999 (and 999b)

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999 (and 999b)

Postby mith » Thu Dec 03, 2020 7:07 pm

Pretty easy:

Code: Select all
+-------+-------+-------+
| . . . | . . . | 9 . . |
| . . . | 9 . . | . 8 7 |
| 9 . . | . 8 . | . 6 . |
+-------+-------+-------+
| . 8 . | . . 5 | . . 9 |
| 7 . 4 | . . 8 | 3 2 . |
| 2 . . | . . . | . 7 . |
+-------+-------+-------+
| . 7 . | . . . | 1 . . |
| . . 3 | 8 . 4 | . . . |
| 6 4 . | . . 3 | . 9 2 |
+-------+-------+-------+
......9.....9...879...8..6..8...5..97.4..832.2......7..7....1....38.4...64...3.92


And the harder bonus puzzle:

Code: Select all
+-------+-------+-------+
| . . . | . . . | 9 . . |
| . . . | 9 . . | . 8 7 |
| 9 . . | . 8 . | . 6 . |
+-------+-------+-------+
| 5 . . | . . . | . 7 . |
| . . 8 | . . 4 | . . 9 |
| 7 3 . | . . 8 | 2 5 . |
+-------+-------+-------+
| 8 . . | . . . | 1 . . |
| 6 4 . | . . 2 | 8 9 . |
| 1 2 . | . . 3 | . . . |
+-------+-------+-------+
......9.....9...879...8..6.5......7...8..4..973...825.8.....1..64...289.12...3...
mith
 
Posts: 369
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Re: 999 (and 999b)

Postby SpAce » Thu Dec 03, 2020 8:14 pm

999:

Code: Select all
.-----------------.---------------------------.-------------------.
| *45  26-13  8   | *23456-1  *23456-1   7    | 9    *134  *1345  |
|  45  1236   126 |  9         345-126  *126  | 245   8     7     |
|  9   123    7   |  345-12    8        *12   | 245   6     345-1 |
:-----------------+---------------------------+-------------------:
|  3   8      16  |  27        27        5    | 46    14    9     |
|  7   1569   4   |  16        169       8    | 3     2     15    |
|  2   1569   169 |  34        34        69-1 | 56    7     8     |
:-----------------+---------------------------+-------------------:
|  8   7      29  |  256       2569      269  | 1     34    34    |
|  1   29     3   |  8         29        4    | 7     5     6     |
|  6   4      5   |  17        17        3    | 8     9     2     |
'-----------------'---------------------------'-------------------'

MSLS: 7x7 {1N14589 23N6 \ 345r1 1[[r1[b2|c6]]|b23] 26b2} => -13 r1c2, -1 r6c6, -1 r3c9, -126 b2p57, -1 r1c45 (Rank 1); btte

(7 cells, 6 digits (123456), only '1' can and must be twice.)

999b:

Code: Select all
.-----------------.---------------------------------.----------------.
| 34  8    c12567 | bc234567-1  bc234567-1  bc567-1 | 9    123  1234 |
| 34  156   1256  |   9           23456-1   ad156   | 345  8    7    |
| 9   157   1257  |   23457-1     8         ad157   | 345  6    1234 |
:-----------------+---------------------------------+----------------:
| 5   169   1469  |   23          23          69-1  | 46   7    8    |
| 2   16    8     |   57          57          4     | 36   13   9    |
| 7   3     1469  |   16          169         8     | 2    5    14   |
:-----------------+---------------------------------+----------------:
| 8   579   3579  |   4567        45679       5679  | 1    23   2356 |
| 6   4     357   |   157         157         2     | 8    9    35   |
| 1   2     59    |   8           569         3     | 7    4    56   |
'-----------------'---------------------------------'----------------'

(15=6|7)r23c6 - (67)r1c456 = (6,57|7,56)r1c3456 - (5|76=1)r23c6 => +1 r23c6; btte

...or Rank 0:

Code: Select all
           \1n             \1567b2       \1
.------------------.----------------------------.----------------.
| 34  8    \567-12 | 234567-1  234567-1   567-1 | 9    123  1234 | *567
| 34  156   1256   | 9         234-156   *156   | 345  8    7    | *N6
| 9   157   1257   | 234-157   8         *157   | 345  6    1234 | *N6
:------------------+----------------------------+----------------:
| 5   169   1469   | 23        23         69-1  | 46   7    8    |
| 2   16    8      | 57        57         4     | 36   13   9    |
| 7   3     1469   | 16        169        8     | 2    5    14   |
:------------------+----------------------------+----------------:
| 8   579   3579   | 4567      45679      5679  | 1    23   2356 |
| 6   4     357    | 157       157        2     | 8    9    35   |
| 1   2     59     | 8         569        3     | 7    4    56   |
'------------------'----------------------------'----------------'

5x5 {23N6 567R1 \ 1[c6|b2] 567b2 1n3} => -1 b2p12357,r4c6; -567 b2p57; -12 r1c3; btte
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   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

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Re: 999 (and 999b)

Postby Ajò Dimonios » Thu Dec 03, 2020 10:01 pm

Code: Select all
+--------------+----------------------+--------------+
| 34 8   12567 | 1234567 1234567 1567 | 9   123 1234 |
| 34 156 1256  | 9       123456  156  | 345 8   7    |
| 9  157 1257  | 123457  8       157  | 345 6   1234 |
+--------------+----------------------+--------------+
| 5  169 1469  | 23      23      169  | 46  7   8    |
| 2  16  8     | 57      57      4    | 36  13  9    |
| 7  3   1469  | 16      169     8    | 2   5   14   |
+--------------+----------------------+--------------+
| 8  579 3579  | 4567    45679   5679 | 1   23  2356 |
| 6  4   357   | 157     157     2    | 8   9   35   |
| 1  2   59    | 8       569     3    | 7   4   56   |
+--------------+----------------------+--------------+


P(9r6c3) and P(1r6c4) are backdoors. P'(9r6c3) => basics {r6c5 = 9; r4c2 = 9; r9c3 = 9; r7c6 = 9; r4c6 = 6;r6c4 = 1 } => + 1r6c4 (common to P(9r6c3)) => stte

Paolo
Last edited by Ajò Dimonios on Fri Dec 04, 2020 12:33 pm, edited 1 time in total.
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Re: 999 (and 999b)

Postby SpAce » Thu Dec 03, 2020 11:55 pm

Woohoo, I installed and tried SudoRules for the first time:

11 non-basic steps:

SudoRules wrote:x-wing-in-rows: n9{r6 r9}{c3 c5} ==> r7c5 ≠ 9, r7c3 ≠ 9, r4c3 ≠ 9
finned-x-wing-in-columns: n7{c2 c6}{r7 r3} ==> r3c4 ≠ 7
biv-chain[3]: r5c2{n1 n6} - b6n6{r5c7 r4c7} - r4n4{c7 c3} ==> r4c3 ≠ 1
z-chain[3]: c7n5{r2 r3} - c2n5{r3 r7} - c6n5{r7 .} ==> r2c5 ≠ 5
z-chain[3]: c7n5{r3 r2} - c2n5{r2 r7} - c6n5{r7 .} ==> r3c4 ≠ 5
whip[5]: c2n5{r3 r7} - c2n7{r7 r3} - r3c6{n7 n1} - r4n1{c6 c2} - c2n9{r4 .} ==> r3c3 ≠ 5
t-whip[6]: r4n1{c6 c2} - r5c2{n1 n6} - r2c2{n6 n5} - c7n5{r2 r3} - r3c2{n5 n7} - r3c6{n7 .} ==> r2c6 ≠ 1, r1c6 ≠ 1
t-whip[3]: b3n1{r1c9 r3c9} - c6n1{r3 r4} - r6n1{c4 .} ==> r1c3 ≠ 1
whip[3]: r2c6{n6 n5} - r1n5{c4 c3} - r1n6{c3 .} ==> r2c5 ≠ 6
whip[3]: r2c6{n5 n6} - b1n6{r2c2 r1c3} - r1n5{c3 .} ==> r3c6 ≠ 5
biv-chain[4]: c2n9{r7 r4} - r4n1{c2 c6} - r3c6{n1 n7} - c2n7{r3 r7} ==> r7c2 ≠ 5
;btte
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   *             |    |               |    |    *
        *        |=()=|    /  _  \    |=()=|               *
            *    |    |   |-=( )=-|   |    |      *
     *                     \  ¯  /                   *   

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Re: 999 (and 999b)

Postby pjb » Fri Dec 04, 2020 12:24 am

for 999: Two msls's

Base: 239
10 cell Truths: r236 c367 +r4c3 r4c7
10 links: 2r2, 2r3, 9r6, 16c3, 16c6, 456c7
6 eliminations: r2c2<>2, r2c5<>2, r3c2<>2, r3c4<>2, r6c2<>9, r7c6<>6,
Naked pairs of 29 at r7c36 => -2 r7c45, -9 r7c5

Base: 36
12 cell Truths: r246 c367 +r7c3 r3c6 r7c6 r3c7
12 links: 6r2, 6r4, 6r6, 129c3, 129c6, 245c7
3 eliminations: r2c2<>6, r2c5<>6, r6c2<>6 => btte

For 999b: Two msls's

Base: 579
11 cell Truths: r234 c267 +r5c2 r5c7
11 links: 5r2, 57r3, 9r4, 16c2, 16c6, 346c7
10 eliminations: r2c3<>5, r2c5<>5, r3c3<>5, r3c3<>7, r3c4<>5, r3c4<>7, r4c3<>9, r1c6<>1, r1c6<>6, r7c6<>6,

Base: 146
13 cell Truths: r234 c236 +r4c7 r7c2 r1c6 r7c6
13 links: 16r2, 1r3, 146r4, 579c2, 2c3, 579c6
5 eliminations: r2c5<>1, r2c5<>6, r3c4<>1, r3c9<>1, r1c3<>2 => btte

Phil
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Re: 999 (and 999b)

Postby Leren » Fri Dec 04, 2020 12:39 am

For 999:

Code: Select all
*--------------------------------------------------------*
| 45  26-13  8   | 123456  123456   7   | 9    134  1345 |
|#45 *13-26 *126 | 9      #1345-26 *126 |*245  8    7    |
| 9  *13-2   7   |#1345-2  8       *12  |*245  6   #1345 |
|----------------+--------------------=-+----------------|
| 3   8     *16  | 27      27       5   |*46  #14   9    |
| 7   69-15  4   | 16      169      8   | 3    2    15   |
| 2  *15-69 *169 |#34     #34      *169 |*56   7    8    |
|----------------+----------------------+----------------|
| 8   7      29  | 256     2569     269 | 1    34   34   |
| 1   29     3   | 8       29       4   | 7    5    6    |
| 6   4      5   | 17      17       3   | 8    9    2    |
*--------------------------------------------------------*

Multifish Truths 14 : 1345r236, 14r4, ; Links 14 : 135c3, 1c36, 45c7 + cells r2c15, r3c49, r4c8, r6c45 => - 13 r1c2, - 26 r2c25, - 2 r3c24, - 15 r5c2, - 69 r6c2; stte

For 999b:

Code: Select all
*-----------------------------------------------------------*
| 34  8    567-12 | 1234567 1234567  567-1 | 9    123  1234 |
|#34 *156 *12-56  | 9      #1234-56 *156   |*345  8    7    |
| 9  *157 *12-57  |#1234-57 8       *157   |*345  6   #1234 |
|-----------------+------------------------+----------------|
| 5  *169 *14-69  |#23     #23      *169   |*46   7    8    |
| 2  *16   8      | 57      57       4     |*36  #13   9    |
| 7   3    69-14  | 16      169      8     | 2    5    14   |
|-----------------+------------------------+----------------|
| 8   579  3579   | 4567    45679    5679  | 1    23   2356 |
| 6   4    357    | 157     157      2     | 8    9    35   |
| 1   2    59     | 8       569      3     | 7    4    56   |
*-----------------------------------------------------------*

Multifish Truths 14 : 1234r234, 13r5 ; Links 14 : 1c26, 124c3, 34c7, + cells r2c15, r3c49, r4c45, r5c8 => - 12 r1c3, - 1 r1c6, - 56 r2c35, -57 r3c34, - 69 r4c3, - 14 r6c3; stte

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Re: 999 (and 999b)

Postby denis_berthier » Fri Dec 04, 2020 3:35 am

SpAce wrote:Woohoo, I installed and tried SudoRules for the first time:

Good.
You can also play with the configuration.


*** First puzzle

Using:
Code: Select all
(bind ?*Subsets* TRUE)
the first puzzle has a path with only Subsets:

Hidden Text: Show
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = S
*** Using CLIPS 6.32-r773
***********************************************************************************************
lots of singles
151 candidates, 773 csp-links and 773 links. Density = 6.83%
whip[1]: c1n5{r2 .} ==> r3c2 ≠ 5, r1c2 ≠ 5, r2c2 ≠ 5
hidden-pairs-in-a-row: r4{n2 n7}{c4 c5} ==> r4c5 ≠ 6, r4c5 ≠ 4, r4c5 ≠ 1, r4c4 ≠ 6, r4c4 ≠ 4, r4c4 ≠ 1
whip[1]: r4n4{c8 .} ==> r6c7 ≠ 4
hidden-pairs-in-a-row: r6{n3 n4}{c4 c5} ==> r6c5 ≠ 9, r6c5 ≠ 6, r6c5 ≠ 1, r6c4 ≠ 6, r6c4 ≠ 1
x-wing-in-columns: n9{c3 c6}{r6 r7} ==> r7c5 ≠ 9, r6c2 ≠ 9
swordfish-in-columns: n2{c3 c6 c7}{r2 r7 r3} ==> r7c5 ≠ 2, r7c4 ≠ 2, r3c4 ≠ 2, r3c2 ≠ 2, r2c5 ≠ 2, r2c2 ≠ 2
naked-pairs-in-a-block: b8{r7c4 r7c5}{n5 n6} ==> r7c6 ≠ 6
swordfish-in-columns: n6{c3 c6 c7}{r4 r2 r6} ==> r6c2 ≠ 6, r2c5 ≠ 6, r2c2 ≠ 6
naked-pairs-in-a-block: b1{r2c2 r3c2}{n1 n3} ==> r2c3 ≠ 1, r1c2 ≠ 3, r1c2 ≠ 1
whip[1]: c3n1{r6 .} ==> r5c2 ≠ 1, r6c2 ≠ 1
stte



*** Second puzzle

Subsets are not enough for the second puzzle. Adding only bivalue-chains is still not enough. Adding z-chains is enough, but at the cost of having long ones (length 8):
Code: Select all
 (bind ?*Subsets* TRUE)
 (bind ?*Bivalue-Chains* TRUE)
 (bind ?*z-Chains* TRUE)

Hidden Text: Show
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = Z+S
*** Using CLIPS 6.32-r773
***********************************************************************************************
naked-single ==> r9c8 = 4, r5c1 = 2, r9c7 = 7, r9c4 = 8, r4c9 = 8, r1c2 = 8
184 candidates, 1145 csp-links and 1145 links. Density = 6.8%
whip[1]: c7n6{r5 .} ==> r6c9 ≠ 6
whip[1]: c7n5{r3 .} ==> r3c9 ≠ 5, r1c9 ≠ 5
whip[1]: c1n4{r2 .} ==> r3c3 ≠ 4, r1c3 ≠ 4, r2c3 ≠ 4
whip[1]: c1n3{r2 .} ==> r3c3 ≠ 3, r1c3 ≠ 3, r2c3 ≠ 3
hidden-pairs-in-a-row: r5{n5 n7}{c4 c5} ==> r5c5 ≠ 6, r5c5 ≠ 3, r5c5 ≠ 1, r5c4 ≠ 6, r5c4 ≠ 3, r5c4 ≠ 1
whip[1]: r5n3{c8 .} ==> r4c7 ≠ 3
hidden-pairs-in-a-row: r4{n2 n3}{c4 c5} ==> r4c5 ≠ 9, r4c5 ≠ 6, r4c5 ≠ 1, r4c4 ≠ 6, r4c4 ≠ 1
x-wing-in-rows: n9{r6 r9}{c3 c5} ==> r7c5 ≠ 9, r7c3 ≠ 9, r4c3 ≠ 9
z-chain[2]: c2n7{r3 r7} - c6n7{r7 .} ==> r3c4 ≠ 7
biv-chain[3]: r5c2{n1 n6} - b6n6{r5c7 r4c7} - r4n4{c7 c3} ==> r4c3 ≠ 1
naked-pairs-in-a-row: r4{c3 c7}{n4 n6} ==> r4c6 ≠ 6, r4c2 ≠ 6
whip[1]: b5n6{r6c5 .} ==> r6c3 ≠ 6
z-chain[3]: c7n5{r2 r3} - c2n5{r3 r7} - c6n5{r7 .} ==> r2c5 ≠ 5
z-chain[3]: c7n5{r3 r2} - c2n5{r2 r7} - c6n5{r7 .} ==> r3c4 ≠ 5
z-chain[6]: r9c3{n5 n9} - r6n9{c3 c5} - r4c6{n9 n1} - r3c6{n1 n7} - c2n7{r3 r7} - c2n5{r7 .} ==> r3c3 ≠ 5
;;; Resolution state RS1
z-chain[8]: r5c2{n1 n6} - r2c2{n6 n5} - c7n5{r2 r3} - r3c6{n5 n7} - r3c3{n7 n2} - r2n2{c3 c5} - r2n1{c5 c6} - r4n1{c6 .} ==> r3c2 ≠ 1
z-chain[5]: r3c2{n7 n5} - r3c6{n5 n1} - r4c6{n1 n9} - c2n9{r4 r7} - c2n7{r7 .} ==> r3c3 ≠ 7
z-chain[7]: r1n5{c6 c3} - r9c3{n5 n9} - r7n9{c2 c6} - r4c6{n9 n1} - r3c6{n1 n7} - r3c2{n7 n5} - c7n5{r3 .} ==> r2c6 ≠ 5
biv-chain[3]: r4n1{c2 c6} - r2c6{n1 n6} - c2n6{r2 r5} ==> r5c2 ≠ 1
singles ==> r5c2 = 6, r4c3 = 4, r4c7 = 6, r5c7 = 3, r5c8 = 1, r6c9 = 4
z-chain[2]: c2n1{r2 r4} - c6n1{r4 .} ==> r2c5 ≠ 1
biv-chain[3]: r4c4{n2 n3} - r3n3{c4 c9} - r1c8{n3 n2} ==> r1c4 ≠ 2
biv-chain[3]: r2c2{n5 n1} - r2c6{n1 n6} - c3n6{r2 r1} ==> r1c3 ≠ 5
whip[1]: r1n5{c6 .} ==> r3c6 ≠ 5
biv-chain[3]: c9n1{r1 r3} - r3c6{n1 n7} - b1n7{r3c2 r1c3} ==> r1c3 ≠ 1
biv-chain[3]: r3c3{n2 n1} - r3c6{n1 n7} - b1n7{r3c2 r1c3} ==> r1c3 ≠ 2
biv-chain[3]: r3c6{n1 n7} - r3c2{n7 n5} - r2c2{n5 n1} ==> r2c6 ≠ 1, r3c3 ≠ 1
stte


What about adding t-whips to the above?
Code: Select all
 (bind ?*Subsets* TRUE)
 (bind ?*Bivalue-Chains* TRUE)
 (bind ?*z-Chains* TRUE)
 (bind ?*t-Whips* TRUE)

We now get a solution with chains length ≤ 6:
Hidden Text: Show
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = tW+S
*** Using CLIPS 6.32-r773
***********************************************************************************************
;;; Same path as before to resolution state RS1
t-whip[6]: r4n1{c6 c2} - r5c2{n1 n6} - r2c2{n6 n5} - c7n5{r2 r3} - r3c2{n5 n7} - r3c6{n7 .} ==> r2c6 ≠ 1, r1c6 ≠ 1
t-whip[3]: b3n1{r1c9 r3c9} - c6n1{r3 r4} - r6n1{c4 .} ==> r1c3 ≠ 1
biv-chain[4]: r5c7{n3 n6} - c2n6{r5 r2} - r2c6{n6 n5} - b3n5{r2c7 r3c7} ==> r3c7 ≠ 3
z-chain[3]: r4c4{n2 n3} - r3n3{c4 c9} - b3n2{r3c9 .} ==> r1c4 ≠ 2
z-chain[4]: r3c7{n4 n5} - r2c7{n5 n3} - r3n3{c9 c4} - r3n4{c4 .} ==> r1c9 ≠ 4
t-whip[4]: r2c6{n6 n5} - r1n5{c6 c3} - c2n5{r3 r7} - r7n9{c2 .} ==> r7c6 ≠ 6
whip[1]: c6n6{r2 .} ==> r1c4 ≠ 6, r1c5 ≠ 6, r2c5 ≠ 6
z-chain[3]: r1n5{c6 c3} - r1n6{c3 c6} - r2c6{n6 .} ==> r3c6 ≠ 5
t-whip[3]: r1n6{c3 c6} - r2c6{n6 n5} - r1n5{c4 .} ==> r1c3 ≠ 7, r1c3 ≠ 2
whip[1]: r1n7{c6 .} ==> r3c6 ≠ 7
stte


What if we add the full power of whips or g-whips? Nothing new. Some of them appear in the resolution path, but the max length of chains remains 6.


Now that we have found the combination of chains that give the best result, we can try to restrict it to the corresponding 2D-chains:
Code: Select all
 (bind ?*Subsets* TRUE)
 (bind ?*Typed-Bivalue-Chains* TRUE)
 (bind ?*Typed-z-Chains* TRUE)
 (bind ?*Typed-t-Whips* TRUE)

We still get a solution, but the necessary chains are much longer (length 24). As this is not interesting, I skip it.

We can also try to introduce typed-whips, but then we need chains of length 8. This is not too much above the optimal 6, so it may be interesting for players who like 2D-chains.

Notice that I don't apply the above progressive method when I have to solve long lists of puzzles.
The fastest approach is to activate only whips in order to get a first estimate of the difficulty.
An alternative approach is to use the default configuration, where all the special cases of whips are activated. This gives an idea of what chains might not be necessary. But this may be too computationally heavy for extremely hard puzzles.

As you can see, there are many possibilities and one is free to choose what he considers the one he likes best.
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Re: 999 (and 999b)

Postby Cenoman » Fri Dec 04, 2020 8:37 am

999
Code: Select all
 +--------------------+--------------------------+---------------------+
 |  45  b26-13  8     | c23456-1 c123456   7     |  9     134   1345   |
 |  45  a1236  a126   |  9        345-126 d126   |  245   8     7      |
 |  9   a123    7     |  345-12   8       d12    |  245   6     1345   |
 +--------------------+--------------------------+---------------------+
 |  3    8      16    |  27       27       5     |  46    14    9      |
 |  7    1569   4     |  16       169      8     |  3     2     15     |
 |  2    1569   169   |  34       34       169   |  56    7     8      |
 +--------------------+--------------------------+---------------------+
 |  8    7      29    |  256      2569     269   |  1     34    34     |
 |  1    29     3     |  8        29       4     |  7     5     6      |
 |  6    4      5     |  17       17       3     |  8     9     2      |
 +--------------------+--------------------------+---------------------+

(6=132)b1p568 - r1c2 = r1c45 - (21=6)r23c6 loop => -6 r2c5, -13r1c2, -12 r2c5,r3c4, -1r1c45; lclste

PM 6x6 (symmetric)
Hidden Text: Show
Code: Select all
1r2c2  2r2c2 3r2c2  6r2c2
1r2c3  2r2c3        6r2c3
1r3c2  2r3c2 3r3c2
       2r1c2               2r1c45
                    6r2c6  2r2c6   1r2c6
                           2r3c6   1r3c6
-------------------------------------------
-1r1c2       -3r1c2 -6r2c5 -2b2p57 -1b2p157


999b
Code: Select all
 +---------------------+-----------------------------+---------------------+
 |  34   8     12567   |  1234567   1234567   1567   |  9     123   1234   |
 |  34   156   1256    |  9         123456    156    |  345   8     7      |
 |  9    157   1257    |  123457    8         157    |  345   6     1234   |
 +---------------------+-----------------------------+---------------------+
 |  5    169   1469    |  23        23        169    |  46    7     8      |
 |  2    16    8       |  57        57        4      |  36    13    9      |
 |  7    3     1469    |  16        169       8      |  2     5     14     |
 +---------------------+-----------------------------+---------------------+
 |  8    579   3579    |  4567      45679     5679   |  1     23    2356   |
 |  6    4     357     |  157       157       2      |  8     9     35     |
 |  1    2     59      |  8         569       3      |  7     4     56     |
 +---------------------+-----------------------------+---------------------+

DP(1234)r1c14589 (4 digits in 5 cells) having three guardians: 5,6,7 r1c45
(5)r1c45 - (5=671)r123c6
(6)r1c45 - (6=571)r123c6
(7)r1c45 - (7=561)r123c6
=> +1 r123c6 (-1 r4c6, -1 b2p1257); lclste
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Re: 999 (and 999b)

Postby Mauriès Robert » Fri Dec 04, 2020 5:22 pm

Hi all,
My resolution of 999 with the basic techniques and a single anti-track :
P'(9r6c6) : (-9r6c6) => 9r7c6->(2r8c5->2r4c4)->2r1c2->6r1c45->12r23c6->1r6c23->6r4c3->6r6c7->... => -1r6c6, -6r6c6 => r6c6=9, stte.
puzzle1: Show
Image

Cordialy,
Robert
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Re: 999 (and 999b)

Postby DEFISE » Fri Dec 04, 2020 6:31 pm

Puzzle 999

Singles: 5r8c8,1r8c1,3r4c1,6r8c9,7r8c7,8r9c7,5r9c3,8r7c1,8r1c3,8r6c9,7r3c3,7r1c6
Alignment: 5-c1-b1 => -5r1c2 -5r2c2 -5r3c2
Hidden pair: 27-r4c4-r4c5 => -1r4c4 -4r4c4 -6r4c4 -1r4c5 -4r4c5 -6r4c5
Alignment: 4-r4-b6 => -4r6c7
Hidden pair: 34-r6c4-r6c5 => -1r6c4 -6r6c4 -1r6c5 -6r6c5 -9r6c5
whip[4]: r3c6{n1 n2}- r2c6{n2 n6}- r1n6{c4 c2}- r1n2{c2 .} => -1r6c6
Alignment: 1-r6-b4 => -1r4c3 -1r5c2
STTE
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Re: 999 (and 999b)

Postby Mauriès Robert » Fri Dec 04, 2020 7:54 pm

DEFISE wrote:Puzzle 999
whip[4]: r3c6{n1 n2}- r2c6{n2 n6}- r1n6{c4 c2}- r1n2{c2 .} => -1r6c6
Alignment: 1-r6-b4 => -1r4c3 -1r5c2
STTE

Well done François!
The anti-track P'(1r3c6) led to the same result, I completely missed it !
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Re: 999 (and 999b)

Postby SpAce » Mon Dec 07, 2020 3:20 am

Hi Denis,

denis_berthier wrote:You can also play with the configuration.

I finally found some time to do that, but didn't quite get the results I expected. I wanted to produce forcing whips, but all I saw was normal whips even though I'd disabled them (anything simpler was disabled as expected). Then I tried to restrict whip length but that didn't work either. I wonder what I messed up.
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Re: 999 (and 999b)

Postby denis_berthier » Mon Dec 07, 2020 3:52 am

SpAce wrote:
denis_berthier wrote:You can also play with the configuration.

I finally found some time to do that, but didn't quite get the results I expected. I wanted to produce forcing whips, but all I saw was normal whips even though I'd disabled them (anything simpler was disabled as expected). Then I tried to restrict whip length but that didn't work either. I wonder what I messed up.


You didn't mess up anything.
Activating forcing-whips automatically activates whips of same length. (It's stated in the user manual.) Moreover, whips[n] have higher priority than forcing-whips[n] because they are structurally simpler.
And, I also have never found any forcing-whip in these conditions.
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Re: 999 (and 999b)

Postby SpAce » Wed Dec 09, 2020 5:01 am

denis_berthier wrote:You didn't mess up anything.
Activating forcing-whips automatically activates whips of same length. (It's stated in the user manual.) Moreover, whips[n] have higher priority than forcing-whips[n] because they are structurally simpler.

Ok. It's your prerogative, but I'm not sure if that's ideal behavior. If I switch off something I expect it to remain that way, instead of getting turned back on as a side effect of something else. I would understand if forcing whips were somehow dependent on whips, but I don't think they are or should be. If the sole reason is a forced hierarchy, then this is not exactly true:

As you can see, there are many possibilities and one is free to choose what he considers the one he likes best.
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Re: 999 (and 999b)

Postby denis_berthier » Wed Dec 09, 2020 6:03 am

SpAce wrote:
denis_berthier wrote:You didn't mess up anything.
Activating forcing-whips automatically activates whips of same length. (It's stated in the user manual.) Moreover, whips[n] have higher priority than forcing-whips[n] because they are structurally simpler.

Ok. It's your prerogative, but I'm not sure if that's ideal behavior. If I switch off something I expect it to remain that way, instead of getting turned back on as a side effect of something else. I would understand if forcing whips were somehow dependent on whips, but I don't think they are or should be. If the sole reason is a forced hierarchy, then this is not exactly true:
denis_berthier wrote:As you can see, there are many possibilities and one is free to choose what he considers the one he likes best.


The rules forced into activity by other ones are clearly stated in the Manual. This forcing is justified by logic:
- any-chain[n+1] forces same-type-of-chain[n] for many obvious reasons (in particular preserving confluence)
- braids force whips because whips are simpler particular cases and it doesn't harm anyone to have a chain named as "whip" instead of all of them being named as "braid"... But the main reason is the very special relation between them.
- similarly g-braids force g-whips AND braids
You can notice that there's no forced activation of other special chains (bivalue-chains, z-chains, ..., typed-chains of any kind) or of any other types of patterns, exotic or not, uniqueness or not, application-specific or not. So, yes, basically, you are free to choose whichever rules you want, within some consistency constraints clearly stated in the Basic User Manual.

As for the specific case of forcing-whips/braids, they are inherently built on partial-whips/braids. If, on extension, a partial-whip/braid gives rise to a full whip/braid, then it's target disappears and any forcing-whip/braid using this target loses any meaning.
I don't know how Robert deals with single tracks that lead to a contradiction within conjugated tracks, but he has to face the same question.

I made the consistency constraints automatic in SudoRules to simplify the user's life.
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