The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| 1 . . | . . 2 | 3 . . |
| . 4 . | . 5 . | 6 7 . |
+-------+-------+-------+
| . 7 . | . 8 . | . 5 . |
| 2 . . | . . 3 | 1 . . |
| . . . | . . . | . . 3 |
+-------+-------+-------+
| . . . | . . 1 | 2 . . |
| . 8 . | . 7 . | . 4 . |
| . . 4 | 8 . . | . . . |
+-------+-------+-------+
.........1....23...4..5.67..7..8..5.2....31..........3.....12...8..7..4...48.....

[denis_berthier]

Code: Select all

(solve-sudoku-grid
   +-------+-------+-------+
   ! . . . ! . . . ! . . . !
   ! 1 . . ! . . 2 ! 3 . . !
   ! . 4 . ! . 5 . ! 6 7 . !
   +-------+-------+-------+
   ! . 7 . ! . 8 . ! . 5 . !
   ! 2 . . ! . . 3 ! 1 . . !
   ! . . . ! . . . ! . . 3 !
   +-------+-------+-------+
   ! . . . ! . . 1 ! 2 . . !
   ! . 8 . ! . 7 . ! . 4 . !
   ! . . 4 ! 8 . . ! . . . !
   +-------+-------+-------+
)


Subsets are not enough, but I tried to preserve all the Subsets. I could do this by adding only typed bivalue-chains restricted to rc-space, i.e. xy-chains. Only one of them is enough.

Code: Select all

***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = TyBC+SFin
***  Using CLIPS 6.32-r770
***********************************************************************************************
255 candidates, 1981 csp-links and 1981 links. Density = 6.12%
hidden-pairs-in-a-block: b7{r8c3 r9c2}{n1 n2} ==> r9c2 ≠ 9, r9c2 ≠ 6, r9c2 ≠ 5, r9c2 ≠ 3, r8c3 ≠ 9, r8c3 ≠ 6, r8c3 ≠ 5, r8c3 ≠ 3
finned-x-wing-in-rows: n3{r8 r3}{c4 c1} ==> r1c1 ≠ 3
finned-x-wing-in-columns: n8{c7 c1}{r6 r1} ==> r1c3 ≠ 8
finned-x-wing-in-columns: n3{c2 c5}{r1 r7} ==> r7c4 ≠ 3
swordfish-in-columns: n1{c2 c5 c8}{r9 r6 r1} ==> r9c9 ≠ 1, r6c4 ≠ 1, r6c3 ≠ 1, r1c9 ≠ 1, r1c4 ≠ 1
swordfish-in-columns: n3{c2 c5 c8}{r7 r1 r9} ==> r9c1 ≠ 3, r7c3 ≠ 3, r7c1 ≠ 3, r1c4 ≠ 3, r1c3 ≠ 3
hidden-pairs-in-a-block: b2{r1c5 r3c4}{n1 n3} ==> r3c4 ≠ 9, r1c5 ≠ 9, r1c5 ≠ 6, r1c5 ≠ 4
hidden-triplets-in-a-row: r9{n1 n2 n3}{c8 c2 c5} ==> r9c8 ≠ 9, r9c8 ≠ 6, r9c5 ≠ 9, r9c5 ≠ 6
swordfish-in-columns: n8{c1 c6 c7}{r6 r3 r1} ==> r6c8 ≠ 8, r6c3 ≠ 8, r3c9 ≠ 8, r3c3 ≠ 8, r1c9 ≠ 8, r1c8 ≠ 8
swordfish-in-columns: n4{c1 c6 c7}{r6 r4 r1} ==> r6c5 ≠ 4, r6c4 ≠ 4, r4c9 ≠ 4, r4c4 ≠ 4, r1c9 ≠ 4, r1c4 ≠ 4
swordfish-in-rows: n2{r3 r4 r8}{c3 c9 c4} ==> r6c4 ≠ 2, r1c9 ≠ 2, r1c3 ≠ 2
hidden-pairs-in-a-block: b3{r1c8 r3c9}{n1 n2} ==> r3c9 ≠ 9, r1c8 ≠ 9
hidden-pairs-in-a-block: b5{r4c4 r6c5}{n1 n2} ==> r6c5 ≠ 9, r6c5 ≠ 6, r4c4 ≠ 9, r4c4 ≠ 6
naked-triplets-in-a-column: c5{r1 r6 r9}{n3 n1 n2} ==> r7c5 ≠ 3
hidden-pairs-in-a-block: b8{r8c4 r9c5}{n2 n3} ==> r8c4 ≠ 9, r8c4 ≠ 6, r8c4 ≠ 5
hidden-triplets-in-a-column: c3{n1 n2 n3}{r4 r8 r3} ==> r4c3 ≠ 9, r4c3 ≠ 6, r3c3 ≠ 9
hidden-pairs-in-a-row: r3{n8 n9}{c1 c6} ==> r3c1 ≠ 3
hidden-pairs-in-a-block: b1{r1c2 r3c3}{n2 n3} ==> r1c2 ≠ 9, r1c2 ≠ 6, r1c2 ≠ 5
swordfish-in-rows: n6{r4 r8 r9}{c1 c6 c9} ==> r7c9 ≠ 6, r7c1 ≠ 6, r6c6 ≠ 6, r6c1 ≠ 6, r5c9 ≠ 6, r1c6 ≠ 6, r1c1 ≠ 6
jellyfish-in-rows: n9{r3 r9 r4 r8}{c6 c1 c9 c7} ==> r7c9 ≠ 9, r7c1 ≠ 9, r6c7 ≠ 9, r6c6 ≠ 9, r6c1 ≠ 9, r5c9 ≠ 9, r2c9 ≠ 9, r1c9 ≠ 9, r1c7 ≠ 9, r1c6 ≠ 9, r1c1 ≠ 9
naked-single ==> r1c9 = 5
hidden-single-in-a-block ==> r2c8 = 9
whip[1]: b6n9{r4c9 .} ==> r4c1 ≠ 9, r4c6 ≠ 9
hidden-pairs-in-a-row: r1{n6 n9}{c3 c4} ==> r1c4 ≠ 7, r1c3 ≠ 7
finned-x-wing-in-columns: n9{c5 c2}{r7 r5} ==> r5c3 ≠ 9
naked-triplets-in-a-column: c9{r2 r5 r7}{n8 n4 n7} ==> r9c9 ≠ 7
biv-chain-rc[4]: r1c1{n7 n8} - r1c7{n8 n4} - r2c9{n4 n8} - r7c9{n8 n7} ==> r7c1 ≠ 7
naked-single ==> r7c1 = 5
whip[1]: b8n5{r9c6 .} ==> r6c6 ≠ 5
naked-triplets-in-a-row: r6{c1 c6 c7}{n8 n4 n7} ==> r6c4 ≠ 7
biv-chain-rc[3]: r6c6{n7 n4} - r6c1{n4 n8} - r1c1{n8 n7} ==> r1c6 ≠ 7
stte

[Cenoman]

In two steps: one AIC and one X-wing

Code: Select all

 +-----------------------------+----------------------------+-------------------------+
 |  356789   23569   2356789   |  134679    13469   46789   | d4589   1289   124589   |
 |  1        569    b56789     | a4679      469     2       |  3     c89    c4589     |
 |  389      4       2389      |  139       5       89      |  6      7      1289     |
 +-----------------------------+----------------------------+-------------------------+
 |  3469     7       1369      |  12469     8       469     |  49     5      2469     |
 |  2        569     5689      |  4569-7    469     3       |  1      689   f46789    |
 |  45689    1569    15689     |  1245679   12469   45679   | e4789   2689   3        |
 +-----------------------------+----------------------------+-------------------------+
 |  35679    3569    35679     |  34569     3469    1       |  2      3689   56789    |
 |  3569     8       12        |  23569     7       569     |  59     4      1569     |
 |  35679    12      4         |  8         2369    569     |  579    1369   15679    |
 +-----------------------------+----------------------------+-------------------------+

1. (7)r2c4 = (7-8)r2c3 = r2c89 - r1c7 = (8-7)r6c7 = (7)r5c9 => -7 r5c4; 6 placements & basics

Code: Select all

 +----------------------------+-----------------------+------------------------+
 | *36789    2369    23679-8  |  13679   1369   4     | *589    129-8  1259-8  |
 |  1        569     56789    |  679     69     2     |  3      89     4       |
 |  39       4       239      |  139     5      8     |  6      7      129     |
 +----------------------------+-----------------------+------------------------+
 |  3469     7       1369     |  1269    8      69    |  49     5      269     |
 |  2        569     5689     |  4569    469    3     |  1      689    7       |
 | *48(-569) 1569    1569-8   |  12569   1269   7     | *48(-9) 269-8  3       |
 +----------------------------+-----------------------+------------------------+
 |  3679(+5) 369(-5) 3679(-5) |  3469    3469   1     |  2      3689   8(-569) |
 |  369(-5)  8       12       |  2369    7      569   |  59     4      1569    |
 |  369(-5)  12      4        |  8       2369   569   |  7      1369   1569    |
 +----------------------------+-----------------------+------------------------+

2. X-Wing (8)c17\r16 => -8 r1c389, r6c38; lclste
(+8r7c9, +48r6c17, locked 5r789c1 =>-5r7c23 & 5r7c123 =>-5r89c1; +5r7c1 and ste)

[Leren]

Another gimmicky solution is to play all 6 Swordfish and a Jellyfish on offer followed by an M Ring :

Code: Select all

*--------------------------------------------------*
| 78   23    69    | 69    13  478 | 48  12   5    |
| 1    56   c78-56 | 467   46  2   | 3   9   b48   |
| 89   4     23    | 13    5   89  | 6   7    12   |
|------------------+---------------+---------------|
| 346  7     13    | 12    8   46  | 49  5    269  |
| 2    569   5689  | 45679 469 3   | 1   68   47-8 |
| 458  1569  569   | 5679  12  457 | 478 26   3    |
|------------------+---------------+---------------|
| 5-7  3569 d5679  | 4569  469 1   | 2   368 a78   |
| 3569 8     12    | 23    7   569 | 59  4    169  |
| 5679 12    4     | 8     23  569 | 579 13   69   |
*--------------------------------------------------*

M Ring (78) : (7=8) r7c9 - r2c9 = (8-7) r2c3 = (7) r7c3 loop => - 56 r2c3, - 8 r5c9, - 7 r7c1; stte. Not the shortest solution but entirely Rank 0, for Rank 0 fans.

I think you can write the M Ring as : MSLS 3 Truths : 8 r2, 7c3, r7c9 / 3 Links : 7 r7, 8 c9, r2c3 => - 56 r2c3, - 8 r5c9, - 7 r7c1; stte

Leren

[SpAce]

M Ring (78) : (7=8) r7c9 - r2c9 = (8-7) r2c3 = (7) r7c3 loop => - 56 r2c3, - 8 r5c9, - 7 r7c1; stte. Not the shortest solution but entirely Rank 0, for Rank 0 fans.

I think you can write the M Ring as : MSLS 3 Truths : 8 r2, 7c3, r7c9 / 3 Links : 7 r7, 8 c9, r2c3 => - 56 r2c3, - 8 r5c9, - 7 r7c1; stte

It's certainly a Rank 0 pattern but not an MSLS by any definition that I've seen -- or rather based on what I've gathered from David's examples as I haven't really seen any definition. If I've understood anything correctly, David had two kinds of MSLS: the common naked type (MSNS) with all cell truths and house links, and the rarely seen hidden type (MSHS) with house truths and cell links. M-Ring is a mixed type:

3x3 (Rank 0): {8R2 7C3 7N9 \ 7r7 8c9 2n3} => -7r7c1, -8r5c9, -56r2c3

I don't think it makes sense to call mixed types MSLS. It makes the whole term meaningless if it covers every Rank 0 pattern. For that we have generic set logic.

[pjb]

Where's there's fish++, there's usually MSLS's:

1)
15 cell Truths: r3489 c1679
15 links: 8r3, 4r4, 5r8, 57r9, 369c1, 69c6, 9c7, 1269c9
25 eliminations: -8 r3c3, -4 r4c4, -5 r8c4, -369 r1c1, -69 r6c1, -369 r7c1, -69 r1c6, -69 r6c6, -9 r1c7, -9 r6c7, -129 r1c9, -9 r2c9, -69 r5c9, -69 r7c9

(basics)

2)
14 cell Truths: r167 c258 +r2c2 r5c2 r2c5 r5c5 r5c8
14 links: 123r1, 12r6, 3r7, 569c2, 469c5, 68c8
12 eliminations: -23 r1c3, -13 r1c4, -1 r6c3, -12 r6c4, -3 r7c34, -69 r9c5, -6 r9c8

(basics)

3)
Double ALS at r4689c6 and r5c23458, with X-Z values 4 and 7 => -47 r6c4, -9 r3c6, -9 r7c45, -8 r5c9 => stte

Phil