## Exotic patterns a resume

Advanced methods and approaches for solving Sudoku puzzles

### Re: Exotic patterns a resume

David P Bird wrote:The targets you specified didn't make sense to me for a JE pattern however. At some point I would like some clarification about whether the target cells in a QExocet pattern must hold different base digits or not.

Selection of target cells in a QExocet may be forced by base cells values. Here is my solver's output -- including a breakdown of the target cells value assignments.

Code: Select all
` ***   r5c8 = <1>      r5c2 = <1479> ### -1479- QExocet   Base = r4c46 <17>   Target = r5c8,r5c2 ***   r4c4 = <1>      r4c2 = <1479> ### -1479- QExocet   Base = r5c89 <19>   Target = r4c4,r4c2`

In the first QExocet, the value <1> may reside in r5c8 or r5c2. The values <479> can only reside in r5c2. Thus, r5c8=1 and r5c2<>1 ... and the base cells contain <1>. If you only consider the base cells and target cell r5c2 for <479>, then my Exocet Single-Target Pattern applies.

In the second QExocet, the value <1> may reside in r4c4 or r4c2. The values <479> can only reside in r4c2. Thus, r4c4=1 and r4c2<>1 ... and the base cells contain <1>. If you only consider the base cells and target cell r4c2 for <479>, then my Exocet Single-Target Pattern applies.

I believe the results of the two QExocets contain the results of your Almost Triple JE.

Code: Select all
` results of two QExocets:   r4c4=1 and r5c8=1 *-----------------------------------------------------------------------------* | 9       8       123     | 7       6       1234    | 5       24      24      | | 7       136     4       | 259     159     1235    | 189     289     2689    | | 126     16      5       | 249     8       124     | 3       2479    24679   | |-------------------------+-------------------------+-------------------------| | 5       479     6       | 1       2       47      | 4789    34789   34789   | | 3       479     8       | 4569    4579    4567    | 2       1       479     | | 14      2       179     | 3       479     8       | 479     6       5       | |-------------------------+-------------------------+-------------------------| | 1248    5       1279    | 248     3       1247    | 6       24789   24789   | | 2468    3467    237     | 24568   457     9       | 478     23478   1       | | 12468   134679  12379   | 2468    147     12467   | 4789    5       234789  | *-----------------------------------------------------------------------------*`

At the risk of adding confusion to the discussion, I'm including my solver's output for when it discovers target cells in the same box. A new feature. To my knowledge, it doesn't add anything of value to what's already known about this puzzle.

Code: Select all
` ***   r5c8 = <1>      r6c7 = <1479> ### -1479- ZExocet   Base = r4c46 <17>   Target = r5c8,r6c7 ***   r4c4 = <1>      r6c5 = <1479> ### -1479- ZExocet   Base = r5c89 <19>   Target = r4c4,r6c5`

_
daj95376
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### Re: Exotic patterns a resume

AACK !!!

I checked champagne's ReadMe file and discovered that the "double" file was for Exocets ... and not (necessarily) JExocets.

I'll scan the (nearly) 1M JExocet puzzles in another file to see if there's anything usable there.

I'm sorry for the mixup!!!

_
daj95376
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Posts: 2624
Joined: 15 May 2006

### Re: Exotic patterns a resume

daj95376 wrote:AACK !!!

I checked champagne's ReadMe file and discovered that the "double" file was for Exocets ... and not (necessarily) JExocets.

I'll scan the (nearly) 1M JExocet puzzles in another file to see if there's anything usable there.

I'm sorry for the mixup!!!

_

Thanks but I've now found a couple of examples I can use by scanning 5000 puzzles from Champagne's 'grey' double Exocet file, one from a batch of about 10 close cousins and the other from 2 close cousins.

As they are a lot rarer than I thought there isn't such a need for many examples. It's been hard going as it takes 7 minutes for the spread sheet just to load the master file! If the mood takes me I might try to find another one or two later today, but then I'll wrap it up.

In case you want to try them with QExocet here are the ones I found:
Hidden Text: Show
98.7.......7.6.5......54...3......7..2.....1...94..8..1......2...48..9.......6..3 2 0 match type 14 r1c5 r1c6 r3c3 r3c7 123 r2c8 r2c9 r3c3 r3c4 1239
98.7.......7.6.5......54...5......3...46..9.......2..11......2..3.....8...98..6.. 2 0 match type 14 r1c5 r1c6 r3c3 r3c7 123 r2c8 r2c9 r3c3 r3c4 1239
98.7.......7.6.5......54...5......3...48..9.......2..11......2..3.....8...94..6.. 2 0 match type 14 r1c5 r1c6 r3c3 r3c7 123 r2c8 r2c9 r3c3 r3c4 1239
98.7.......7.6.5......54...5......3..2......1..64..9..31.....2...98..3.......3..8 2 0 match type 4 r1c5 r1c6 r3c3 r3c7 123 r2c8 r2c9 r3c3 r3c4 1239
98.7.......7.6.5......54...5......3..2......1..84..9..31.....2...98..3.......3..6 2 0 match type 4 r1c5 r1c6 r3c3 r3c7 123 r2c8 r2c9 r3c3 r3c4 1239
98.7.......7.6.5......54...53.....2...86..3.......3..12.......4.1.....3...69..8.. 2 0 match type 4 r1c5 r1c6 r3c3 r3c7 123 r2c8 r2c9 r3c3 r3c4 1238
98.7.......7.6.5......54...6......3...48..9.......2..11......2..3.....6...96..8.. 2 0 match type 14 r1c5 r1c6 r3c3 r3c7 123 r2c8 r2c9 r3c3 r3c4 1239
98.7.......7.6.5......54...7......3..2......1..68..9..31.....2...96..3.......3..8 2 0 match type 4 r1c5 r1c6 r3c3 r3c7 123 r2c8 r2c9 r3c3 r3c4 1239
98.7.......7.6.5......54...7......3..2.....1...89..6...3.....4...96..8.......1..2 2 0 match type 14 r1c5 r1c6 r3c3 r3c7 123 r2c8 r2c9 r3c3 r3c4 1238
98.7.......7.6.5......54...73.....2...86..3.......3..12.......9.1.....3...69..8.. 2 0 match type 4 r1c5 r1c6 r3c3 r3c7 123 r2c8 r2c9 r3c3 r3c4 1238
98.7.....6.....7....7.5..4.3..........48..9......32.6..1...9..2..95..8......6..1. 2 0 match type 40 r1c8 r1c9 r2c3 r2c4 1235 r3c1 r3c2 r2c4 r1c7 123
98.7.....6.....7....7.5..4.3..........48..9......32.6..1...9..2..95..8......6..1. 2 0 match type 40 r1c8 r1c9 r2c3 r2c4 1235 r3c1 r3c2 r2c4 r1c7 123

DPB
David P Bird
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Location: Middle England

### Re: Exotic patterns a resume

David P Bird wrote:Thanks but I've now found a couple of examples I can use by scanning 5000 puzzles from Champagne's 'grey' double Exocet file, one from a batch of about 10 close cousins and the other from 2 close cousins.

As they are a lot rarer than I thought there isn't such a need for many examples. It's been hard going as it takes 7 minutes for the spread sheet just to load the master file! If the mood takes me I might try to find another one or two later today, but then I'll wrap it up.

In case you want to try them with QExocet here are the ones I found:

If your JExocet are the same as my QExocets, then all of your puzzles have a 3-value JExocet combined with a 4-value JExocet. That's okay, but my solver doesn't pair them up as a double QExocet -- logistics of processing.

I completed a pass through champagne's JExocet file -- 998,226 puzzles -- and found these (25) 4-value QExocet pairs for you to check as double JExocets.

Hidden Text: Show
98.7..6..76..5......5......8...4..3..2......1..79..5....86..9......1..4......3..2;209511;GP;12_11;1;r3c1 r3c2 r2c4 r2c7 1234;;
.......12.....3..4..1.4.5....2.6..5..3.7.....8....9.....4.5..2..7....6..9..8..4..;254067;dob;12_12_03;1;r1c7 r2c7 r4c9 r7c9 3789;;
.......12.....3..4..4.1.5....1.6..5..3.7.....8....9.....6.2..4..7.8..6..9.....2..;254068;dob;12_12_03;1;r1c7 r2c7 r4c9 r7c9 3789;;
.......12.....3..4..4.1.5....1.6..5..3.7.....8....9.....6.2..4..9...62..7..8..6..;254069;dob;12_12_03;1;r1c7 r2c7 r4c9 r7c9 3789;;
........1..2..3.4..4..5.6......1.5.....6....7..8..4.9..8...9.2.2.3......4.97.....;455527;dob;12_12_03;1;r8c2 r9c2 r2c1 r6c1 1567;;
98.7..6..75..9......6..5...8...4..3..2...9..1..75..9..1.......2..89..5.......3.4.;605062;GP;12_12;1;r3c1 r3c2 r2c4 r2c7 1234;;
.......12.....3..4..2.1.5....1.4..5..3...6...7..8.......4.9..2..8....9..6..7..4..;653819;dob;12_12_19;1;r1c7 r2c7 r4c9 r7c9 3678;;
.......12.....3..4..2.4.5....4.5..2..6....7..8..9..4....7.1..5..3...8...9..6.....;653820;dob;12_12_19;1;r1c7 r2c7 r4c9 r7c9 3689;;
.......12....134....42....5..23..1...6.....7.8...9......31..5...7...8...9...3..6.;653821;dob;12_12_19;1;r2c8 r2c9 r1c3 r1c4 6789;;
........1.....123...2.3.45...1.4...5.6...7...8..9.......4.2...3.7.8..5..9......6.;744214;dob;12_12_19;1;r1c7 r1c8 r2c3 r2c5 6789;;
.....1..2..3....4..5..6.7.......4.1..7..8.3..5..9......67..8..9.852.....3...7.8..;744248;dob;12_12_19;1;r7c1 r8c1 r3c3 r5c3 1249;;
98.7..6....5.6..7.....59...8....43...2......1..65...8.13......2..89...3.....3.4..;849275;GP;13_03;1;r1c5 r1c6 r3c3 r3c8 1234;;
98.7..6..7...5......4..9.7..7...3.8...95....2..3.1.....4...5.9...86..5......2...1;879105;GP;13_03;1;r1c3 r2c3 r4c1 r7c1 1256;;
98.7..6..75..4......3..9.7.8....5.9...5.2..6......4..13....7.8....4....6....1.2..;959771;GP;13_05;1;r1c3 r2c3 r4c2 r7c2 1246;;
98.7..6..7...5......4..8.7.4.3.2.....9...7.3...75....1.4...5.9....6..5......1...2;1023217;GP;13_07;1;r1c3 r2c3 r5c1 r7c1 1256;;
98.7.....6.....5....4.6..9..9..3..6...62.......3..61...4..9..8....5..7.......1..2;1429910;GP;14_06;1;r1c3 r2c3 r4c1 r7c1 1257;;
98.7.....7...86.....6..57..4......3..2......1..86..9...3......4..78..5......1..2.;1443437;GP;14_06;1;r1c5 r1c6 r2c3 r2c7 1234;;
98.7..6..5...4......3..8.5.8....3.9..92.......3......1..8..9.2....6..4......1...7;1458080;GP;14_06;1;r5c1 r6c1 r3c2 r7c2 1467;;
98.7..6..75.........6.5....4......3..2..9...1..75..8....98..7......3..2......1..4;1483787;GP;14_06;1;r3c1 r3c2 r2c4 r2c7 1234;;
98.7..6..75.........6.5....4......3..7...2..1..89..5....76..8......3...2.....1.4.;1483788;GP;14_06;1;r3c1 r3c2 r2c4 r2c7 1234;;
98.7..6..75.........6.5....4...9..3...75..9.......2..1..89..7......3...4.....1.2.;1483790;GP;14_06;1;r3c1 r3c2 r2c4 r2c7 1234;;
98.76.5..75.........6......4....3.....8.5.9.....2...1..3...6..4..7.9.8.....1...2.;1514141;GP;14_06;1;r3c1 r3c2 r2c5 r2c7 1234;;
98.76.5..75.........6......4....3.....8.5.9.....2...1..3...6..4..9.8.7.....1...2.;1514142;GP;14_06;1;r3c1 r3c2 r2c5 r2c7 1234;;
9876.....5...8.......7.95..4......3..9..7.6....2.....11......2..6..9.8.....3....4;1515379;GP;14_06;1;r2c4 r2c6 r3c2 r1c7 1234;;
98.7..6..75.........6.5.....4..3..2...75..8.......1..4..89..5......2..1......5..3;1609736;GP;14_09;1;r3c1 r3c2 r2c4 r2c7 1234;;
daj95376
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### Re: Exotic patterns a resume

DAJ wrote:I completed a pass through champagne's JExocet file -- 998,226 puzzles -- and found these (25) 4-value QExocet pairs for you to check as double JExocets.

My spreadsheet helper doesn't find JEexocets for me but just provides a colouring scheme to help me find them by eye. Nevertheless I've run through your 25 finds and only #12 is a double JE at the start [wrong!]. I say 'at the start' because later eliminations could turn them into doubles.

In 22 of them although a second potential base pair exists, no companion cell is available for one of the targets.
In the other 2 that fail companion cells exist but they have too many 'S' cells.
The double JE for #12 is (1234)Double JE:r1c56,r3c3,r3c8; r2c12,r3c4,r1c8

DPB

Correction #12 isn't a double JE either, I blundered in checking the grid.
David P Bird
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### Re: Exotic patterns a resume

champagne wrote:
daj95376 wrote:Champagne's second exocet, r4c4 r4c6 r6c3 r6c7 1479, seems questionable. Consider the following assignments:

Code: Select all
` r4c4=1   and   r1c6,r2c7,r3c2,r5c8,r6c1,r7c3,r9c5=1   and   (given) r8c9=1 *--------------------------------------------------------------------------------* |  9       8       23      |  7       6      =1       |  5       24      24      | |  7       36      4       |  259     59      235     | =1       289     2689    | |  26     =1       5       |  249     8       24      |  3       2479    24679   | |--------------------------+--------------------------+--------------------------| |  5       479     6       | B149     2      B47      |  4789    34789   34789   | |  3       479     8       |  4569    4579    4567    |  2      =1       479     | | =1       2      T79      |  3       479     8       | T479     6       5       | |--------------------------+--------------------------+--------------------------| |  248     5      =1       |  248     3       247     |  6       24789   24789   | |  2468    3467    237     |  24568   457     9       |  478     23478 [=1]      | |  2468    34679   2379    |  2468   =1       2467    |  4789    5       234789  | *--------------------------------------------------------------------------------*`

A perfectly acceptable template for base cell r4c4 being true for "1" and the target cells being false for "1".

_

EDIT

My comment disappeared

That questionable exocet appeared in my code with the highest degree of eliminations, however, it did not come immediately.

I have the same "1" pattern as Danny, but I applied here the idea of the "extended exocet", so the program showed that that pattern was not valid.

This was the last status (optional) of my code one year ago, when I prepared the file.
champagne
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Location: France Brittany

### The first V-loop puzzle

here champagne wrote:Here is an interesting puzzle published on a French forum.

.........1....72...7..84.6...8....93.6..4..7.93....6...9.73..8...59....2.........

after easy moves, we come to that [sic] PM
Code: Select all
`A     B    C     |D    E     F     |G      H   I      24568 2458 2469  |1256 12569 3     |145789 145 145789 1     458  3469  |56   569   7     |2      345 4589   235   7    239   |125  8     4     |1359   6   159    -----------------------------------------------------457   145  8     |1256 12567 1256  |145    9   3      25    6    12    |3    4     9     |158    7   158    9     3    147   |8    157   15    |6      2   145    -----------------------------------------------------246   9    1246  |7    3     1256  |145    8   1456   34678 148  5     |9    16    168   |1347   134 2      23678 128  12367 |4    1256  12568 |13579  135 15679  `

we can then see the SK loop

Code: Select all
`r3c13 r3c79 r12c8 r89c8 r7c79 r7c13 r89c2 r12c2 25   39    15    34    15    46    12    48    25    `

After a renaming, this became the original "V-loop" puzzle. Have any more been found since the above was posted in 2012
ronk
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### Re: The first V-loop puzzle

ronk wrote:After a renaming, this became the original "V-loop" puzzle. Have any more been found since the above was posted in 2012

IIRC, champagne has a file of V-Loop puzzles. I'm not sure if any of them also qualify as SK-Loop puzzles. I snagged the following from his collection.

Code: Select all
`..8...5...6...3.7.4.......1.7..32......9.5......67..2.5.......4.2.3...6...1...8..#7654;TkP;31389.......1.3...4.7...6...2...5.3.2.......6........78.5...2...6...4.7...3.1.......9#8400;tax;tarek-ultra-020498.7.....7.6.......54...7..4..6..9......5..3......2..1..94..6......1..5......3..2#8402;GP;H20401....6.8....7....2....3.5.....5....7.6...4.1.....2.3...14..8...6.2....4.89.......#8405;elev;H2351.....9...3...7.4...5.....2.....6.7.....1.....4.3.8...9.......5.7.8...3...2...1..#8668;tax;tarek071223170000- 95895..7...9...3...5.4.6.......8.4..51......7.2......34..1.9.......6.1.5...3...8...7..#9712;TkP;3164..2...3...7...1.5.6.......8.4...5......43.......1.7.4.8.......2.5.7...1...3...6..#9717;TkP;3101..9...7...4...1.2.8.......5.2...3......9.6.......12.3.7.......8.3.1...4...5...9..#9762;TkP;3715..1...2...3...4.5.6.......7.....3.8.....1.....4.9.8...7.......1.5.8...4...2...6..#38022;ig;champagne`

_
daj95376
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Joined: 15 May 2006

### Re: The first V-loop puzzle

daj95376 wrote:
ronk wrote:After a renaming, this became the original "V-loop" puzzle. Have any more been found since the above was posted in 2012

IIRC, champagne has a file of V-Loop puzzles. I'm not sure if any of them also qualify as SK-Loop puzzles. I snagged the following from his collection.

_

Hi Danny,

my code uses a code exceeding the limits given by ronk to qualify a pattern of "sk loop", but I never tried to extract the puzzles as the one given as sample. To stay on the safe side, I use the qualifier "V" loop, but surely, most of them will have a "sk loop" pattern.

IMO, in the area of "potential hardest puzzles", you have very small chances to find another example, but in the world of sudoku, nothing is sure.

Lower ratings have not really been explored. You have too many puzzles. There you would have more chances to find oddities.

The same remark could be done on Exocets.

In the file of potential hardest you have plenty of Exocets with a base of 4 digits. I am not sure that you can find one with a base of 3 digits. With lower ratings, the majority of the exocets found swithes to a 3 digits base as far as I remember from old explorations.
champagne
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Location: France Brittany

### Re: 7658;GP;H1521

Hi everybody,

regarding V-Loops, back in 2012 on the very first page of this thread there was a discussion about an interesting example with reversed clue sets:

champagne wrote:a very interesting pattern posted by ronk to day in another thread

here

98.7.....7.6...8...54......6..8..3......9..2......4..1.3.6..7......5..9......1..4 # 7658;GP;H1521

that pattern proves 16 eliminations.

16 Truths = {5689N47 47N5689}
16 Links = {7r4 8r7 3c4 6c7 125b5 459b6 249b8 125b9}
16 Eliminations --> r4c23<>7, r5c69<>5, r7c13<>8, r8c69<>2, r23c4<>3, r69c5<>2, r13c7<>6, r69c8<>5

champagne also showed an all row multi fish that yields the very same eliminations:

T16 = {3678r5689}
L16 = {3c4, 6c7, 378b4, 678b7, 69n5, 58n6, 69n8, 58n9}

In a later post he showed showed a mixed row and column"full rank 0 logic" in the same puzzle:

T20 = {12459r47, 12459c47}
L20 = {125b5, 459b6, 249b8, 125b9, 23n4, 13n7, 4n23, 7n13}

And ronk pointed out, that there is an all column multi fish complementary to the all row one:

T16 = {3678c5689}
L16 = {7r4, 8r7, 368b2, 367b3, 69n5, 58n6, 69n8, 58n9}

ronk wrote:There are at least four ways, with two pairs of complementary 0-rank logic sets. One pair is the 5-digit sk-loop in both its naked set and hidden set forms. The second pair are 4-digit fish, one using rows and one using columns. each having coincident [edit2: cover cells] at r58c69 and r69c58.

Realistically, I don't think there is a fifth way. [edit1: This guess is not true.]

The edit suggests that he found a fifth way but unfortunately he didn't tell what it was.
Thinking about multi fish again I experimented in xsudo with this puzzle and found another all row multi fish using the complementary clue set:

T22 = {12459r247, 1245r1, 129r3}
L22 = {124c5, 259c6, 145c8, 259c9, 12b1, 4n23, 7n13, 23n4, 13n7}

and of course the complementary all column version:

T22 = {12459c47, 1245c1, 1249c2, 1259c3}
L22 = {145r5, 259r6, 124r8, 259r9, 12b1, 4n23, 7n13, 23n4, 13n7}

and finally, saving the best for last, using all box thruths:

T12 = {367b5, 678b6, 378b8, 368b9}
L12 = {7r4, 8r7, 3c4, 6c7, 69n5, 58n6, 69n8, 58n9}

So thats now a 5th, 6th and 7th way to skin this particular cat with SLGs.

Greetings, Obi

Obi-Wahn

Posts: 61
Joined: 05 January 2007

### Re: Exotic patterns a resume

Just for fun I ran a Multisector Locked set survey on this puzzle and came up with the following 29 MSLS arrangements for the same 16 eliminations.

Hidden Text: Show
MSLS 1 : Base 78; r1234 c5689 & r7c5689 : 20 Links; 78r3 7r4 & 8r7 ; 124c5 259c6 145c8 259c9 ; 36b2 36b3 ;
MSLS 2 : Base 78; r1237 c5689 & r4c5689 : 20 Links; 78r3 8r7 & 7r4 ; 124c5 259c6 145c8 259c9 ; 36b2 36b3 ;
MSLS 3 : Base 78; r12347 c5689 : 20 Links; 78r3 7r4 8r7 ; 124c5 259c6 145c8 259c9 ; 36b2 36b3 ;
MSLS 4 : Base 378; r1234 c5689 & r7c5689 : 20 Links; 78r3 7r4 & 8r7 ; 124c5 259c6 145c8 259c9 ; 36b2 36b3 ;
MSLS 5 : Base 378; r1237 c5689 & r4c5689 : 20 Links; 78r3 8r7 & 7r4 ; 124c5 259c6 145c8 259c9 ; 36b2 36b3 ;
MSLS 6 : Base 378; r12347 c5689 : 20 Links; 78r3 7r4 8r7 ; 124c5 259c6 145c8 259c9 ; 36b2 36b3 ;
MSLS 7 : Base 678; r1234 c5689 & r7c5689 : 20 Links; 6r1 678r3 7r4 & 8r7 ; 124c5 259c6 145c8 259c9 ; 3b2 3b3 ;
MSLS 8 : Base 678; r1237 c5689 & r4c5689 : 20 Links; 6r1 678r3 8r7 & 7r4 ; 124c5 259c6 145c8 259c9 ; 3b2 3b3 ;
MSLS 9 : Base 678; r2347 c5689 & r1c5689 : 20 Links; 678r3 7r4 8r7 & 6r1 ; 124c5 259c6 145c8 259c9 ; 3b2 3b3 ;
MSLS 10 : Base 678; r12347 c5689 : 20 Links; 6r1 678r3 7r4 8r7 ; 124c5 259c6 145c8 259c9 ; 3b2 3b3 ;
MSLS 11 : Base 3678; r1234 c5689 & r7c5689 : 20 Links; 6r1 678r3 7r4 & 8r7 ; 124c5 259c6 145c8 259c9 ; 3b2 3b3 ;
MSLS 12 : Base 3678; r1237 c5689 & r4c5689 : 20 Links; 6r1 678r3 8r7 & 7r4 ; 124c5 259c6 145c8 259c9 ; 3b2 3b3 ;
MSLS 13 : Base 3678; r12347 c5689 : 20 Links; 6r1 678r3 7r4 8r7 ; 124c5 259c6 145c8 259c9 ; 3b2 3b3 ;
MSLS 14 : Base 36; c1234 r5689 & r5689c7 : 20 Links; 6c2 3c4 & 6c7 ; 145r5 259r6 124r8 259r9 ; 378b4 78b7 ;
MSLS 15 : Base 36; c1237 r5689 & r5689c4 : 20 Links; 6c2 6c7 & 3c4 ; 145r5 259r6 124r8 259r9 ; 378b4 78b7 ;
MSLS 16 : Base 36; c12347 r5689 : 20 Links; 6c2 3c4 6c7 ; 145r5 259r6 124r8 259r9 ; 378b4 78b7 ;
MSLS 17 : Base 367; c1234 r5689 & r5689c7 : 20 Links; 67c2 7c3 3c4 & 6c7 ; 145r5 259r6 124r8 259r9 ; 38b4 8b7 ;
MSLS 18 : Base 367; c1237 r5689 & r5689c4 : 20 Links; 67c2 7c3 6c7 & 3c4 ; 145r5 259r6 124r8 259r9 ; 38b4 8b7 ;
MSLS 19 : Base 367; c1247 r5689 & r5689c3 : 20 Links; 67c2 3c4 6c7 & 7c3 ; 145r5 259r6 124r8 259r9 ; 83b4 8b7 ;
MSLS 20 : Base 367; c12347 r5689 : 20 Links; 67c2 7c3 3c4 6c7 ; 145r5 259r6 124r8 259r9 ; 38b4 8b7 ;
MSLS 21 : Base 368; c1234 r5689 & r5689c7 : 20 Links; 8c1 6c2 8c3 3c4 & 6c7 ; 145r5 259r6 124r8 259r9 ; 37b4 7b7 ;
MSLS 22 : Base 368; c1237 r5689 & r5689c4 : 20 Links; 8c1 6c2 8c3 6c7 & 3c4 ; 145r5 259r6 124r8 259r9 ; 37b4 7b7 ;
MSLS 23 : Base 368; c1247 r5689 & r5689c3 : 20 Links; 8c1 6c2 3c4 6c7 & 8c3 ; 145r5 259r6 124r8 259r9 ; 73b4 7b7 ;
MSLS 24 : Base 368; c2347 r5689 & r5689c1 : 20 Links; 6c2 8c3 3c4 6c7 & 8c1 ; 145r5 259r6 124r8 259r9 ; 73b4 7b7 ;
MSLS 25 : Base 368; c12347 r5689 : 20 Links; 8c1 6c2 8c3 3c4 6c7 ; 145r5 259r6 124r8 259r9 ; 37b4 7b7 ;
MSLS 26 : Base 3678; c1234 r5689 & r5689c7 : 20 Links; 8c1 67c2 78c3 3c4 & 6c7 ; 145r5 259r6 124r8 259r9 ; 3b4 ;
MSLS 27 : Base 3678; c1237 r5689 & r5689c4 : 20 Links; 8c1 67c2 78c3 6c7 & 3c4 ; 145r5 259r6 124r8 259r9 ; 3b4 ;
MSLS 28 : Base 3678; c2347 r5689 & r5689c1 : 20 Links; 67c2 78c3 3c4 6c7 & 8c1 ; 145r5 259r6 124r8 259r9 ; 3b4 ;
MSLS 29 : Base 3678; c12347 r5689 : 20 Links; 8c1 67c2 78c3 3c4 6c7 ; 145r5 259r6 124r8 259r9 ; 3b4 ;

I haven't run MSLS for a couple of years but I think they are all different from the 7 arrangements already posted. That's 36 ways to skin this particular cat - 27 more lives than a cat normally has !!!

Leren
Leren

Posts: 3319
Joined: 03 June 2012

### Re: Exotic patterns a resume

I'm not that familiar with MSLS, but many of them look like different ways to reach the same result.
Nevertheless they show definitly two more SLGs to bring the lifes of this cat to the proper number of nine:

T20 = {12347n5689}
L20 = {7r4, 8r7, 14c58, 2c569, 5c689, 9c69, 368b2, 367b3}

and

T20 = {5689n12347}
L20 = {14r58, 2r689, 5r569, 9r69, 3c4, 6c7, 378b4, 678b7}

although there are possiblities to cover some candidates with rows or columns respectively instead of boxes, but they don't yield other eliminations.

 Nah, it's still alive and kicking.
A combined rows and boxes truth set:

T20 = {12459r47, 12459b23}
L20 = {14c58, 2c569, 5c689, 9c69, 4n23, 7n13, 23n4, 13n7}

and the complementary columns and boxes truth set:

T20 = {12459c47, 12459b47}
L20 = {14r58, 2r689, 5r569, 9r69, 4n23, 7n13, 23n4, 13n7}

Boy, that's one tough kitty!

[edit2] Okay, it turns out I can create a sizable number of different truth sets of size 18 to 22 by only partially transforming the cell truths to rows, columns or boxes.

I can independently choose 123n56 or 12459b2, 123n89 or 12459b3, 4n5689 or 12459r4, 7n5689 or 12459r7. Thats 16 combinations, and another 16 for the column box combination, including the 4 already posted above.
So that's 28 more SLGs. Boy that escalated quickly.

Obi-Wahn

Posts: 61
Joined: 05 January 2007

### Re: Exotic patterns a resume

The chain representing the MSLS is
(125#2=3)r56c4 - (3=249#2)r89c4 - (249#2=8)r7c56 - (8=125#2)r7c89 -
(125#2=6)r89c7 - (6=459#2)r56c7 - (459#2=7)r4c89 - (7=125#2)r4c56 – Loop => 16 Eliminations

The usual understanding for an ABC#2 term is that it will be true when it contains at least two truths and false otherwise.
With this understanding it is an AIC continuous loop which will allow all the eliminations for (3678) which appear as single digit terms.

However it’s clear from the MSLS that when the three digit terms are false they must contain one truth. As this can't duplicate either of the true digits in its conjugate term, it must be the third digit. This then justifies the eliminations in boxes 5689.

So this is neither a fully-fledged AIC loop nor an SK loop, but yet another loop type. As I found the original definition of 'V loops' confusing and was busy chasing other ideas at the time I just assumed they were hidden pair loops too.

So Champagne, is this a model that is true for all 'V loops' or not?
.
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

### Re: Exotic patterns a resume

It's worse than I thought. There are far more possible combinations, for example this monster with a mix of row, colmn, box and cell thruths:

T19 = {12459r7, 12459c7, 12459b2, 4n5689}
L19 = {7r4, 124c5, 259c6, 459b6, 125b9, 7n13, 23n4, 13n7}

I can transform 12459c7 to 5689n7, 123n89 or 12459b3. Or even partial combinations like 12c7 + 459b3.
But for some combinations, Xsudo doesn't find a solution.

Obi-Wahn

Posts: 61
Joined: 05 January 2007

### Re: Exotic patterns a resume

David P Bird wrote:The chain representing the MSLS is
(125#2=3)r56c4 - (3=249#2)r89c4 - (249#2=8)r7c56 - (8=125#2)r7c89 -
(125#2=6)r89c7 - (6=459#2)r56c7 - (459#2=7)r4c89 - (7=125#2)r4c56 – Loop => 16 Eliminations

The usual understanding for an ABC#2 term is that it will be true when it contains at least two truths and false otherwise.
With this understanding it is an AIC continuous loop which will allow all the eliminations for (3678) which appear as single digit terms.

However it’s clear from the MSLS that when the three digit terms are false they must contain one truth. As this can't duplicate either of the true digits in its conjugate term, it must be the third digit. This then justifies the eliminations in boxes 5689.

So this is neither a fully-fledged AIC loop nor an SK loop, but yet another loop type. As I found the original definition of 'V loops' confusing and was busy chasing other ideas at the time I just assumed they were hidden pair loops too.

So Champagne, is this a model that is true for all 'V loops' or not?
.

I'll check in details later, but my first reaction is that we have no SK loop and no 'V' loop here.

IMO the only difference between the SK loop and the "V" loop is the constraint added by "ronk" to have 2 unknown cells in the boxes not belonging to the loop to qualify it of "sk loop".

To have a "V" loop, You must have the possibility to chain disjoints pairs of candidates in the sequence row-box-column-box-row-box-column-box-loop

in XSUDO, this is normally a 16 truths (4x4cells in 4 boxes) and 16 links (2x2 rows 2x2 columns 4x2 boxes).
champagne
2017 Supporter

Posts: 6709
Joined: 02 August 2007
Location: France Brittany

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