The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . . |
| . 9 . | 8 . 7 | . . . |
| . . 3 | . 5 . | 4 . . |
+-------+-------+-------+
| . 8 . | 9 . . | . 6 . |
| . . . | . 2 . | 5 . . |
| . 5 . | 6 . . | . 7 . |
+-------+-------+-------+
| . . 4 | . 1 . | 3 . . |
| . 7 . | 5 . 6 | . 9 . |
| . . . | . . . | . . . |
+-------+-------+-------+
..........9.8.7.....3.5.4...8.9...6.....2.5...5.6...7...4.1.3...7.5.6.9..........

[SCLT]

Very few basic steps: we can place a 5 in r4c6 and that's it. The candidate grid at this point is pretty imtimidating:

Code: Select all

+-----------------------+--------------------+-------------------------+
| 1245678  1246  125678 | 1234  3469   12349 | 126789  12358  12356789 |
| 12456    9     1256   | 8     346    7     | 126     1235   12356    |
| 12678    126   3      | 12    5      129   | 4       128    126789   |
+-----------------------+--------------------+-------------------------+
| 12347    8     127    | 9     347    5     | 12      6      1234     |
| 134679   1346  1679   | 1347  2      1348  | 5       1348   13489    |
| 12349    5     129    | 6     348    1348  | 1289    7      123489   |
+-----------------------+--------------------+-------------------------+
| 25689    26    4      | 27    1      289   | 3       258    25678    |
| 1238     7     128    | 5     348    6     | 128     9      1248     |
| 1235689  1236  125689 | 2347  34789  23489 | 12678   12458  1235678  |
+-----------------------+--------------------+-------------------------+


One massive Multi-Fish on base 1234 in rows 2,4,6,8.
16 truths {1234r2, 1234r4, 1234r6, 1234r8} / 16 links {1234c1, 12c3, 34c5, r6c6, 12c7, r2c8, 1234c9}
49 Eliminations: -124r1c1 -56r2c1 -12r3c1 -7r4c1 -134r5c1 -9r6c1 -2r7c1 -8r8c1 -123r9c1 -12r1c3 -1r5c3 -12r9c3 -34r1c5 -34r9c5 -8r6c6 -12r1c7 -12r9c7 -5r2c8 -123r1c9 -56r2c9 -12r3c9 -134r5c9 -89r6c9 -2r7c9 -8r8c9 -124r9c9

In the above eliminations I have sneakily included the eliminations that arise from the 1234 hidden quads in columns 1 and 9 which the multi-fish obviously shines a light on very easily. I hope you'll forgive me.

For reference, here's what the candidate grid looks like after that huge volley:

Code: Select all

+------------------+------------------+--------------------+
| 5678  1246  5678 | 1234  69   12349 | 6789  12358  56789 |
| 124   9     1256 | 8     346  7     | 126   123    123   |
| 678   126   3    | 12    5    129   | 4     128    6789  |
+------------------+------------------+--------------------+
| 1234  8     127  | 9     347  5     | 12    6      1234  |
| 679   1346  679  | 1347  2    1348  | 5     1348   89    |
| 1234  5     129  | 6     348  134   | 1289  7      1234  |
+------------------+------------------+--------------------+
| 5689  26    4    | 27    1    289   | 3     258    5678  |
| 123   7     128  | 5     348  6     | 128   9      124   |
| 5689  1236  5689 | 2347  789  23489 | 678   12458  5678  |
+------------------+------------------+--------------------+


Now the puzzle falls to mere basics. Hidden single 5 in r2c3, then there's a 678 naked pair in box 1 and a 12 naked pair in row 3, then singles to the end:

Code: Select all

+-------+-------+-------+
| 8 4 7 | 3 6 1 | 9 2 5 |
| 2 9 5 | 8 4 7 | 6 3 1 |
| 6 1 3 | 2 5 9 | 4 8 7 |
+-------+-------+-------+
| 4 8 2 | 9 7 5 | 1 6 3 |
| 7 3 6 | 1 2 8 | 5 4 9 |
| 1 5 9 | 6 3 4 | 8 7 2 |
+-------+-------+-------+
| 9 6 4 | 7 1 2 | 3 5 8 |
| 3 7 1 | 5 8 6 | 2 9 4 |
| 5 2 8 | 4 9 3 | 7 1 6 |
+-------+-------+-------+


[SpAce]

Almost the same as SCLT's, except that my Multifish is column-based.

Code: Select all

            *1234             *1234           *1234              *1234
.---------------------------.-------------------------.-----------------------------.
| 5678-124  \124-6  5678-12 | \1234   69-34   \1234-9 | 6789-12  \123-58  56789-123 | \1234  \n2468
| 12456      9      1256    |  8      346      7      | 126      \123-5   12356     |        \n8
| 678-12     126    3       |  12     5        129    | 4         128     6789-12   | \12
:---------------------------+-------------------------+-----------------------------:
| 12347      8      127     |  9      347      5      | 12        6       1234      |
| 679-134    346-1  1679    |  1347   2        1348   | 5         1348    89-134    | \134
| 12349      5      129     |  6      348     \134-8  | 1289      7       123489    |        \n6
:---------------------------+-------------------------+-----------------------------:
| 5689-2     26     4       |  27     1        289    | 3         258     5678-2    | \2
| 1238       7      128     |  5      348      6      | 128       9       1248      |
| 5689-123  \123-6  5689-12 | \234-7  789-34  \234-89 | 678-12   \124-58  5678-124  | \1234  \n2468
'---------------------------'-------------------------'-----------------------------'

MF(1234): 16x16 {1234C2468 \ [1234r19|19n2468] 12r3 134r5 2r7 2n8 6n6} => 49 elims; btte

the row-based variant: Show

MF(1234): 16x16 {1234R2468 \ [1234c19|2468n19] 12c3 34c5 12c7 2n8 6n6} => 49 elims; btte

That was a nice ten-minute workout. What's interesting is that it seems to require almost all of the (non-redundant) eliminations before yielding.

[SpAce]

In the above eliminations I have sneakily included the eliminations that arise from the 1234 hidden quads in columns 1 and 9 which the multi-fish obviously shines a light on very easily. I hope you'll forgive me.

They're legitimate eliminations if you list the alternate cell links for them. See my solution for one way to do that. Of course one or the other set is enough because basics take care of the rest, but both eliminations are available at once if wanted.

[pjb]

Alternatively, an MSLS:

25 cell Truths: r13579 c12468
25 links: 1234r1, 12r3, 134r5, 2r7, 1234r9, 56789c1, 6c2, 7c4, 89c6, 58c8
32 eliminations: -12 r1c3, -34 r1c5, -12 r1c7, -123 r1c9, -12 r3c9, -1 r5c3, -134 r5c9, -2 r7c9, -12 r9c3, -34 r9c5, -12 r9c7, -124 r9c9, -56 r2c1, -7 r4c1, -9 r6c1, -8 r8c1, -8 r6c6, -5 r2c8 => btte;

Phil

[denis_berthier]

Code: Select all

(solve-sudoku-grid
   +-------+-------+-------+
   ! . . . ! . . . ! . . . !
   ! . 9 . ! 8 . 7 ! . . . !
   ! . . 3 ! . 5 . ! 4 . . !
   +-------+-------+-------+
   ! . 8 . ! 9 . . ! . 6 . !
   ! . . . ! . 2 . ! 5 . . !
   ! . 5 . ! 6 . . ! . 7 . !
   +-------+-------+-------+
   ! . . 4 ! . 1 . ! 3 . . !
   ! . 7 . ! 5 . 6 ! . 9 . !
   ! . . . ! . . . ! . . . !
   +-------+-------+-------+
)


Using only elementary techniques, in their natural order of complexity:

Code: Select all

***********************************************************************************************
***  SudoRules 20.1.s based on CSP-Rules 2.1.s, config = S
***  Using CLIPS 6.32-r770
***********************************************************************************************
hidden-single-in-a-row ==> r4c6 = 5
254 candidates, 1928 csp-links and 1928 links. Density = 6.0%
swordfish-in-columns: n4{c2 c4 c8}{r5 r1 r9} ==> r9c9 ≠ 4, r9c6 ≠ 4, r9c5 ≠ 4, r5c9 ≠ 4, r5c6 ≠ 4, r5c1 ≠ 4, r1c6 ≠ 4, r1c5 ≠ 4, r1c1 ≠ 4
hidden-single-in-a-column ==> r6c6 = 4
whip[1]: b5n1{r5c6 .} ==> r5c1 ≠ 1, r5c2 ≠ 1, r5c3 ≠ 1, r5c8 ≠ 1, r5c9 ≠ 1
swordfish-in-columns: n3{c2 c4 c6}{r5 r9 r1} ==> r9c5 ≠ 3, r9c1 ≠ 3, r5c9 ≠ 3, r5c8 ≠ 3, r5c1 ≠ 3, r1c9 ≠ 3, r1c8 ≠ 3, r1c5 ≠ 3
hidden-single-in-a-column ==> r2c8 = 3
jellyfish-in-columns: n2{c2 c8 c4 c6}{r9 r7 r3 r1} ==> r9c9 ≠ 2, r9c7 ≠ 2, r9c3 ≠ 2, r9c1 ≠ 2, r7c9 ≠ 2, r7c1 ≠ 2, r3c9 ≠ 2, r3c1 ≠ 2, r1c9 ≠ 2, r1c7 ≠ 2, r1c3 ≠ 2, r1c1 ≠ 2
jellyfish-in-columns: n1{c2 c6 c4 c8}{r9 r3 r5 r1} ==> r9c9 ≠ 1, r9c7 ≠ 1, r9c3 ≠ 1, r9c1 ≠ 1, r3c9 ≠ 1, r3c1 ≠ 1, r1c9 ≠ 1, r1c7 ≠ 1, r1c3 ≠ 1, r1c1 ≠ 1
hidden-quads-in-a-column: c1{n1 n2 n3 n4}{r2 r6 r8 r4} ==> r8c1 ≠ 8, r6c1 ≠ 9, r4c1 ≠ 7, r2c1 ≠ 6, r2c1 ≠ 5
hidden-quads-in-a-row: r1{n1 n2 n3 n4}{c2 c8 c6 c4} ==> r1c8 ≠ 8, r1c8 ≠ 5, r1c6 ≠ 9, r1c2 ≠ 6
whip[1]: c8n5{r9 .} ==> r7c9 ≠ 5, r9c9 ≠ 5
naked-triplets-in-a-block: b9{r7c9 r9c7 r9c9}{n6 n7 n8} ==> r9c8 ≠ 8, r8c9 ≠ 8, r8c7 ≠ 8, r7c8 ≠ 8
naked-pairs-in-a-column: c7{r4 r8}{n1 n2} ==> r6c7 ≠ 2, r6c7 ≠ 1, r2c7 ≠ 2, r2c7 ≠ 1
stte

[mith]

If you stop after the second jellyfish, there are actually four hidden quads available (though only one is necessary here - either r1 or c9).

I'm mostly convinced two is the limit of required hidden quads, at least in an empty rows/columns configuration, and I've posted at least one of those. Maybe there is one with four available that requires two.

[denis_berthier]

If you stop after the second jellyfish, there are actually four hidden quads available (though only one is necessary here - either r1 or c9).

If SudoRules doesn't use them, it's because easier eliminations are available.

[mith]

Yeah, I'm not saying you should have used 4 hidden quads, just that they are there.

What ordering does SudoRules use in that case? SE does c1, c9; Hodoku just does r1. (I couldn't have flipped this vertically so Hodoku would use r1, r9, but I liked the way it looked better this way.) I was a little surprised to see c1, r1 in SudoRules. Does it alternate c1, r1, c2, r2, etc? Order based on number of candidates remaining or something like that?

[denis_berthier]

What ordering does SudoRules use in that case? SE does c1, c9; Hodoku just does r1. (I couldn't have flipped this vertically so Hodoku would use r1, r9, but I liked the way it looked better this way.) I was a little surprised to see c1, r1 in SudoRules. Does it alternate c1, r1, c2, r2, etc? Order based on number of candidates remaining or something like that?

For Subsets in SudoRules, there are only two general rules:
- size 2 before 3 before 4 (as for any other rule)
- Naked before Hidden before Super-Hidden (i.e. Fish)

As for the rest, it's conceptually random.

[storm_norm22]

I took a stab at this and looks like its just these massive fish that solve it, two swordfish and two jelly fish, maybe 3