## FN-2187

Post puzzles for others to solve here.

### FN-2187

Code: Select all
`+-------+-------+-------+| . . . | . . 9 | . . . || . . 8 | 7 . . | . . 6 || . 1 9 | . 4 . | . 2 . |+-------+-------+-------+| . 2 . | . 1 . | . 4 . || . . 3 | 6 . . | . . 8 || . . . | . . . | 2 . . |+-------+-------+-------+| . . . | . . 7 | . . . || . . 6 | 8 . . | . . 7 || . 4 . | . . . | . 1 . |+-------+-------+-------+.....9.....87....6.19.4..2..2..1..4...36....8......2.......7.....68....7.4.....1.`
mith

Posts: 301
Joined: 14 July 2020

### Re: FN-2187

1) MSLS: 15 cell Truths: r3469 c3469
15 links: 5r3, 5r4, 145r6, 25r9, 7c3, 39c4, 368c6, 39c9
19 eliminations

2) MSLS: 14 cell Truths: r169 c349 +r4c3 r3c4 r4c4 r3c9 r4c9
14 links: 124r1, 14r6, 2r9, 57c3, 359c4, 359c9
8 eliminations

3) Double ALS at r4c13469 and r25678c2, with X-Z values 6 and 7 => -6 r6c1, -7 r6c1, -3 r4c7, -9 r4c7, -3 r1c2, -5 r1c2

4) Simple AIC: (7=6)r4c7 - (6)r4c1 = (6)r3c1 - (6)r1c2 = (6-8)r1c5 = (8-7)r6c5 = (7)r5c5 => -7 r5c78; stte

Phil
pjb
2014 Supporter

Posts: 2230
Joined: 11 September 2011
Location: Sydney, Australia

### Re: FN-2187

mith wrote:
Code: Select all
`+-------+-------+-------+| . . . | . . 9 | . . . || . . 8 | 7 . . | . . 6 || . 1 9 | . 4 . | . 2 . |+-------+-------+-------+| . 2 . | . 1 . | . 4 . || . . 3 | 6 . . | . . 8 || . . . | . . . | 2 . . |+-------+-------+-------+| . . . | . . 7 | . . . || . . 6 | 8 . . | . . 7 || . 4 . | . . . | . 1 . |+-------+-------+-------+.....9.....87....6.19.4..2..2..1..4...36....8......2.......7.....68....7.4.....1.`

Just for showing how CSP-Rules can now deal (almost) directly with such graphical representations.
The "almost" is because "|" is a reserved character and cannot be used in the input. I have to replace it manually by ":" or "!".

In any case, here is how I can now ask SudoRules to solve this puzzle (it can also accept *s at the corners if you prefer so):

Code: Select all
`(solve-sudoku-grid   +-------+-------+-------+   : . . . : . . 9 : . . . :   : . . 8 : 7 . . : . . 6 :   : . 1 9 : . 4 . : . 2 . :   +-------+-------+-------+   : . 2 . : . 1 . : . 4 . :   : . . 3 : 6 . . : . . 8 :   : . . . : . . . : 2 . . :   +-------+-------+-------+   : . . . : . . 7 : . . . :   : . . 6 : 8 . . : . . 7 :   : . 4 . : . . . : . 1 . :   +-------+-------+-------+)`

or:
Code: Select all
`(solve-sudoku-grid   +-------+-------+-------+   ! . . . ! . . 9 ! . . . !   ! . . 8 ! 7 . . ! . . 6 !   ! . 1 9 ! . 4 . ! . 2 . !   +-------+-------+-------+   ! . 2 . ! . 1 . ! . 4 . !   ! . . 3 ! 6 . . ! . . 8 !   ! . . . ! . . . ! 2 . . !   +-------+-------+-------+   ! . . . ! . . 7 ! . . . !   ! . . 6 ! 8 . . ! . . 7 !   ! . 4 . ! . . . ! . 1 . !   +-------+-------+-------+)`

And the resolution path (once more, a good number of Subsets - Mith, I definitely like your examples):

Code: Select all
`**************************************************************************************************  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin***  Using CLIPS 6.32-r770***********************************************************************************************250 candidates, 1917 csp-links and 1917 links. Density = 6.16%naked-pairs-in-a-row: r3{c4 c9}{n3 n5} ==> r3c7 ≠ 5, r3c7 ≠ 3, r3c6 ≠ 5, r3c6 ≠ 3, r3c1 ≠ 5, r3c1 ≠ 3hidden-pairs-in-a-block: b8{r7c4 r8c6}{n1 n4} ==> r8c6 ≠ 5, r8c6 ≠ 3, r8c6 ≠ 2, r7c4 ≠ 9, r7c4 ≠ 5, r7c4 ≠ 3, r7c4 ≠ 2hidden-pairs-in-a-block: b2{r1c5 r3c6}{n6 n8} ==> r1c5 ≠ 5, r1c5 ≠ 3, r1c5 ≠ 2finned-x-wing-in-rows: n7{r3 r4}{c7 c1} ==> r6c1 ≠ 7, r5c1 ≠ 7finned-x-wing-in-columns: n2{c4 c3}{r1 r9} ==> r9c1 ≠ 2biv-chain[2]: c4n2{r1 r9} - r8n2{c5 c1} ==> r1c1 ≠ 2swordfish-in-columns: n2{c3 c4 c9}{r7 r1 r9} ==> r9c6 ≠ 2, r9c5 ≠ 2, r7c5 ≠ 2, r7c1 ≠ 2swordfish-in-columns: n8{c2 c5 c8}{r7 r6 r1} ==> r7c7 ≠ 8, r7c1 ≠ 8, r6c6 ≠ 8, r6c1 ≠ 8, r1c7 ≠ 8swordfish-in-columns: n1{c3 c4 c9}{r6 r7 r1} ==> r7c1 ≠ 1, r6c1 ≠ 1, r1c7 ≠ 1swordfish-in-rows: n7{r3 r4 r9}{c1 c7 c3} ==> r6c3 ≠ 7, r5c7 ≠ 7, r1c7 ≠ 7, r1c3 ≠ 7, r1c1 ≠ 7hidden-pairs-in-a-block: b3{r1c8 r3c7}{n7 n8} ==> r1c8 ≠ 5, r1c8 ≠ 3swordfish-in-rows: n4{r2 r5 r8}{c7 c1 c6} ==> r7c7 ≠ 4, r6c6 ≠ 4, r6c1 ≠ 4, r1c7 ≠ 4, r1c1 ≠ 4naked-pairs-in-a-block: b3{r1c7 r3c9}{n3 n5} ==> r2c8 ≠ 5, r2c8 ≠ 3, r2c7 ≠ 5, r2c7 ≠ 3, r1c9 ≠ 5, r1c9 ≠ 3naked-single ==> r2c8 = 9hidden-pairs-in-a-block: b1{r1c3 r2c1}{n2 n4} ==> r2c1 ≠ 5, r2c1 ≠ 3, r1c3 ≠ 5hidden-pairs-in-a-block: b4{r5c1 r6c3}{n1 n4} ==> r6c3 ≠ 5, r5c1 ≠ 9, r5c1 ≠ 5hidden-triplets-in-a-column: c1{n1 n2 n4}{r5 r8 r2} ==> r8c1 ≠ 9, r8c1 ≠ 5, r8c1 ≠ 3hidden-triplets-in-a-row: r1{n1 n2 n4}{c9 c4 c3} ==> r1c4 ≠ 5, r1c4 ≠ 3hidden-triplets-in-a-column: c6{n1 n2 n4}{r8 r2 r5} ==> r5c6 ≠ 5, r2c6 ≠ 5, r2c6 ≠ 3naked-pairs-in-a-block: b2{r1c4 r2c6}{n1 n2} ==> r2c5 ≠ 2hidden-triplets-in-a-row: r7{n1 n2 n4}{c4 c3 c9} ==> r7c9 ≠ 9, r7c9 ≠ 5, r7c9 ≠ 3, r7c3 ≠ 5naked-pairs-in-a-block: b7{r7c3 r8c1}{n1 n2} ==> r9c3 ≠ 2finned-x-wing-in-columns: n5{c3 c6}{r9 r4} ==> r4c4 ≠ 5biv-chain[3]: r4c3{n5 n7} - b7n7{r9c3 r9c1} - c1n8{r9 r4} ==> r4c1 ≠ 5biv-chain[3]: r3n7{c1 c7} - r3n8{c7 c6} - r4n8{c6 c1} ==> r4c1 ≠ 7biv-chain[3]: r4n7{c3 c7} - r4n6{c7 c1} - b4n8{r4c1 r6c2} ==> r6c2 ≠ 7biv-chain[3]: r6n7{c5 c8} - r1c8{n7 n8} - c5n8{r1 r6} ==> r6c5 ≠ 3, r6c5 ≠ 5, r6c5 ≠ 9biv-chain[3]: r6n7{c8 c5} - c5n8{r6 r1} - r1c8{n8 n7} ==> r5c8 ≠ 7naked-single ==> r5c8 = 5naked-single ==> r8c8 = 3naked-pairs-in-a-row: r4{c4 c9}{n3 n9} ==> r4c7 ≠ 9, r4c7 ≠ 3, r4c6 ≠ 3, r4c1 ≠ 9singles and a whip[1] to the end`
denis_berthier
2010 Supporter

Posts: 1672
Joined: 19 June 2007
Location: Paris

### Re: FN-2187

No Chains :

Hidden Text: Show
Code: Select all
`NP (35) Row 3 => - 35 r3c167NQ (1235) Box 2 => - 235 r1c5HP (14) Box 8 => - 2359 r7c4, - 235 r8c6Swordfish in 1's r258 c167 => - 1 r1c7, r67c1Swordfish in 2's r258 c156 => - 2 r179c1, r79c5, r9c6Swordfish in 4's r258 c167 => - 4 r16c1, r6c6, r17c7NQ (3568) Col 6 => - 35 r2c6, - 5 r5c6NQ (3567) Box 1 => - 57 r1c3, - 35 r2c1NQ (3578) Box 3 => - 35 r1c9, r2c78; => r1c8 = 9NT (124) Row 2 => - 2 r2c5NP (35) Box 2 => -35 r1c4HP (14) Box 4 => - 579 r5c1, - 57 r6c3HT (124) Row 7 => - 5 r7c3, - 359 r7c9NT (124) Col 3 => - 2 r9c3HP (12) Box 7 => - 359 r8c1Swordfish in 7's r349 c137 => - 7 r16c1, r15c7Swordfish in 8's r349 c167 => - 8 r67c1, r6c6, r17c7NP (35) Box 3 => - 35 r1c8Jellyfish in 5's in Columns 3469 Rows 3469 => - 5 r4c17, r6c1258, r9c157MSLS 27 Cell Truths r1c7, r2c2567, r4c6, r5c25678, r6c2568, r7c2578, r8c25678, r9c567     27 Links       7r5 67r6 6r7 6r9 ; 3589c2 2359c5 12345c6 13459c7 35c8 ; 8b5 8b9 ; => - 35 r1c2,- 39 r4c7, - 6 r6c1; => r6c1 = 9NP (75) Row 5 => - 75 r5c5, - 5 r5c7; stte`

Leren
Leren

Posts: 3928
Joined: 03 June 2012

### Re: FN-2187

In three steps, two MSLS's and one M2-Wing (actually five Swordfishes & one M2-Wing...)
Code: Select all
` +---------------------------+------------------------+---------------------------+ |  356-247   3567    245-7  |  1235   68      9      |  35-1478  3578    1345    |  | <2345     <35      8      |  7     <235    <1235   | <13459   <359     6       |359  | >67        1       9      |  35     4      >68     | >78       2       35      |    6  +---------------------------+------------------------+---------------------------+ | >56789     2      >57     | >359    1      >358    | >35679    4      >359     |    3569  | <1459-7   <579     3      |  6     <2579   <245    | <159-7   <579     8       |579  |  569-1478  56789   145-7  |  3459   35789   35-48  |  2        35679   1359    |  +---------------------------+------------------------+---------------------------+ |  359-128   3589    125    |  14     3569-2  7      |  3569-48  35689   23459   |  | <12359    <359     6      |  8     <2359   <14     | <3459    <359     7       |359  | >35789-2   4      >257    | >2359  >3569-2 >356-2  | >35689    1      >2359    |    23569  +---------------------------+------------------------+---------------------------+    124                                2       124       14    78                7                        8         78`

1. MSLS1 (<):
18 cell truths: r258 c125678; 18 links: 124c1, 2c5, 124c6, 14c7, 359r2, 579r5, 359r8
14 eliminations: -24 r1c1, -14 r1c7, -14 r6c1, -4 r6r6, -12 r7c1, -2 r7c5, -4 r7c7, -2 r9c156

2. MSLS2 (>):
16 cell truths:r3c167, r4c134679, r9c1345679 ;16 links: 78c1, 7c3, 9c6, 78c7, 6r3, 3569r4, 23569r9
12 eliminations: -7 r1c13, -78 r1c7, -7 r5c17, -78 r6c1, -7 r6c3, -8 r6c6, -8 r7c17

Code: Select all
` +-----------------------+-----------------------+------------------------+ |  356     3567    24   |  12     68      9     |  35      78     14     |  |  24      35      8    |  7      35      12    |  14      9      6      |  |  67      1       9    |  35     4       68    |  78      2      35     |  +-----------------------+-----------------------+------------------------+ |  56789   2       57   |  359    1       358   |  35679   4      359    |  |  14      579     3    |  6      2579    24    |  159     57     8      |  |  569     56789   14   |  3459   35789   35    |  2       3567   1359   |  +-----------------------+-----------------------+------------------------+ |  359     3589    12   |  14     3569    7     |  3569    3568   24     |  |  12      359     6    |  8      2359    14    |  3459    35     7      |  |  35789   4       57   |  2359   3569    356   |  35689   1      2359   |  +-----------------------+-----------------------+------------------------+`

3. M2-Wing: (7)r5c5=(7-8)r6c5=r1c5-(8=7)r1c8 =>-7r5c8; lclste

And the usual challenge in this forum, one-step solution:
Code: Select all
` +---------------------------+--------------------------+---------------------------+ |  234567    3567    2457   |  1235     68      9      |  134578   3578   c1345    |  |  2345      35      8      |  7        235     1235   |  13459    359     6       |  |  67        1       9      | B35       4       68     |  78       2      C35      |  +---------------------------+--------------------------+---------------------------+ |  56789Y    2       57X    |  359y     1       358Z   |  35679Y   4      D359     |  |  14579    d579     3      |  6      Ee2579z   245    |Dd1579   Dd579     8       |  |  1456789   56789   1457   |  3459y  Ff3579-8z 3458   |  2        35679 Dc1359    |  +---------------------------+--------------------------+---------------------------+ |  123589    3589    125    |  14       23569   7      |  345689   35689  c23459   |  |  12359     359     6      |  8        2359    14     |  3459     359     7       |  |  235789    4      a257W   |Aa2359x    23569   2356   |  35689    1      b2359    |  +---------------------------+--------------------------+---------------------------+`

AAAHP(25)r9c34 (Kraken AAALS r9c34)
(52)r9c34 - r9c9 = (241)r167c9 - (1=597)r5c278 - r5c5 = (7)r6c5
(3)r9c4 - r3c4 = r3c9 - (3=1597)b6p3459 - r5c5 = (7)r6c5
(9)r9c4 - r46c4 = (97)r56c5
(7)r9c3 - r4c3 = (7-68)r4c17 = (8)r4c6
------------------
=> -8 r6c5; lclste
Cenoman
Cenoman

Posts: 1517
Joined: 21 November 2016
Location: Paris, France

### Re: FN-2187

My solution for this one:

Hidden Text: Show
Basics + 5 Swordfish + 1 Jellyfish to here:

Code: Select all
`+----------------+------------------+----------------+| 356  3567 24   | 12    68    9    | 35   78   14   || 24   *35  8    | 7     *35   12   | 14   9    6    || 67   1    9    | 35    4     68   | 78   2    35   |+----------------+------------------+----------------+| 6789 2    *57  | 359   1     358  | 3679 4    359  || 14   *579 3    | 6     2579  24   | 159  57   8    || 69   6789 14   | 3459  3789  35   | 2    367  1359 |+----------------+------------------+----------------+| 359  3589 12   | 14    *3569 7    | 3569 3568 24   || 12   359  6    | 8     *2359 14   | 3459 35   7    || 3789 4    7-5  | f2359 369   f356 | 3689 1    2359 |+----------------+------------------+----------------+`

Finned Franken Swordfish: 5 r2b48 c235 fr9c4 fr9c6 => -5r9c3
(yzf's solver instead gives a Sashimi Mutant Swordfish for this elimination)
singles and a naked pair tte.

Hodoku/yzf's will catch a Finned X-Wing and Finned Jellyfish first, but they aren't needed.

(FN-2187, of course, is Finn from the Star Wars sequel trilogy.)
mith

Posts: 301
Joined: 14 July 2020