. While these may be puzzles I've already completely solved (or maybe not), there is not any hidden surprise or backdoor (at least not that I know of) or some other trick awaiting and I certainly haven't made any exhaustive search for all possible interesting patterns (so I hope to learn something also). It is simply an interesting puzzle. There are no rules, but hopefully, people will resist the urge to run it through a computer solver. So feel free to post any interesting pattern/chain you come up with (or solve the rest of the puzzle if you want).

Extreme #114 ER=7.2, a few moves past the ssts point:
Code: Select all
*--------------------------------------------------------------------*
 | 7      128    4      | 18     5      189    | 6      3      129    |
 | 58     125    9      | 36     4      36     | 18     7      12     |
 | 3      18     6      | 189    2      7      | 5      48     49     |
 |----------------------+----------------------+----------------------|
 | 59     6      2      | 7      8      49     | 3      145    145    |
 | 1      45     7      | 26     3      26     | 49     459    8      |
 | 89     48     3      | 49     1      5      | 2      6      7      |
 |----------------------+----------------------+----------------------|
 | 6      7      8      | 1245   9      124    | 14     1245   3      |
 | 24     9      1      | 23458  6      2348   | 7      2458   45     |
 | 24     3      5      | 1248   7      1248   | 1489   12489  6      |
 *--------------------------------------------------------------------*


Note edit: A typo resulted in my not entering one digit: Note that r4c9 contains 145 not 15.
Last edited by DonM on Mon Feb 16, 2009 8:06 pm, edited 1 time in total.
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Postby Luke » Mon Feb 16, 2009 9:22 pm

Sounds like good clean fun. I also like the "no computer solvers" proviso. I'll try to find something good later but at first glance, diagonals like this always catch my eye:
Code: Select all
UR, r1c2<>1.
 *--------------------------------------------------------------------*
 | 7     *128    4      |*18     5      189    | 6      3      129    |
 | 58     125    9      | 36     4      36     | 18     7      12     |
 | 3     *18     6      |*189    2      7      | 5      48     49     |
 |----------------------+----------------------+----------------------|
 | 59     6      2      | 7      8      49     | 3      145    145    |
 | 1      45     7      | 26     3      26     | 49     459    8      |
 | 89     48     3      | 49     1      5      | 2      6      7      |
 |----------------------+----------------------+----------------------|
 | 6      7      8      | 1245   9      124    | 14     1245   3      |
 | 24     9      1      | 23458  6      2348   | 7      2458   45     |
 | 24     3      5      | 1248   7      1248   | 1489   12489  6      |
 *--------------------------------------------------------------------*

The x-wing overlay on 2 in r12c29 takes out the same candidate.
The x-wing overlay on 9 in r59c78 takes out the 4 in r9c8.
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Postby DonM » Tue Feb 17, 2009 12:15 am

Hi Luke- for the benefit of those who may not be familiar with URs, can you expound a bit on the UR exclusion.
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Postby storm_norm » Tue Feb 17, 2009 1:56 am

xy-wing {1,4,8} removes 4 from r789c8
Code: Select all
.---------------------.---------------------.---------------------.
| 7      128    4     | 18     5      189   | 6      3      129   |
| 58     125    9     | 36     4      36    | 18     7      12    |
| 3      18     6     | 189    2      7     | 5      48     49    |
:---------------------+---------------------+---------------------:
| 59     6      2     | 7      8      49    | 3      145    145   |
| 1      45     7     | 26     3      26    | 49     459    8     |
| 89     48     3     | 49     1      5     | 2      6      7     |
:---------------------+---------------------+---------------------:
| 6      7      8     | 1245   9      124   | 14     125    3     |
| 24     9      1     | 23458  6      2348  | 7      258    45    |
| 24     3      5     | 1248   7      1248  | 1489   1289   6     |
'---------------------'---------------------'---------------------'
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Postby storm_norm » Tue Feb 17, 2009 2:18 am

Code: Select all
.---------------------.---------------------.---------------------.
| 7     U128    4     | 18     5      189   | 6      3     U129   |
| 58    U125    9     | 36     4      36    | 18     7     U12    |
| 3     *18     6     |*-189   2      7     | 5      48    *49    |
:---------------------+---------------------+---------------------:
| 59     6      2     | 7      8      49    | 3      145    145   |
| 1      45     7     | 26     3      26    | 49     459    8     |
| 89     48     3     | 49     1      5     | 2      6      7     |
:---------------------+---------------------+---------------------:
| 6      7      8     | 1245   9      124   | 14     125    3     |
| 24     9      1     | 23458  6      2348  | 7      258    45    |
| 24     3      5     | 1248   7      1248  | 1489   1289   6     |
'---------------------'---------------------'---------------------'

notice the marked cells contain the deadly pattern on {1,2}.
if the 9 is removed from r9c1 then we know that the resulting UR can be avoided by removing the 1's in r12c2, this would force 1 into r3c2.
in other words, neither the 9 in r1c9 nor the 1 in r3c2 can both be false or the deadly pattern is forced to exist.
creates this inference...

UR12[(9)r9c1 = (1)r3c2]...

can be used in this chain

(9)r3c4 = (9)r3c9 - UR12[(9)r9c1 = (1)r3c2]; r3c4 <> 1

and...

Code: Select all
.---------------------.---------------------.---------------------.
| 7     U128    4     |U18     5      189   | 6      3     1-29   |
| 58     125    9     | 36     4      36    |*18     7     *12    |
| 3     U18     6     |U189    2      7     | 5     *48    *49    |
:---------------------+---------------------+---------------------:
| 59     6      2     | 7      8      49    | 3      145    145   |
| 1      45     7     | 26     3      26    | 49     459    8     |
| 89     48     3     | 49     1      5     | 2      6      7     |
:---------------------+---------------------+---------------------:
| 6      7      8     | 1245   9      124   | 14     125    3     |
| 24     9      1     | 23458  6      2348  | 7      258    45    |
| 24     3      5     | 1248   7      1248  | 1489   1289   6     |
'---------------------'---------------------'---------------------'

the marked UR {1,8} says that neither the 2 in r1c2 nor the 9 in r3c4 can both be false or the deadly pattern is forced to exist.
creates this inference...
UR18[(2)r1c2 = (9)r3c4]...

can be extended into this chain

UR18[(2)r1c2 = (9)r3c4] - (9=4)r3c9 - (4=8)r3c8 - (8=1)r2c7 - (1=2)r2c9; r1c9 <> 2
Last edited by storm_norm on Tue Feb 17, 2009 12:01 am, edited 4 times in total.
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Postby Luke » Tue Feb 17, 2009 3:52 am

DonM wrote:Hi Luke- for the benefit of those who may not be familiar with URs, can you expound a bit on the UR exclusion.

Potential unique rectangles with bivalues catch my attention because if a strong link is involved, something good always happens. To cite Havard from HERE:
With a Unique Rectangle with the numbers [ab] that has two cells with "extra candidates" ([xabx]), and these cells are on a diagonal from each other, and you have a strong link between any two of the cells in the Rectangle for candidate [a], then you can eliminate candidate [a] from the cell with extra candidates that is not part of the strong link.

In this case, there's a strong link on (1) in r3c24, and the "cell with extra candidates that is not part of the strong link" is r1c2.

Incidentally, if there are two strong links:
If a potential UR has bivalues on the diagonals and two strong links meeting in an "elbow' in one of the bivalue cells, after applying the above rule the strong candidate can be placed in the elbow.

If there are four strong links (x-wing):
If a potential UR has bivalues on the diagonals and one of the components forms an x-wing, then to quote Keith, "The diagonal pairs must have the x-wing component."

As for the other ones:
The x-wing overlay on 2 in r12c29 takes out the same candidate.
The x-wing overlay on 9 in r59c78 takes out the 4 in r9c8.

If there's an x-wing on one of the candidates and only one bivalue cell is involved, then the non-x-wing component on the diagonal of the bivalue cell can be eliminated. How's that for a mouthful.:)
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Re: Suggest A Move (SAM#1)

Postby aran » Tue Feb 17, 2009 7:42 am

DonM wrote:
Code: Select all
*--------------------------------------------------------------------*
 | 7      128    4      | 18     5      189    | 6      3      129    |
 | 58     125    9      | 36     4      36     | 18     7      12     |
 | 3      18     6      | 189    2      7      | 5      48     49     |
 |----------------------+----------------------+----------------------|
 | 59     6      2      | 7      8      49     | 3      145    145    |
 | 1      45     7      | 26     3      26     | 49     459    8      |
 | 89     48     3      | 49     1      5      | 2      6      7      |
 |----------------------+----------------------+----------------------|
 | 6      7      8      | 1245   9      124    | 14     1245   3      |
 | 24     9      1      | 23458  6      2348   | 7      2458   45     |
 | 24     3      5      | 1248   7      1248   | 1489   12489  6      |
 *--------------------------------------------------------------------*


Developing the 24s prominent in the lowest boxes :
1. 245r8c189=8r8c8-(8=4)r3c8-(4=9)r3c9-(9=18)r13c4-(18=24)r9c4 : =><24>r8c4
1a. subchain : -(9=18)r13c4-(18=9)r1c6-(9=4)r4c6 : =><4>r8c6
2. 24r9c14=18r19c4-(18=9)r3c4-(9=4)r3c9-(4=8)r3c8-(8=1)r2c7-(1=4)r7c7-(4=5)r8c9 :=><24>r9c78 (memory for the <2> highlighted)
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Re: Suggest A Move (SAM#1)

Postby Luke » Tue Feb 17, 2009 9:16 am

aran wrote:
DonM wrote:
Code: Select all
*--------------------------------------------------------------------*
 | 7      128    4      | 18     5      189    | 6      3      129    |
 | 58     125    9      | 36     4      36     | 18     7      12     |
 | 3      18     6      | 189    2      7      | 5      48     49     |
 |----------------------+----------------------+----------------------|
 | 59     6      2      | 7      8      49     | 3      145    145    |
 | 1      45     7      | 26     3      26     | 49     459    8      |
 | 89     48     3      | 49     1      5      | 2      6      7      |
 |----------------------+----------------------+----------------------|
 | 6      7      8      | 1245   9      124    | 14     1245   3      |
 | 24     9      1      | 23458  6      2348   | 7      2458   45     |
 | 24     3      5      | 1248   7      1248   | 1489   12489  6      |
 *--------------------------------------------------------------------*


Developing the 24s prominent in the lowest boxes :
1. 245r8c189=8r8c8-(8=4)r3c8-(4=9)r3c9-(9=18)r13c4-(18=24)r9c4 : =><24>r8c4
1a. subchain : -(9=18)r13c4-(18=9)r1c6-(9=4)r4c6 : =><4>r8c6
2. 24r9c14=18r19c4-(18=9)r3c4-(9=4)r3c9-(4=8)r3c8-(8=1)r2c7-(1=4)r7c7-(4=5)r8c9 :=><24>r9c78 (memory for the <2> highlighted)

In regards to chain 1: why not <24> r8c46? My reasoning is r8c6 can also see the starting and ending sets just like r8c4.
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Postby DonM » Tue Feb 17, 2009 10:10 am

Luke451 wrote:If there are four strong links (x-wing):
If a potential UR has bivalues on the diagonals and one of the components forms an x-wing, then to quote Keith, "The diagonal pairs must have the x-wing component."


Thanks Luke for the indepth explanation of your UR eliminations. You have concisely outlined 3 of the potential UR situations that are not all that infrequent and yet I think are frequently overlooked. The one above is, of course, now labelled as a Type 6 UR, but the Sudopedia example describes the result in terms of the elimination of the digit that forms the 4-strong link X-wing in the corners that have the extra digits. I think the way you describe it above (as quoted by Keith) is easier to remember. Fwiw: Someone- I forget who- coined the 4-strong link X-wing as a 'perfect x-wing' to distinguish it from a 'regular' x-wing.

storm_norm wrote:notice the marked cells contain the deadly pattern on {1,2}.
if the 9 is removed from [r9c1] r1c9:) then we know that the resulting UR can be avoided by removing the 1's in r12c2, this would force 1 into r3c2.
in other words, neither the 9 in r1c9 nor the 1 in r3c2 can both be false or the deadly pattern is forced to exist.
creates this inference...

UR12[(9)r9c1 = (1)r3c2]... can be used in this chain

(9)r3c4 = (9)r3c9 - UR12[(9)r9c1 = (1)r3c2]; r3c4 <> 1

and...

the marked UR {1,8} says that neither the 2 in r1c2 nor the 9 in r3c4 can both be false or the deadly pattern is forced to exist.
creates this inference... UR18[(2)r1c2 = (9)r3c4]... can be extended into this chain

UR18[(2)r1c2 = (9)r3c4] - (9=4)r3c9 - (4=8)r3c8 - (8=1)r2c7 - (1=2)r2c9; r1c9 <> 2


storm_norm, I find the above really useful. These are examples of another source of some good strong links that I have been seriously neglecting!

Thanks also Aran. Overall, a lot of useful stuff in just a short period of time.

UR patterns abound in this grid. Just for giggles, here's a long-winded way of getting the same elimination r1c2<>1 that Luke got (using the far more efficient UR(18)r13c24 route):

AUR(12)r1c29
||
(8)r1c2
||
(5)r5c2 - (5=8)r2c2 - (8=1)r3c2
||
(9)r1c9 - als(9=18)r1c46 => r1c2<>1
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Postby ronk » Tue Feb 17, 2009 10:50 am

There's a Type 2 uniqueness test on (236)BUG-Lite:r258c46 that implies r8c46<>2. [edit: changed "MUG" to "BUG-Lite"]

aran wrote:Developing the 24s prominent in the lowest boxes :
1. 245r8c189=8r8c8-(8=4)r3c8-(4=9)r3c9-(9=18)r13c4-(18=24)r9c4 : =><24>r8c4

That's an invalid deduction. What's to prevent r8c189=258 and r9c4=4 ?
Last edited by ronk on Thu Feb 19, 2009 7:02 am, edited 1 time in total.
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Postby storm_norm » Tue Feb 17, 2009 11:22 am

storm_norm, I find the above really useful. These are examples of another source of some good strong links that I have been seriously neglecting!

thank you,
interestingly, if it were possible, the elimination of those two candidates simultaneously solve the puzzle. but not to be:(
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Postby DonM » Tue Feb 17, 2009 11:57 am

storm_norm wrote:
storm_norm, I find the above really useful. These are examples of another source of some good strong links that I have been seriously neglecting!

thank you,
interestingly, if it were possible, the elimination of those two candidates simultaneously solve the puzzle. but not to be:(


Extreme #114 is a tricky little devil for an ER=7.2!:)
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Postby Luke » Tue Feb 17, 2009 3:35 pm

DonM wrote:Fwiw: Someone- I forget who- coined the 4-strong link X-wing as a 'perfect x-wing' to distinguish it from a 'regular' x-wing.

Something tells me you’re too modest to blow your own horn, so I won’t be looking this up to refresh your memory.:)

With four cells sporting (49), there almost had to be a w-wing:
Code: Select all
 *--------------------------------------------------------------------*
 | 7      128    4      | 18     5     *189    | 6      3     *129    |
 | 58     125    9      | 36     4      36     | 18     7      12     |
 | 3      18     6      | 189    2      7      | 5      48    *49     |
 |----------------------+----------------------+----------------------|
 | 59     6      2      | 7      8     *49     | 3      145   -415    |
 | 1      45     7      | 26     3      26     | 49     459    8      |
 | 89     48     3      | 49     1      5      | 2      6      7      |
 |----------------------+----------------------+----------------------|
 | 6      7      8      | 1245   9      124    | 14     1245   3      |
 | 24     9      1      | 23458  6      2348   | 7      2458   45     |
 | 24     3      5      | 1248   7      1248   | 1489   12489  6      |
 *--------------------------------------------------------------------*
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Postby DonM » Tue Feb 17, 2009 11:30 pm

Luke451 wrote:
DonM wrote:Fwiw: Someone- I forget who- coined the 4-strong link X-wing as a 'perfect x-wing' to distinguish it from a 'regular' x-wing.

Something tells me you’re too modest to blow your own horn, so I won’t be looking this up to refresh your memory.:)

With four cells sporting (49), there almost had to be a w-wing:
Code: Select all
 *--------------------------------------------------------------------*
 | 7      128    4      | 18     5     *189    | 6      3     *129    |
 | 58     125    9      | 36     4      36     | 18     7      12     |
 | 3      18     6      | 189    2      7      | 5      48    *49     |
 |----------------------+----------------------+----------------------|
 | 59     6      2      | 7      8     *49     | 3      145   -415    |
 | 1      45     7      | 26     3      26     | 49     459    8      |
 | 89     48     3      | 49     1      5      | 2      6      7      |
 |----------------------+----------------------+----------------------|
 | 6      7      8      | 1245   9      124    | 14     1245   3      |
 | 24     9      1      | 23458  6      2348   | 7      2458   45     |
 | 24     3      5      | 1248   7      1248   | 1489   12489  6      |
 *--------------------------------------------------------------------*


Excellent! If you notice above where I printed the original grid, I had made a typo where I didn't put the 4 in r4c9. What I had done was print the puzzle state after the W-wing by mistake.
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Postby 999_Springs » Wed Feb 18, 2009 3:06 am

xy-chain: r7c6-4-r7c7-1-r2c7-8-r2c1-5-r4c1-9-r4c6-4-r7c6 => r7c6<>4

sue de coq: 1245r7c[edit]78 + 12r7c6 + 45r8c9: r7c4<>12, r8c8r9c78<>45

This is one of the most frustrating puzzles I have ever encountered. There are many xy-chains and things that get close to eliminating something, but not quite. The total number of minutes and swear words used to get this far is about 30.

Oh, wait. Those eliminations don't do anything. (Sigh)
Last edited by l$ on Wed Feb 18, 2009 4:38 pm, edited 1 time in total.
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