The New Sudoku Players' Forum

[storm_norm]

Code: Select all

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

Code: Select all

.------------------------.------------------------.------------------------.
| 9       3457    4578   | 137     6       145    | 478     2       1478   |
| 38      234567  45678  | 1237    45      1245   | 46789   145678  14789  |
| 2567    24567   1      | 27      8       9      | 3       4567    47     |
:------------------------+------------------------+------------------------:
| 38      379     789    | 12      79      6      | 5       14      124    |
| 4       1       57     | 8       357     2357   | 27      9       6      |
| 567     5679    2      | 4       579     157    | 78      1378    1378   |
:------------------------+------------------------+------------------------:
| 67      4679    3      | 5       2       478    | 1       4678    4789   |
| 1       245679  45679  | 69      347     3478   | 246789  34678   234789 |
| 267     8       4679   | 69      1       347    | 24679   3467    5      |
'------------------------'------------------------'------------------------'

swordfish on 6
UR {6,9}
(2)r9c1 = (2)r9c7 - (2)r8c9 = (2)r4c9 - (2=7)r5c7 - (7=5)r5c3 - (5)r8c3 = (5)r8c2; r8c2 <> 2
that gets it going
good luck
and enjoy !!

norm

[Draco]

There's another UR using {69} in c7 that sets r2c7<>478, which helps a little but not a lot.

I poked at the puzzle and found that r1c4<>1 cracks it to SSTS... but my direct path to that is a fairly complex contradiction net (9 multi-node steps). Uggh (if you really want to see it I can post -- let me know). It does not require either of the UR's.

Once there a two-color cancellation on 1's and an XY-Wing leave the puzzle at singles.

I'd wager ther is something more elegant to show r1c4<>1.

Cheers...

- drac

[storm_norm]

There's another UR using {69} in c7 that sets r2c7<>478, which helps a little but not a lot.

I poked at the puzzle and found that r1c4<>1 cracks it to SSTS... but my direct path to that is a fairly complex contradiction net (9 multi-node steps). Uggh (if you really want to see it I can post -- let me know). It does not require either of the UR's.

Once there a two-color cancellation on 1's and an XY-Wing leave the puzzle at singles.

I'd wager ther is something more elegant to show r1c4<>1.

Cheers...

- drac

sorry, the UR {6,9} I posted about was exactly yours.
and I tried doing the same thing in col 3, but had no luck.
my reasoning for the failed attempt in col 3 goes...
there is only one other 6 and one other 9 in col 3 besides the ones in the UR pattern.
if either of them are false then the deadly pattern is forced to exist.
but I can't find a contradiction from this.

this move...
(1=2)r5c7 - (2=7)r3c4 - (7=4)r3c9 - (4)r4c9 = (4)r4c8; r4c8 <> 1
gets it to here

Code: Select all

.------------------------.------------------------.------------------------.
| 9       3457    4578   | 137     6       145    | 478     2       1478   |
| 38      23457   45678  | 1237    45      1245   | 69      15678   14789  |
| 567     24567   1      | 27      8       9      | 3       567     47     |
:------------------------+------------------------+------------------------:
| 38      379     789    | 12      79      6      | 5       4       12     |
| 4       1       57     | 8       357     2357   | 27      9       6      |
| 567     5679    2      | 4       579     157    | 78      1378    1378   |
:------------------------+------------------------+------------------------:
| 67      4679    3      | 5       2       478    | 1       678     4789   |
| 1       45679   45679  | 69      347     3478   | 24789   3678    234789 |
| 2       8       4679   | 69      1       347    | 4679    37      5      |
'------------------------'------------------------'------------------------'

coloring on 1's removes 1 from r2c4
---
ok, back
finished and its not pretty. some of these weren't needed probably.
(7)r4c5 = (7)r4c23 - (7=5)r5c3 - (5)r6c1 = (5)r3c1 - (5)r3c8 = (5-1)r2c8 = (1)r6c8 - (1=2)r4c9 - (2=7)r5c7; r5c56 <> 7
(4=5)r2c5 - (5)r2c8 = (5-6)r3c8 = (6-9)r2c7 = (9)r2c9; r2c9 <> 4
(4=5)r2c5 - (5)r2c8 = (5)r3c8 - (5)r3c1 = (5)r6c1 - (5=7)r5c3 - (7=2)r5c7 - (2)r5c6 = (2)r2c6; r2c6 <> 4
loop... (2=7)r5c7 - (7=5)r5c3 - (5)r6c1 = (5)r3c1 - (5)r3c8 = (5-1)r2c8 = (1)r6c8 - (1=2)r4c9; r6c9<>1, r6c2<>5, r3c2 <> 5, r2c8<>78,
(7)r5c3 = (7)r4c23 - (7=9)r4c5 - (9)r6c5 = (9-6)r6c2 = (6)r6c1 - (6=7)r7c1; r89c3 <> 7, r6c1 <> 7
(7=2)r3c4 - (2)r4c4 = (2)r4c9 - (2=7)r5c7 - (7=5)r5c3 - (5)r6c1 = (5)r3c1; r3c1 <> 7
(4=8)r7c6 - (8=6)r7c8 - (6)r3c8 = (6-9)r2c7 = (9)r2c9 - (9)r7c9 = (9)r7c2; r8c2 <> 4
ER 4... r1c6 <> 4
w-wing {1,5} removes 5 from r2c6
(1=2)r4c4 - (2=3)r5c6 - (3=5)r5c5 - (5=7)r5c3 - (7=3)r4c2 - (3)r1c2 = (3)r1c4; r1c4 1

[aran]

Code: Select all

.------------------------.------------------------.------------------------.
| 9       3457    4578   | 137     6       145    | 478     2       1478   |
| 38      23457   45678  | 1237    45      1245   | 69      15678   14789  |
| 567     24567   1      | 27      8       9      | 3       567     47     |
:------------------------+------------------------+------------------------:
| 38      379     789    | 12      79      6      | 5       4       12     |
| 4       1       57     | 8       357     2357   | 27      9       6      |
| 567     5679    2      | 4       579     157    | 78      1378    1378   |
:------------------------+------------------------+------------------------:
| 67      4679    3      | 5       2       478    | 1       678     4789   |
| 1       45679   45679  | 69      347     3478   | 24789   3678    234789 |
| 2       8       4679   | 69      1       347    | 4679    37      5      |
'------------------------'------------------------'------------------------'

A bit of thinning out :
1. 78r16c7=4r1c7-(4=7)r3c9-(7=2)r3c4-(2=1)r4c4-(1=2)r4c9-(2=7)r5c7-(7=8)r6c5 : <78>r89c7
2 3678r6789c8=1r6c8-(1=2)r4c9-(2=7)r5c7-(7=8)r6c7-(78=4)r1c7-(4=7)r3c9 : <7>r23c8
3. 79r46c5=5r6c5-5r6c1=5r3c1-(5=6)r3c8-(6=378)r789c8-(378=1)r6c8 -(15=7)r6c6 : <7>r5c56
4. 4r3c2=4r3c9-(4=78)r1c7-(78=2)r5c7-2r5c6=2r4c4-(2=7)r3c4-(7=56)r3c1 : <567>r3c2

[Draco]

sorry, the UR {6,9} I posted about was exactly yours.
and I tried doing the same thing in col 3, but had no luck.
my reasoning for the failed attempt in col 3 goes...
there is only one other 6 and one other 9 in col 3 besides the ones in the UR pattern.
if either of them are false then the deadly pattern is forced to exist.
but I can't find a contradiction from this.

this move...
(1=2)r5c7 - (2=7)r3c4 - (7=4)r3c9 - (4)r4c9 = (4)r4c8; r4c8 <> 1
gets it to here

Code: Select all

.------------------------.------------------------.------------------------.
| 9       3457    4578   | 137     6       145    | 478     2       1478   |
| 38      23457   45678  | 1237    45      1245   | 69      15678   14789  |
| 567     24567   1      | 27      8       9      | 3       567     47     |
:------------------------+------------------------+------------------------:
| 38      379     789    | 12      79      6      | 5       4       12     |
| 4       1       57     | 8       357     2357   | 27      9       6      |
| 567     5679    2      | 4       579     157    | 78      1378    1378   |
:------------------------+------------------------+------------------------:
| 67      4679    3      | 5       2       478    | 1       678     4789   |
| 1       45679   45679  | 69      347     3478   | 24789   3678    234789 |
| 2       8       4679   | 69      1       347    | 4679    37      5      |
'------------------------'------------------------'------------------------'

coloring on 1's removes 1 from r2c4

Oooooh -- I thought your UR resulted in r8c2 <> 2 (using that in the loop you wrote somehow). My bad.

Turns out my big, ugly contradiction net works directly from your original PM's without the UR, swordfish, etc:

Code: Select all

r1c4=1 r4c4=2 r3c4=7 r3c2=2
r1c4=1 r2c4=3 r2c1=8 r4c3=8
r4c4=2 r2c6=2
r4c4=2 r8c9=2 r6c9=3
r3c4=7 r3c9=4
r4c4=2 [r4c9<>2] + r3c9=4 [r4c9<>4] = r4c9=1
[r2c4<>1 + r2c6<>1] + r4c9=1 [r2c9<>1] = r2c8=1 r3c8=5 r2c7=6 r2c9=9
[r3c2<>6 + r3c8<>6] = r3c1=6 r6c1=5 r6c2=6 r6c5=9 r4c5=7
r3c1=6 r7c1=7
[r8c9<>7 + r3c9<>7 + r6c9<>7] + r7c1=7 [r7c9<>7] + [r2c9<>7] = r1c9=7
[r8c9<>8 + r6c9<>8 + r2c9<>8 + r1c9<>8] = r7c9=8
[r4c3<>9 + r4c5<>9] = r4c2=9
r7c9=8 r7c2=9
------ Cancellations ------
r1c4<>1

The contradiction is r47c2=9 (can be a little hard to spot in all those links). From there the swordfish on 6's is still there, along with the same endgame I noted initially (multi-coloring on 1's for r4c9 <> 1. XY Wing from r3c9 forces r4c4 <> 2, then it's singles).

Your path is cleaner insofar as it isn't a net. The net I used to get there is unlikely to be found by a human solver (who has the patience for 9 iterations & multiple branches?).

Cheers...

- drac

PS: Aran, just saw your post as I was proofing this one. If I tracked your moves properly (you did not apply swordfish it seems), you wind up with

Code: Select all

9   3457  4578  | 137  6   145  | 478 2    1478 
38  23457 45678 | 1237 45  1245 | 69  1568 14789
567 24    1     | 27   8   9    | 3   56   47   
----------------+---------------+----------------
38  379   789   | 12   79  6    | 5   4    12   
4   1     57    | 8    35  235  | 27  9    6     
567 5679  2     | 4    579 157  | 78  1378 1378 
----------------+---------------+----------------
67  4679  3     | 5    2   478  | 1   678  4789 
1   45679 45679 | 69   347 3478 | 249 3678 234789
2   8     4679  | 69   1   347  | 469 37   5

The swordfish is still there along with a hidden [56] in r3. Multicolor 1's force r2c4<>1... and that wraps up the "simple" stuff I can see.

[daj95376]

Swordfish, XY-Chain, turbot fish/ER/Kite, and a chain. But I didn't do it manually.

[storm_norm]

Draco,
that forcing net is something huge.

[Draco]

Draco,
that forcing net is something huge.

Ya, that it is!

Turns out there is another backdoor: r4c3<>9. The net that gets there from your PMs is not as big or ugly, but still takes 7 iterations.

A bit shorter if you start from Aran's work (Daj, is that where your moves start from?) but still not pretty.

Cheers...

- drac

PS: No way I would find these sans solver ...

[daj95376]

Daj, is that where your moves start from?

My solution starts from the initial puzzle (not grid).

[Allan Barker]

Hi,

Another cleaner is this simple ALS loop that eliminates 14 candidates.
Two ALS + a link in box 4. (works before or after the fish on 6)

A = r3c49, B = r156c7, * = (2)box5

Code: Select all

+----------------------+--------------------+--------------------------+
| 9      3457    4578  | 137    6    145    |B(478)    2        178-4  |
| 38     234567  45678 | 137-2  45   1245   | 69-478 15678-4    1789-4 |
| 256-7  2456-7  1     |A(27)   8    9      | 3        56-47   A(47)   |
+----------------------+--------------------+--------------------------+
| 38     379     789   | 1(2)*  79   6      | 5        14       124    |
| 4      1       57    | 8      357  357(2)*|B(27)     9        6      |
| 567    5679    2     | 4      579  157    |B(78)     1378     1378   |
+----------------------+--------------------+--------------------------+
| 67     4679    3     | 5      2    478    | 1        4678     4789   |
| 1      245679  45679 | 69     347  3478   | 2469-78  34678    234789 |
| 267    8       4679  | 69     1    347    | 2469-7   3467     5      |
+----------------------+--------------------+--------------------------+
     
14 Eliminations -->
      r2c4 <> 2
      r2c789<>4 , r1c9<> 4 , r3c8<>4
      r3c128<>7 , r289c7<>7,
      r28c7<>8 


[storm_norm]

Allen,
thankyou for that massive move.
norm

[aran]

PS: Aran, just saw your post as I was proofing this one. If I tracked your moves properly (you did not apply swordfish it seems), you wind up with

Code: Select all

9   3457  4578  | 137  6   145  | 478 2    1478 
38  23457 45678 | 1237 45  1245 | 69  1568 14789
567 24    1     | 27   8   9    | 3   56   47   
----------------+---------------+----------------
38  379   789   | 12   79  6    | 5   4    12   
4   1     57    | 8    35  235  | 27  9    6     
567 5679  2     | 4    579 157  | 78  1378 1378 
----------------+---------------+----------------
67  4679  3     | 5    2   478  | 1   678  4789 
1   45679 45679 | 69   347 3478 | 249 3678 234789
2   8     4679  | 69   1   347  | 469 37   5

The swordfish is still there along with a hidden [56] in r3. Multicolor 1's force r2c4<>1... and that wraps up the "simple" stuff I can see.

Draco, thanks for putting up the grid.
Taking it from there and <12>r2c4, <7>r3c1, more thinning out :
1.3678r6789c8=1r6c8-(1=2)r4c9-(2=7)r5c7-(7=5)r5c3-5r6c1=5r3c1-(5=6)r3c8-(6=378)r789c8 : =><68>r2c8
2.2r8c9=2r4c9......same chain as 1.....=378r789c8 : <378>r8c9 => r6c9=3 =><3>r6c8
3.(7=4)r3c9-(4=78)r1c7-7r5c7=7r5c3-7r6c1=7r7c1 : <7>r7c9, and pointing 7s <7>r6c8 <7>r1c7

Thereafter there's no shortage of simple moves eg
4.3r1c2=3r1c4-(3=7)r2c4-(7=2)r3c4-(2=4)r3c2 : <4>r1c2
5.3r1c2=3r1c4-(3=7)r2c4-(7=2)r3c4-(2=1)r4c4...and all the way to =5r3c1 : <5>r1c2
6.6r2c3=(6-5)r3c1=5r6c1-(5=7)r5c3 : <7>r2c3
7.37r1c24=1r1c4-(1=2)r4c4-2r4c9=(2-7)r5c7=7r5c3 : <7>r1c3 and pointing 7s box 1=> <7>r4678c2

one way to finish
8.7r2c2=7r2c4-(7=2)r3c4-2r4c4=2r5c6-(2=7)r5c7-(7=5)r5c3-5r6c1=5r3c1 : => <5>r2c2
9.7r2c2=7r2c4-(7=2)r3c4-(2=4)r3c2 : =><4>r2c2
10.6r6c2=6r6c1-(6=5)r3c1-5r3c8=(5-1)r2c8=1r6c8-(1=2)r4c9-(2=7)r5c7-(7=5)r5c3 : => <5>r6c2 hence r8c2=5 and <5>r8c3
11. deadly rectangle avoidance 69r89c34 :
7r89c3=>5r5c3
4r89c3-4r12c3=4r3c2-(4=7)r3c9-(7=2)r3c4-2r4c4=2r5c6-(2=7)r5c7 =>r5c3
therefore r5c3=5.
Singles to end
Given the solution (essentially removal of 5s from column 2), looks like a number of the moves above weren't required (probably 1,2,3,6,7) but I'm leaving this as I found it.

[DonM]

The solution assumes the eliminations from the SF(6)c367r289 because that is the ssts position. Concerning that- the PM grid shown turns out to be the ssts position, but without the sf eliminations which are part of the ssts position. Yet the sf is mentioned as if it is an additional move. This makes things rather confusing. IMO, best to start off with the complete ssts position so everyone is starting off at the same point.

1: (2)r4c9=r4c4-(2=7)r3c4-(7=4)r3c9-als(4=78)r16c7-(7=2)r5c7-loop => r3c128<>7, r2c789<>4, r3c8<>4, r1c9<>4, r2c7<>7, r89c7<>7, r2c4<>2
2: (4=1)r4c8-(1=2)r4c5-(2=7)r3c4-(7=4)r3c9 => r4c9<>4 -> r4c8=4 -> 2str-kite(1)r26c8/r4c49: r2c4<>1
3: (2=7)r5c7-(7=5)r5c3-als(5=67)r67c1-(7=2)r9c1 => r9c7<>2 -> r9c1=2 ->r8c2<>2 -> np(56)r3c18: r3c2<>6
4: (2)r8c9=r8c7-(2=7)r5c7-(7=5)r5c3-r6c1=r3c1-(5=6)r3c8-als(6=378) => r8c9<>3 -> r6c9=3
5: (5)r5c3=hp(35-2)r5c56=r5c7-(2=1)r4c9-r6c8=(1-5)r2c8=r3c8-r3c1=(5)r6c1-loop => r36c2<>5, r2c8<>7,8
6: AUR(69)r89c47
||
(248)r8c7
||
(4)r9c7-grp(4)r78c9=(4-7)r3c9=(7-2)r3c4=(2-1)r4c4=r4c9-r6c8=(1-5)r2c8=(5-6)r3c8=(6)r2c7
=> r8c7<>6
7: (9=6)r9c4-r9c7=(6-9)r2c7=r2c9-r7c9=(9)r7c2 => r9c3<>9
8: (5)r1c6=grp(5)r1c23-r3c1=(5)r6c1 => r6c6<>5 -> nt(178)r6c678:r6c125<>7 -> np(56)r36c1: r7c1<>6=7 -> nt(469)r9c347: r9c6<>4
9: (9=6)r6c2-(6=5)r6c1-(5=7)r5c3-(7=2)r5c7-r5c6=r2c6-(2=7)r3c4-(7=3)r2c4-r2c1=r4c1-als(3=79)r4c25 => r4c3<>9 -> r6c2=9

STTE

[daj95376]

It's been several days since the puzzle was posted, so I'm cheating and posting a solver assisted solution.

After basics (before Swordfish or UR):

Code: Select all

2-String Kite (grouped)  r1c1b1                           <> 5  [r6c6]

XY-Chain (4=7)r3c9 - (7=2)r3c4 - (2=1)r4c4 - (1=4)r4c8    <> 4  [r23c8],[r4c9]

turbot fish/Empty Rectangle/2-String Kite/finned X-Wing   <> 1  [r2c4]

(8)r4c3 = (8)r4c1 - (8=3)r2c1 - (3)r2c4 = (3-1)r1c4 = (1)r4c4 - (1=7)r6c6 - (7=9)r4c5 => [r4c3]<>9
___________________________________________________________________________________________________


[PIsaacson]

Allan,

My ALS engine found your example dual-linked ALS as a Death Blossom, but using a different stem r4c49.<2> and with 16 eliminations. I checked with Xsudo and they all appear to be found by the same base/cover set that my new base/cover engine discovered. I use different notation, but it matches exactly. The base/cover engine found 2 additional eliminations that dual-linked ALS rules didn't catch using the stem cells + all the ALS cells.

Code: Select all

From Xsudo:
+----------------------+------------------+--------------------------+
| 9      3457    4578  | 137    6    145  | (478)    2        178-4  |
| 38     234567  45678 | 137-2  45   1245 | 69-478   15678-4  1789-4 |
| 256-7  2456-7  1     | (27)   8    9    | 3        56-47    (47)   |
+----------------------+------------------+--------------------------+
| 38     379     789   | (12)   79   6    | 5        4-1      (12-4) |
| 4      1       57    | 8      357  2357 | (27)     9        6      |
| 567    5679    2     | 4      579  157  | (78)     1378     1378   |
+----------------------+------------------+--------------------------+
| 67     4679    3     | 5      2    478  | 1        4678     4789   |
| 1      245679  45679 | 69     347  3478 | 2469-78  34678    234789 |
| 267    8       4679  | 69     1    347  | 2469-7   3467     5      |
+----------------------+------------------+--------------------------+


1372 16 Nodes, Raw Rank = 2 (linksets - sets)
     7 Sets = {34N4 156N7 34N9}
     9 Links = {7r3 12r4 2c4 78c7 4c9 2b6 4b3}
     16 Eliminations, 0 Assignments -->
     r2c789<>4, r3c128<>7, r289c7<>7, r28c7<>8, r14c9<>4, r2c4<>2, r3c8<>4, r4c8<>1,

Code: Select all

From my ALS + base/cover engine:
Puzzle: 9...6..2............1.893.......65..41.8...96..24.......352.1..1.........8..1...5 puzzle 1 db.sud

 9         3457      4578     |137       6         145      |478       2         1478
 38        234567    45678    |1237      45        1245     |46789     145678    14789
 2567      24567     1        |27        8         9        |3         4567      47
 --------- --------- ---------+--------- --------- ---------+--------- --------- ---------
 38        379       789      |12        79        6        |5         14        124
 4         1         57       |8         357       2357     |27        9         6
 567       5679      2        |4         579       157      |78        1378      1378
 --------- --------- ---------+--------- --------- ---------+--------- --------- ---------
 67        4679      3        |5         2         478      |1         4678      4789
 1         245679    45679    |69        347       3478     |246789    34678     234789
 267       8         4679     |69        1         347      |24679     3467      5

do_subsets - reducing r9c1.<267> by <6>
do_subsets - reducing r2c2.<234567> by <6>
do_subsets - reducing r8c2.<245679> by <6>
do_subsets - reducing r2c8.<145678> by <6>
do_subsets - reducing r8c8.<34678> by <6>
do_subsets - reducing r9c8.<3467> by <6>
do_subsets - fish row subset[3] d6 at r367\c128
 
do_death_blossom - reducing r2c4.<1237> by <2> dual[2]
do_death_blossom - reducing r1c9.<1478> by <4> dual[2]
do_death_blossom - reducing r2c7.<46789> by <4> dual[2]
do_death_blossom - reducing r2c8.<14578> by <4> dual[2]
do_death_blossom - reducing r2c9.<14789> by <4> dual[2]
do_death_blossom - reducing r3c8.<4567> by <4> dual[2]
do_death_blossom - reducing r2c7.<6789> by <7> dual[2]
do_death_blossom - reducing r3c1.<2567> by <7> dual[2]
do_death_blossom - reducing r3c2.<24567> by <7> dual[2]
do_death_blossom - reducing r3c8.<567> by <7> dual[2]
do_death_blossom - reducing r8c7.<246789> by <7> dual[2]
do_death_blossom - reducing r9c7.<24679> by <7> dual[2]
do_death_blossom - reducing r2c7.<689> by <8> dual[2]
do_death_blossom - reducing r8c7.<24689> by <8> dual[2]
do_death_blossom - db[2] stem cells r4c49.<2> ALS[1] -2- r3c49.<n247> ALS[2] -2- r156c7.<n2478>  <47>

do_base_cover - reducing r4c8.<14> by <1>
do_base_cover - reducing r4c9.<124> by <4>
do_base_cover - rank 2 base rc(17, 34, 39, 44, 49, 57, 67) cover rn(37, 41, 42) cn(42, 77, 78, 94) bn(34, 62)

I think the "more correct" base set should just include 2r4 for the stem cells, but then it omits the r4c8<>1 elimination.