JExocet Compendium

Advanced methods and approaches for solving Sudoku puzzles

Re: JExocet Compendium

Postby David P Bird » Sat May 07, 2016 12:30 pm

Leren, Here's an off-the-cuff response:

The covering rows that Champagne stipulates could be any two covering houses - rows, columns or, in the case of Denis Berther's extension, boxes.

It's very difficult to formulate a precise definition of a pattern, but one essential is that they should be capable of being identified without having to track any logic streams but just by counting and checking the defined elements exist in a qualifying distribution.

We have the concept that an almost pattern is one that just misses qualifying because one required criterion isn't met, and using that terminology you can bring many of your cases into the fold by embedding it in a chain. Compendium file 9 gives some examples of this.

If more than one chain is needed then it becomes a net-based process.

Definitions are required to make our discussions clear and while any route to solving a puzzle is valid, trying to get some methods to appear more acceptable by bending definitions shouldn't be on the agenda. It's easy enough to add an explanatory qualifier – eg 'memory' chains. 'Reasonableness' is a nice concept but experience shows there can never be any agreement about what is and what isn't reasonable within our community.

I'll review how these points are covered in the compendium, check for conflicting terminology, and consider possible modifications later.

David
David P Bird
2010 Supporter
 
Posts: 960
Joined: 16 September 2008
Location: Middle England

Later Use of JE Inferences

Postby David P Bird » Tue May 10, 2016 8:54 am

This tortuous puzzle is from Andrew Stuart's < Unsolvable Series > which contains a single JExocet. It illustrates how repeated use of the JE's derived inferences (starred steps) can allow a purely linear solution.

...4...8..9...1..37...8..1.....5..4...57......3...6..26....21...1..9....3.2.....9 SudokuWiki Unsolvable 198
Code: Select all
 *-------------------------*-------------------------*-------------------------* Cover Rows
 | 125     256     136     | <4>     2367    3579    | 25679   <8>     567     | .57.
 | 2458    <9>     468     | 256     267     <1>     | 24567   2567    <3>     |
 | <7>     2456    346     | 23569   <8>     359     | 24569   <1>     456     | 45..
 *-------------------------*-------------------------*-------------------------*
 | 1289    2678    1678    | 12389   <5>     389     | 3678    <4>     1678    | ..78
 | 12489   2468    <5>     | <7>     1234    3489    | 368     369     168     | 4..8
 | 1489    <3>     1478    | 189     14      <6>     | 578     579     <2>     |
 *-------------------------*-------------------------*-------------------------*
 | <6>     4578    9       | 358     347     <2>     | <1>     357     4578  T |
 | 458 B   <1>     478 B   | 3568    <9>     34578   | 2345678 23567   45678   |
 | <3>     4578    <2>     | 1568    1467    4578  T | 45678   567     <9>     |
 *-------------------------*-------------------------*-------------------------*
           CLb                               CL1                       CL2

(4578)JExocet2:r8c13,r9c6,r7c9
=> r7c8 <> 3, r9c45 <> 6 ((1) is locked as the non-base digit in both mirror nodes)
=> r9c6 <> 48 (base digits absent from mirror node)
. . Single (6)r8c4
. . (23)HPair:r8c78 => r8c7 <> 4578, r8c8<> 57, r8c6 <> 3
Incompatibility checks are inconclusive but (57)target:r9c6 show that (48) can't both be true in the base cells.

* (5)JE:r9c46,r8c1 = (7)r8c3 - (7)r6c3 = (57-9)r6c78 = (239-6)r258c8 = (6)r9c8 => r9c8 <> 5
(5=2)r2c4 - (2)r2c8 = (23-9)r58c8 = (9-5)r6c8 = (5)r6c7 => r2c7 <> 5
* (5=2)r2c4 - (2)r2c8 = (23-9)r58c8 = (59-7)r6c78 = (7)r6c3 - (7=5)JE:r8cb7,r9b8,r7b9 => r2c1,r2c8 <> 5
. . Single (5)r2c4
* JE: => r7c9 <> 5 (absent from mirror node)
* (5)r8c6 = (5)JE:r9c6,r8c1 => r8c9 <> 5
. . (5)LineBox:c9b3 => r13c7 <> 5
(8)r6c13 = (8)r6c4 - (8)r79c4 = (8)r8c6 - (8)r8c13 = (8)r79c2 => r45c2 <> 8
. . (8)LineBox:c2b7 => r8c13,
* JE => r7c9,r9c4 <> 8 (non-base digit in a target and its mirror)
. . (1)Single:r9c4
* (5)r6c7 = (5)r9c7 - (5=7)JE:r7b9,r8b7 - (7)r6c3 = (57)r6c78 => r6c7 <> 8

Continuation: Show
(6)r9c8 = (6-8)r9c7 = (8)r9c2 - (8)r7c2 = (8)r7c4 - (8=9)r6c4 - (9)r6c8 = (239)r258 => r25c8 <> 6
. . (6)Single:r9c8
(4)r3c2 = (4)r79c2 – (4=7)r8c3 – (7)r69c2 = (267-5) = (5)r3c2 => r3c2 <> 26
(4)r5c6 = (4)r8c6 – (4)r8c13 = (4)r79c2 => r5c2 <> 4
(2)r3c4 = (2)r3c7 – (2=3)r8c7 – (3)r8c8 = (3-9)r5c8 = (9)r6c8 – (9=8)r6c4 – (8=3)r7c4 => r3c4 <> 3
(1=4)r6c5 - (4)r5c6 = (4-8)r8c6 = (8-3)r7c4 = (3-2)r4c4 = (2)r5c5 => r5c5 <> 1
. .Single (1)r6c5
(2)r5c5 = (2-3)r4c4 = (3-8)r7c4 = (8-4)r8c6 = (4)r5c6 => r5c5 <> 4
. . Single (4)r4c6
(8)r4c6 = (8)r8c6 – (8)r8c9 = (8)r8c7 => r4c7 <> 8
(2)r3c4 = (2)r3c7 – (2=3)r8c7 – (3)r8c8 = (3)r5c8 – (3=2)r5c5 => r12c5,r4c4 <> 2
. . Singles (2)3c4,r5c5, (6)r5c2
(2)r2c8 = (23-9)r58c8 = (9)r6c8 - (9=8)r6c4 - (8)r7c4 = (8)r8c6 - (8)r8c9 = (8)r9c7 = (238)r589c7 => r12c7,r8c8 <> 2
. . Singles to the end
David P Bird
2010 Supporter
 
Posts: 960
Joined: 16 September 2008
Location: Middle England

Re: JExocet Compendium

Postby David P Bird » Wed Jun 08, 2016 9:07 am

This is another SodokuWiki unsolvable puzzle that has a couple of notable features

1..4...89......1....9..1.452...6...7..85..4...7.........18..9.......3....6..2..3. SudokuWiki Unsolvable 203
Code: Select all
 *----------------------*----------------------*----------------------*
 | <1>    235    23567  | <4>    357    2567   | 2367   <8>    <9>    |
 | 345678 23458  234567 | 23679  35789  256789 | <1>    267    236    |
 | 3678   238    <9>    | 2367   378    <1>    | 2367   <4>    <5>    |
 *----------------------*----------------------*----------------------*
 | <2>    13459  345    | 139    <6>    489    | 358    159    <7>    | .3..
 | 369    139    <8>    | <5>    1379   279    | <4>    1269   1236   |
 | 34569  <7>    3456   | 1239   13489  2489   | 23568  12569  12368  | 236.
 *----------------------*----------------------*----------------------*
 | 3457   2345   <1>    | <8>    457    4567   | <9>    2567   246    |
 | 45789  24589  2457   | 1679   14579  <3>    | 25678  12567  12468  | 2.67
 | 45789  <6>    457    | 179    <2>    4579   | 578    <3>    148    | ...7
 *----------------------*----------------------*----------------------*
                 CL1      CL2                    CLb

(2367)JE2:r2c89,r1c3,r3c4
=> r1c3 <> 5 (non-base digit in target)
=> r1c2 <> 5, r3c5 <> 8 (1 is non-base digit in these mirror nodes)
=> r1c3 <> 26, r3c4 <> 67 (base digits missing in mirror cells)
=> r2c89 <> 6 (not in either target)
(5)BoxLine:b1r2 => r2c56 <> 5
(8)BoxLine:b2r2 => r2c12 <> 8
(6)BoxLine:b3c7 => r68c7 <> 6
At this point it seems that another (237)JE2 exists with the second pair of base cells either being r1c23 or r3c45 but both of these would need column1 as a cross line and this would break the rule for two cover houses per base digit.
However as (1) is always the third digit in the mini-lines with the base cells and targets, all mini-lines following the / diagonal direction in the JE band will hold the same three digits (a rope pattern).

Code: Select all
 *----------------------*----------------------*----------------------*
 | <1>    23     37     | <4>    357    2567   | 2367   <8>    <9>    |
 | 34567  2345   234567 | 23679  3789   26789  | <1>    27     23     |
 | 3678   238    <9>    | 23     37     <1>    | 2367   <4>    <5>    |
 *----------------------*----------------------*----------------------*
 | <2>    13459  345    | 139    <6>    489    | 358    159    <7>    |
 | 369    139    <8>    | <5>    1379   279    | <4>    1269   1236   |
 | 34569  <7>    3456   | 1239   13489  2489   | 2358   12569  12368  |
 *----------------------*----------------------*----------------------*
 | 3457   2345   <1>    | <8>    457    4567   | <9>    2567   246    |
 | 45789  24589  2457   | 1679   14579  <3>    | 2578   12567  12468  |
 | 45789  <6>    457    | 179    <2>    4579   | 578    <3>    148    |
 *----------------------*----------------------*----------------------*

Tier 1 repeat pattern 
 *----------------------*----------------------*----------------------*
 | <1>    b      a      | <4>    d5     d5     | c      <8>    <9>    |
 | d45    d45    d45    | c9     c89    c89    | <1>    ab     ab     |
 | c8     c8     <9>    | b      a      <1>    | d      <4>    <5>    |
 *----------------------*----------------------*----------------------*

(2)r13c7 = (2)r2c89 - (2)r2c3 = (2)r8c3 => r8c7 <> 2
(3+257=6)r1c2356 - (6+2789=3)r2c45689 => 1c7,r2c34,r3c12 <> 3 (on the same mini-line diagonal)
(3=7)r3c5 - (7)r5c7 = (7-2)r5c6 = (2)r5c89 - (2)r6c7 = (2)r13c7 - (2=3)r2c9
=> r3c7,r1c5,r2c123 <> 3 (same mini-line diagonal)
Single (3)r2c9
JE: => r4c2, r6c1,5 <> 3 (non-'S' cells in cover rows for true base digit)
(7)r5c5 = (7-2)r5c6 = (2)r5c89 - (2)r6c7 = (2)r13c7 - (2=7)r2c8 - (7)r13c7,r2c4 = (7)XWing:r89c47 - (7)r89c13, = (7-3)r7c1 = (3)r5c1 => r5c5 <> 3
Singles (3)r3c5,r1c3 (mirror cell & target)
This breaks the back of the puzzle

The two notable features are
1 Recognising that 3 digits stay together in the mini-lines (a rope pattern)
2 Using the knowledge that if (7) was true in the base cells then there would be an X-Wing in its 'S' cells

(Other eliminations for (3) and (7) before the killer step are available but prove to be insignificant.)

DPB
.
[Edit] typos reported by Gordon F (thanks)
David P Bird
2010 Supporter
 
Posts: 960
Joined: 16 September 2008
Location: Middle England

Re: JExocet Compendium Corrections

Postby David P Bird » Sat Mar 18, 2017 11:19 pm

There were serious flaws in File 03 'JE & SK Loop Combinations' because it included some false conjectures which resulted in a flawed solution to the Easter Monster – please accept my apologies for this. Consequently this file and the corresponding example file have been re-written.

Most of the other files have been updated to correct typos and poorly worded sentences, but with no major changes to content. These were reported to me by Gordon Fick for which I am very grateful. My thanks also go to Leren for extracting JE2/SK Loop puzzles for me to analyse during the file 3 re-write.

David P Bird
.
David P Bird
2010 Supporter
 
Posts: 960
Joined: 16 September 2008
Location: Middle England

Previous

Return to Advanced solving techniques