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The Eureka Challenge: puzzle 31 (EC-31)
Author Message
Posted by:
ttt

25-Jan-2010
01:50 am

EC-31  

 

Please see RULES for EC  here  by DonM

gsf’s non-symmetry puzzle, received via PM on Player’s Forum – ER9.0

 

000300700040000010002006005080900300500000020006040000070080009100005040003200000

 *--------------------------------------------------------------------*

 | 689    1569   1589   | 3      1259   12489  | 7      689    2468   |

 | 36789  4      5789   | 578    2579   2789   | 2689   1      2368   |

 | 3789   139    2      | 1478   179    6      | 489    389    5      |

 |----------------------+----------------------+----------------------|

 | 247    8      147    | 9      12567  127    | 3      567    1467   |

 | 5      139    1479   | 1678   1367   1378   | 14689  2      14678  |

 | 2379   1239   6      | 1578   4      12378  | 1589   5789   178    |

 |----------------------+----------------------+----------------------|

 | 246    7      45     | 146    8      134    | 1256   356    9      |

 | 1      269    89     | 67     3679   5      | 268    4      23678  |

 | 4689   569    3      | 2      1679   1479   | 1568   5678   1678   |

 *--------------------------------------------------------------------*

 

Enjoy…!


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Posted by:
Steve Kurzhals

28-Jan-2010
06:40 am

EC 31

Forward: Two Nasty partially continuous loops, one which limits r2c9 to (36), the other limits r2c9 to (23), could be combined to yield the results of my first three steps. I broke these up, and tried to score them fairly, albeit the one step is a bracket within brackets type A*AIC. A later possible loop seems to indicate that something like Alan Barker's program could yield my first 5 steps in one ugly monstrous step.

1) AIC + FSF: HT(234)r128c9 = (4)r1c6 - r3c4 = r7c4 - r9c6 = HP(48-89)r9c1r8c2 = HT(956-562)r189c2 = (2-3)r6c2 = FSF r367c168r3c2 - r2c1 = (3)r2c9 => r2c9<>68
2) A*AIC + FSF + 2 recycles: Considers two krakens: (8)r3, (268)r8c7. Diagram at end.
(3)r2c9 = (3-8)r3c8 = [(8)r3c7 = [(8)r4c1 = (8-4)r3c4 = r7c4 - r9c6 = (4)r9c1] - (8)r9c1 = (8)r8c3] - (8)r8c7 = [(6)r2c1 = r2c7 - (6=*2)r8c7 - r8c2 = (2-3)r6c2 = FSF(3) r367c168r3c2] => r2c1<>3; Three singles; LC(9)r8c23 => r9c12<>9
Scoring: FSF add on: +.5 Two recycles -2. AAIC+AIC add on: Call this 4+2 pts? step total 4.5
3) AIC + recycle: (2)r8c9 = (2-4)r1c9 = r1c6 - r3c4 = r7c4 - r9c6 = HT(489)r9c1r8c23 => r8c2<>2; two singles
4) ALS xz rc (4) => NP(56)r7c3r9c2 = NP(16)r7c46 => r9c5<>6; LC(6)r78c4 => r5c4<>6
5) AIC + recycle: (7)r8c4 = (7-2)r8c9 = (2-4)r1c9 = r1c6 - r3c4 = (4-6)r7c4 = (6)r8c4 loop => r18c9<>68, r7c4<>1
6) (6)r7c7 = (6-4)r7c4 = r3c4 - r3c7 = NT(689)r1c8r3c78 => r9c8,r2c7<>6; two singles;
7) XY Chain: (56)r9c2 (69)r8c2 (98)r8c3 (84)r9c1 (47)r4c1 (75)r4c8 => r9c8<>5
8) XY Wing: (87)r9c8, (48)r9c1, (47)r4c1 => r4c8<>7; two singles:
9) AIC + recycle: (7)r8c2 = r8c9 - (7=8)r9c8 - (8=4)r9c1 - (4=7)r4c1 - r3c1 = (7)r2c3 => r2c4<>7; one single
10) XY Chain: (29)r2c7, (98)r3c8. (87)r9c8, (72)r2c9 => r1c9,r8c7<>2; ste

Scoring: 1 A*AIC + 5 AIC + ALS xz + 3 XY Chains + 2 FSF plug ins - 5 recycles = 6+10+4+1-5 = 16

Diagram of step 2: r2c1<>3; Depth 11, Depth 10 possible: trade (3)box 3 for (3)r3.

(3)r2c9 = (3-8)r3c8           -------------------
            ||               |                   |
            (8)r3c7 ---------         (8)r8c3 ---|
            ||                        ||         |
            (8)r3c1 ------------------(8)r9c1    |
            ||                         |         |
            (8-4)r3c4 = r7c4 - r9c6 = (4)r9c1   (8)r8c7
                                                ||
                               (6)r2c1 = r2c6 - (6)r8c7
                                                ||
     FSF(3)r367c168r3c2 = (3-2)r6c2 = (2)r8c2 - (2)r8c7


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Posted by:
ttt

29-Jan-2010
11:57 pm

*--------------------------------------------------------------------*

 | 689    1569   1589   | 3      1259   12489  | 7      689    2468   |

 | 36789  4      5789   | 578    2579   2789   | 2689   1      2368   |

 | 3789   139    2      | 1478   179    6      | 489    389    5      |

 |----------------------+----------------------+----------------------|

 | 247    8      147    | 9      12567  127    | 3      567    1467   |

 | 5      139    1479   | 1678   1367   1378   | 14689  2      14678  |

 | 2379   1239   6      | 1578   4      12378  | 1589   5789   178    |

 |----------------------+----------------------+----------------------|

 | 246    7      45     | 146    8      134    | 1256   356    9      |

 | 1      269    89     | 67     3679   5      | 268    4      23678  |

 | 4689   569    3      | 2      1679   1479   | 1568   5678   1678   |

 *--------------------------------------------------------------------*

 

01: (139=2)r356c2-(3)r6c2=(Fish 3's: r6c6=r6c1-r5c2=r3c2-r3c8=r7c8)-(3)r7c6=(3-9)r8c5=(9)r9c56

=> r9c2<>9

02: (23)r28c9=(2-4)r1c9=(4)r1c6-(4)r3c4=(4)r7c4-(456=2)r7c13/r9c2-(2)r8c2=(2)r6c2-(3)r6c2=(Fish 3's: r6c6=r6c1-r5c2=r3c2-r3c8=r7c8)-(3)r7c6=(3)r7c8-(3)r3c8=(3)r2c9 => r2c9<>68

03: Present as diagram: => r2c6<>2

 

AAHS(1247)r4c16

 ||

(27)r4c16-(2)r4c5=(2)r12c5*

 ||

(4)r4c1-(4)r9c1=(4)r9c6-(4)r1c6=(4-2)r1c9=(2)r2c79*

 ||

(1)r4c6-(1)r7c6

         ||

        (3)r7c6-(3)r7c8=(3)r3c8-(3=2)r2c9*

         ||

        (4)r7c6-(4)r1c6=(4-2)r1c9=(2)r2c79*

 

04: Present as diagram: => r2c7<>89

 

      AAHS(3689)r13c8

         ||

(6)r4c8-(6)r1c8=(6)r2c7*

 ||      ||

 ||     (89)r13c8*

 ||      ||

 ||     (3)r3c8-(3-6)r2c1=(6)r2c7

 ||

(5)r4c8-(5)r4c5

 ||      ||

 ||     (5)r2c5-(2)r2c5=(236)r2c179*

 ||      ||

 ||     (5)r1c5-(5)r1c2=(5)r9c2-(5=4)r7c3--(4)r7c4=(4)r3c4-(4)r1c6=(4-2)r1c9=(236)r2c179*

 ||                                       |

(7)r4c8-(7)r4c1                           |

         ||                               |

        (2)r4c1-(2)7c1=(XY-wing:456)r7c13/r9c2-

         ||                               |

        (4)r4c1-(4)r9c1=(4)r9c6-----------

 

05: Present as diagram: => r7c7<>2, r7c1 & r6c2=2

 

(2)r2c7*

 ||

(2)r1c9-(4)r1c9=(4)r1c6-(4)r9c6=(4-8)r9c1=(8)r8c3-(8=26)r28c7*

 ||

(2-3)r2c9=(3)r3c8-(8)r3c8

                   ||

                  (8)r3c7-(8=26)r28c7*

                   ||

                  (8)r3c1-(8)r9c1=(8)r8c3-(8=26)r28c7*

                   ||

                  (8-4)r3c4=(4)r7c4-(4)r9c6=(4-8)r9c1=(8)r8c3-(8=26)r28c7*

 

06: 3's  r3c2=r5c2-r3c5=r8c5-r8c9=r2c9 => r2c1<>3, some singles

07: (26=8)r28c7-(8)r8c3=(8-4)r9c1=(4-5)r7c3=(5)r7c7 => r7c7<>6, STTE

 

Follow Steve's suggestion for scoring of A*AIC:

Score: 1(Color)x1 + 3(AICs)x2 + 3(A*AICs)x6 + 2(surcharge #1&2)x.5 – 1(recycle)x1 = 25 pts


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Posted by:
Luke

30-Jan-2010
09:40 am

Hi, guys. As usual, two great solutions before I even have my foot in the door. At my level, it’s helpful to learn from your approaches, and take away what I can understand.

 

ttt, I’ve noticed you make good use of the strong links provided by hidden pairs throughout the puzzle. When I first scan the puzzle now, I look for them and jot them in the margin for later reference. They come in handy.

 

 Among those present from the start:

 

(36=6)r2c179

(23=2)r128c9 (This one you used in move 1)

(37=7)r8c459

(24=2) r1

(56=6) r4

(56=6) c2

. . .etc. . .

 

 *--------------------------------------------------------------------*

 | 689    1569   1589   | 3      1259   12489  | 7      689    2468   |

 | 36789  4      5789   | 578    2579   2789   | 2689   1      2368   |

 | 3789   139    2      | 1478   179    6      | 489    389    5      |

 |----------------------+----------------------+----------------------|

 | 247    8      147    | 9      12567  127    | 3      567    1467   |

 | 5      139    1479   | 1678   1367   1378   | 14689  2      14678  |

 | 2379   1239   6      | 1578   4      12378  | 1589   5789   178    |

 |----------------------+----------------------+----------------------|

 | 246    7      45     | 146    8      134    | 1256   356    9      |

 | 1      269    89     | 67     3679   5      | 268    4      23678  |

 | 4689   569    3      | 2      1679   1479   | 1568   5678   1678   |

 *--------------------------------------------------------------------*

 

What I have found so far includes the following move, which happened to use the same (23=2) that you used. . . it has that convenient link out on the (4).

 

(23=2)r128c9-(4)r1c9=r1c6-r9c6=(4-8)r9c1=(8)r8c3 =>r8c9<>8.

 

Here’s another one off the same start. I don’t know if it’s correct. I’m trying to use what has been called a “pausing chain” by some, but when I first heard about it, it was referred to as “memory.” If this is legitimate, it probably sh/be written as a net somehow.

 

Red indicates use of bold “memory.”

 

(23=2)r128c9-(4)r1c9=r1c6-r3c4=(4)r7c4-r9c6=r9c1-(4=5)r7c3-(5=2694)r7c1,r89c2-(grp9=123)r356c2-(2)r46c1=r7c1-(2=13645)r7c678 =>r8c9<>6.

 

 


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Posted by:
Steve Kurzhals

30-Jan-2010
09:54 pm
 ttt,
First, I would like to thank you for providing these interesting puzzles.

Secondly, I think eventually we should try to formalize a scoring formula for A*AICs.  I really do not have anything specific in mind.  However, I believe that your first diagram is much less complex than your next two.  Your first diagram indicates that one could build a straight-line AAIC  type presentation that would not require nested brackets.  The latter diagrams would require such nested bracketing,  (or coloring of links, etc.), I believe.

I would suggest thus that your first diagram is a legitimate AAIC, even though it uses two tri-sis.  My reasoning is that  no singular point  in the logic  uses a structure more complex than an AIC+1degree of freedom.  Thus the logic used is clearly simple AAIC logic.  I would argue then that the logical technique employed is AAIC, even if it uses more than one tri-sis.

Thus, I would support assigning a score of 4 + perhaps .5 for each additional tri-sis used, if and only if the additional tri-sis are weakly  linked (either directly or by a connecting AIC segment) so that the remaining bi portions of the tri-sis exist in their own independent AICs.  In other words, if no nested brackets need be used.

However, if nested brackets need to be used, perhaps an additional +2 for each nested depth.

For examples:
a=[c=d-e=f]-...... is an AAIC with tri-sis [abc]  or perhaps tri sis [aef], score 4.

[a=b-c=d]=e-f=[g=h-i=j].... is an AAIC with two independent tri-sis AAIC segments,  perhaps [abe] and [fgh],  score 4.5.

- [a=b-c=d] = [e=f-g=h] - ......  is an AAIC with a quad sis, but two independent AAIC segments using for example the quad sis [c,d,e,f].  Perhaps this should also score 4.5, as it is essential equal in complexity in bracket structure to the previous one.

- a=b-c=[d=e-f=[g=h-i=j]-k=l] - m=n -  is an A*AIC with two tri-sis, for example [c,d,e] and [f,g,h], but requires nested brackets. This perhaps should be scored 6, as it nests the idea of an AAIC structure within itself.

I would appreciate input from others on these issues.  There probably exists an easier way to handle these ideas.  Also, perhaps I am way -over analyzing and complicating things.





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Posted by:
Steve Kurzhals

30-Jan-2010
10:54 pm

Luke, below is my take on your AAIC.  I use "pauses" to notate AIC's that have shorter segments within them that also forbid something.  Memory is more directly similar to a tchain-like or TM type of construct.  Generally, it also describes one way to analyze an AAIC such as yours.  However, I find it more useful to think in the language of AAIC's in simpler cases such as this one.  Hopefully I can successfully demonstrate why I think this is a simple case of one of the least complex types of tri-sis considerations within an AAIC.


First, excuse me as I converted some of your ALS into AHS.   The tri sis i would use is (6)r7, broken into (6)r7c1, r7c4, grp r7c78.  I would use nested brackets and asterisks to indicate endpoints of the tri-sis:

HP(23)r28c9 = (2-4)r1c9 = r1c6 - r3c4 = (4)r7c4 - [(6)r7c4 = * (6-2)r7c1 = HT(256-569)r189c2 = (HP89-84)r8c3,r9c1 = (4)r9c6] = (6*)r7c78 => r8c9<>6

For readability, I probably would place the three members of the tri-sis closer together in the chain, thus reversing the AIC within the brackets.  Alternatively,  I might  place the tri-sis at the beginning of the entire animal:

(6*) = [(6) =* (6) ........ ] - (4) = ....... HP

This would diagram as, imo, a mild AAIC as one of the members of the tri-sis is directly involved in the forbidding:
(6)r7c78
||
(6-2)r7c1 = HT(256-569)r189c2 = HP(98-84)r8c3r9c1 = (4)r9c6
||                                                   |
||  -------------------------------------------------
|| |
(6-4)r7c4 = r3c4 - r1c6 = HT(234)r128c9


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Posted by:
Luke

31-Jan-2010
04:40 pm

Steve, thanks for looking at that! Getting feedback from some of you guys is like a scrub chess player getting feedback from Garry Kasparov.

 

Steve: “I would use nested brackets and asterisks to indicate endpoints…”

 

Youda thought I’d have figured out b4 now what this meant, but I hadn’t. This will make it easier for me to understand your moves in the future.

 

Thanks for finding the tri-sis angle. AAICs and their notation are not well documented on the main sudoku boards/sites. It’s mainly learning by observation, and I’m adept at forming misconceptions.

 

I’m also beginning to appreciate more the power of hidden pairs and triples in manual solving. They’re so easy to overlook.

 

 *--------------------------------------------------------------------*

 | 689    1569   1589   | 3      1259   12489  | 7      689    2468   |

 | 36789  4      5789   | 578    2579   2789   | 2689   1      2368   |

 | 3789   139    2      | 1478   179    6      | 489    389    5      |

 |----------------------+----------------------+----------------------|

 | 247    8      147    | 9      12567  127    | 3      567    1467   |

 | 5      139    1479   | 1678   1367   1378   | 14689  2      14678  |

 | 2379   1239   6      | 1578   4      12378  | 1589   5789   178    |

 |----------------------+----------------------+----------------------|

 | 246    7      45     | 146    8      134    | 1256   356    9      |

 | 1      269    89     | 67     3679   5      | 268    4      23678  |

 | 4689   569    3      | 2      1679   1479   | 1568   5678   1678   |

 *--------------------------------------------------------------------*

 

Steve:

(6)r7c78
||
(6-2)r7c1 = HT(256-569)r189c2 = HP(98-84)r8c3r9c1 = (4)r9c6
||                                                   |
||  -------------------------------------------------
|| |
(6-4)r7c4 = r3c4 - r1c6 = HT(234)r128c9

 

I had to come back three times b4 that HT sank in. I initially tried to pound it in with my own square peg:

 

(6-2)r7c1=(2)r8c2-(2=139)r356c2-gp(9)r89c2=HP(89)r8c3,r9c1-(4)r9c1=(4)r9c6-etc

 

(Tomorrow, one last issue on this puzzle: Fish 3’s. There seems to be no limit to my ignorance. . .)

 


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Posted by:
Ronk

31-Jan-2010
08:57 pm
 Luke: I had to come back three times b4 that HT sank in. I initially tried to pound it in with my own square peg:

 

(6-2)r7c1=(2)r8c2-(2=139)r356c2-gp(9)r89c2=HP(89)r8c3,r9c1-(4)r9c1=(4)r9c6-etc

 

Maybe an octagonal peg will work better: :-)

 

(6-2)r7c1 = (2-6)r8c2 = HP(65-59)r19c2 = HP(98-84)r8c3,r9c1 = (4)r9c6

 

It splits a strong link in b7 from an AHP in c2, so might be easier to see.

 


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