The New Sudoku Players' Forum

[shye]

Code: Select all

+-------+-------+-------+
| . 4 . | . 5 2 | 3 . . |
| . . . | . . 6 | . . . |
| . . 6 | . 1 . | 7 . 4 |
+-------+-------+-------+
| 4 . . | . . . | . 3 1 |
| . 2 3 | . 9 . | 8 . 6 |
| 1 . . | . . . | . . . |
+-------+-------+-------+
| . 1 2 | . 6 . | 5 . . |
| . 3 4 | . 8 . | . . 2 |
| . . . | 2 . 3 | . . . |
+-------+-------+-------+
.4..523.......6.....6.1.7.44......31.23.9.8.61.........12.6.5...34.8...2...2.3...

if you've solved my other puzzles before this will be familiar ground, but hopefully different enough to be interesting
looking for other kinds of eliminations with these patterns

[marek stefanik]

Code: Select all

   +------------------------+------------------------+------------------------+
   | 89-7    4       1      | 789     5       2      | 3       6       89     |
   | 23      5789    5789   | 34789   347     6      | 129     12589   589    |
   | 23      589     6      | 389     1       89     | 7       2589    4      |
   +------------------------+------------------------+------------------------+
   | 4       56789   5789   | 5678    27      578    | 29      3       1      |
   | 57      2       3      | 147-5   9       147-5  | 8       457     6      |
   | 1       56789   5789   | 345678  2347    4578   | 249     259-47  579    |
   +------------------------+------------------------+------------------------+
   | 78      1       2      | 479     6       479    | 5       478     3      |
   | 679     3       4      | 15      8       15     | 69      79      2      |
   | 5689-7  5789    5789   | 2       47      3      | 1469    189-47  789    |
   +------------------------+------------------------+------------------------+

The main step is rank0, no need for multilinks:
6 Truths = {4B9 7B79 5N18 9N5}
6 Links = {4r9 4c8 5r5 7r9 7c18}

Then solved with ERs (89r1b7/c1 => -89r9c9).

Marek

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 789    4      1      ! 789    5      2      ! 3      6      89     !
   ! 235789 5789   5789   ! 34789  347    6      ! 129    12589  589    !
   ! 23589  589    6      ! 389    1      89     ! 7      2589   4      !
   +----------------------+----------------------+----------------------+
   ! 4      56789  5789   ! 5678   27     578    ! 29     3      1      !
   ! 57     2      3      ! 1457   9      1457   ! 8      457    6      !
   ! 1      56789  5789   ! 345678 2347   4578   ! 249    24579  579    !
   +----------------------+----------------------+----------------------+
   ! 789    1      2      ! 479    6      479    ! 5      4789   3      !
   ! 679    3      4      ! 1579   8      1579   ! 69     79     2      !
   ! 56789  5789   5789   ! 2      47     3      ! 1469   14789  789    !
   +----------------------+----------------------+----------------------+

Solved with very elementary rules, with only Subsets and reversible chains of length ≤ 4
hidden-pairs-in-a-row: r8{n1 n5}{c4 c6} ==> r8c6 ≠ 9, r8c6 ≠ 7, r8c4 ≠ 9, r8c4 ≠ 7
whip[1]: b8n9{r7c6 .} ==> r7c1 ≠ 9, r7c8 ≠ 9
hidden-pairs-in-a-column: c1{n2 n3}{r2 r3} ==> r3c1 ≠ 9, r3c1 ≠ 8, r3c1 ≠ 5, r2c1 ≠ 9, r2c1 ≠ 8, r2c1 ≠ 7, r2c1 ≠ 5
biv-chain[2]: c9n5{r6 r2} - r3n5{c8 c2} ==> r6c2 ≠ 5
finned-swordfish-in-rows: n7{r8 r1 r5}{c8 c1 c4} ==> r6c4 ≠ 7
finned-swordfish-in-rows: n7{r8 r1 r5}{c8 c1 c4} ==> r4c4 ≠ 7
jellyfish-in-columns: n7{c2 c5 c3 c9}{r9 r4 r2 r6} ==> r9c8 ≠ 7, r9c1 ≠ 7, r6c8 ≠ 7, r6c6 ≠ 7, r4c6 ≠ 7, r2c4 ≠ 7
z-chain[3]: r5n1{c4 c6} - c6n7{r5 r7} - c6n4{r7 .} ==> r5c4 ≠ 4
biv-chain[3]: r5n4{c8 c6} - c6n7{r5 r7} - r9c5{n7 n4} ==> r9c8 ≠ 4
biv-chain[3]: r7n8{c1 c8} - b9n4{r7c8 r9c7} - r9n6{c7 c1} ==> r9c1 ≠ 8
biv-chain[4]: r4c7{n9 n2} - r4c5{n2 n7} - r9c5{n7 n4} - c7n4{r9 r6} ==> r6c7 ≠ 9
biv-chain[4]: c1n5{r5 r9} - r9n6{c1 c7} - c7n4{r9 r6} - r5n4{c8 c6} ==> r5c6 ≠ 5
biv-chain[4]: c6n7{r5 r7} - r9c5{n7 n4} - c7n4{r9 r6} - r5n4{c8 c6} ==> r5c6 ≠ 1
singles ==> r5c4 = 1, r8c4 = 5, r8c6 = 1
finned-x-wing-in-rows: n5{r3 r5}{c8 c2} ==> r4c2 ≠ 5
biv-chain[3]: c4n7{r1 r7} - r7n9{c4 c6} - r3c6{n9 n8} ==> r1c4 ≠ 8
finned-x-wing-in-rows: n8{r1 r7}{c1 c9} ==> r9c9 ≠ 8
whip[1]: c9n8{r2 .} ==> r2c8 ≠ 8, r3c8 ≠ 8
naked-pairs-in-a-block: b9{r8c8 r9c9}{n7 n9} ==> r9c8 ≠ 9, r9c7 ≠ 9, r8c7 ≠ 9, r7c8 ≠ 7
singles ==> r8c7 = 6, r9c1 = 6, r5c1 = 5, r4c6 = 5
biv-chain[2]: b9n9{r9c9 r8c8} - c1n9{r8 r1} ==> r1c9 ≠ 9
stte

[eleven]

Code: Select all

 *---------------------------------------------------------------------------*
 | #789     4       1      |  79-8     5      2      |  3      6      #89    |
 |  23      5789    5789   |  34789    347    6      |  129    12589   59-8  |
 |  23      589     6      |  389      1      89     |  7      2589    4     |
 |-------------------------+-------------------------+-----------------------|
 |  4       56789   5789   |  5678     27     578    |  29     3       1     |
 |  5-7     2       3      |  1457     9      1457   |  8      457     6     |
 |  1       56789   5789   |  345678   2347   4578   |  249    24579   579   |
 |-------------------------+-------------------------+-----------------------|
 | #78      1       2      |  479      6      479    |  5      4-78    3     |
 | #679     3       4      |  15       8      15     | #69    #79      2     |
 |  569-78  5789    5789   |  2        47     3      |  1469   1489-7 #789   |
 *---------------------------------------------------------------------------*

6789 in 7 cells r178c1,r1c9,b9p459.
None can be triple -> 7,8,9 must be twice.
- 7 must be in r17c1 and b9p59 => -7r59c1,r79c8
- 8 must be in skyscraper r17c1,r19c9 => -8r7c8,r9c1,r2c9,r1c4
stte

[shye]

interesting solves so far, but not the logic i was going for ｡•́ < •̀｡ elevens solve looks very close to what i had in mind, halfway there

i'm unsure what the etiquette is on posting the solve path i designed, so if this isn't something people like around here i'll hold back my eagerness to share in the future ヽ(´▽`)/
for now i'll post it in hidden text

Hidden Text: Show

Code: Select all

.------------------------.--------------------.-------------------.
| #789      4       1    | 789     5     2    | 3     6      #89  |
|  23       5789    5789 | 34789   347   6    | 129   12589   589 |
|  23       589     6    | 389     1     89   | 7     2589    4   |
:------------------------+--------------------+-------------------:
|  4        56789   5789 | 5678    27    578  | 29    3       1   |
|  57       2       3    | 1457    9     1457 | 8     457     6   |
|  1        56789   5789 | 345678  2347  4578 | 249   24579   579 |
:------------------------+--------------------+-------------------:
| #78       1       2    | 479     6     479  | 5     478     3   |
| #679      3       4    | 15      8     15   | 69    79      2   |
| #5689-7  #5789   #5789 | 2       47    3    | 1469  14789  #789 |
'------------------------'--------------------'-------------------'

unsure what youd call it exactly, but i imagine it as a bivalue oddagon on 8 and 9 with grouped links thru b7
guardians 7r1c1 = 7r9c9 => -7r9c1

Code: Select all

.-----------------------.---------------------.-------------------.
| #789     4       1    | 789     5      2    | 3     6       89  |
|  23      5789    5789 | 34789   347    6    | 129   12589   589 |
|  23      589     6    | 389     1      89   | 7     2589    4   |
:-----------------------+---------------------+-------------------:
|  4       56789   5789 | 5678    27     578  | 29    3       1   |
|  5-7     2       3    | 1457    9      1457 | 8     457     6   |
|  1       56789   5789 | 345678  2347   4578 | 249   24579   579 |
:-----------------------+---------------------+-------------------:
| #78      1       2    | 479     6      479  | 5     478     3   |
| #679     3       4    | 15      8      15   | 69    79      2   |
|  5689   #5789   #5789 | 2       4-7    3    | 1469  14789  #789 |
'-----------------------'---------------------'-------------------'

7r1c1 - 7r78c1 = 7r9c23 - 7r9c9 = 7r1c1
all weak links become strong, -7r5c1 & -7r9c5 (& -7r9c8 which doesnt matter rly)
stte

edit + side note: i found a morph of this puzzle i rly like the look of (r132465789 c123546879) which i'm gonna end up publishing it as probably, but dont feel obliged to switch to this version if you dont want to tho

[denis_berthier]

i'm unsure what the etiquette is on posting the solve path i designed

There's no problem with publishing your own resolution path. Indeed, if it is different from what other people have found, it's a plus for everyone to know what you had in mind.

Code: Select all

.------------------------.--------------------.-------------------.
| #789      4       1    | 789     5     2    | 3     6      #89  |
|  23       5789    5789 | 34789   347   6    | 129   12589   589 |
|  23       589     6    | 389     1     89   | 7     2589    4   |
:------------------------+--------------------+-------------------:
|  4        56789   5789 | 5678    27    578  | 29    3       1   |
|  57       2       3    | 1457    9     1457 | 8     457     6   |
|  1        56789   5789 | 345678  2347  4578 | 249   24579   579 |
:------------------------+--------------------+-------------------:
| #78       1       2    | 479     6     479  | 5     478     3   |
| #679      3       4    | 15      8     15   | 69    79      2   |
| #5689-7  #5789   #5789 | 2       47    3    | 1469  14789  #789 |
'------------------------'--------------------'-------------------'

unsure what youd call it exactly, but i imagine it as a bivalue oddagon on 8 and 9 with grouped links thru b7
guardians 7r1c1 = 7r9c9 => -7r9c1

I tried my oddagon rules, but couldn't find a standard oddagon.
Instead I found a jellyfish for the same elimination (plus more):
jellyfish-in-columns: n7{c2 c5 c3 c9}{r9 r4 r2 r6} ==> r9c1 ≠ 7, r9c8 ≠ 7, r6c8 ≠ 7, r6c6 ≠ 7, r6c4 ≠ 7, r4c6 ≠ 7, r4c4 ≠ 7, r2c4 ≠ 7

[denis_berthier]

.
After the resolution path in W4, I tried to find solutions with fewer steps.

I found no 1-step or 2-step solution with chains of reasonable length (i.e. not much more than the W-rating = 4). I set the max-length to 6.

With my newly coded fewer-steps algo, I could easily find solutions with 4 steps in W6 (indeed, all my 5 tries had 4 steps). Here is one, starting from

Code: Select all

resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 789    4      1      ! 789    5      2      ! 3      6      89     !
   ! 235789 5789   5789   ! 34789  347    6      ! 129    12589  589    !
   ! 23589  589    6      ! 389    1      89     ! 7      2589   4      !
   +----------------------+----------------------+----------------------+
   ! 4      56789  5789   ! 5678   27     578    ! 29     3      1      !
   ! 57     2      3      ! 1457   9      1457   ! 8      457    6      !
   ! 1      56789  5789   ! 345678 2347   4578   ! 249    24579  579    !
   +----------------------+----------------------+----------------------+
   ! 789    1      2      ! 479    6      479    ! 5      4789   3      !
   ! 679    3      4      ! 1579   8      1579   ! 69     79     2      !
   ! 56789  5789   5789   ! 2      47     3      ! 1469   14789  789    !
   +----------------------+----------------------+----------------------+

=====> STEP #1:
jellyfish-in-columns: n7{c2 c5 c3 c9}{r9 r4 r2 r6} ==> r4c4 ≠ 7, r9c8 ≠ 7, r9c1 ≠ 7, r6c8 ≠ 7, r6c6 ≠ 7, r6c4 ≠ 7, r4c6 ≠ 7, r2c4 ≠ 7, r2c1 ≠ 7

=====> STEP #2:
whip[6]: r8n5{c4 c6} - c6n1{r8 r5} - c6n7{r5 r7} - r9c5{n7 n4} - c6n4{r7 r6} - c7n4{r6 .} ==> r8c4 ≠ 1
hidden-single-in-a-block ==> r8c6 = 1
hidden-single-in-a-block ==> r5c4 = 1
hidden-single-in-a-block ==> r8c4 = 5
whip[1]: b8n9{r7c6 .} ==> r7c1 ≠ 9, r7c8 ≠ 9

=====> STEP #3:
whip[6]: r7c1{n8 n7} - r8n7{c1 c8} - r9c9{n7 n9} - r8n9{c8 c1} - r1c1{n9 n8} - r1c9{n8 .} ==> r7c8 ≠ 8
hidden-single-in-a-row ==> r7c1 = 8

=====> STEP #4:
whip[4]: r8n7{c1 c8} - r7c8{n7 n4} - r5c8{n4 n5} - r5c1{n5 .} ==> r1c1 ≠ 7
stte

This leaves open the possibility of a solution with 3 steps in W6.

[shye]

awesome, thanks!

I tried my oddagon rules, but couldn't find a standard oddagon.
Instead I found a jellyfish for the same elimination (plus more):
jellyfish-in-columns: n7{c2 c5 c3 c9}{r9 r4 r2 r6} ==> r9c1 ≠ 7, r9c8 ≠ 7, r6c8 ≠ 7, r6c6 ≠ 7, r6c4 ≠ 7, r4c6 ≠ 7, r4c4 ≠ 7, r2c4 ≠ 7

yea its not standard by any means, but similar i think, so i'd definitely be welcome to know what its actually called
slightly more longhand way of showing it: if r1c1 + r9c9 were limited to [89], r1c1 would be equal to r9c9 via r1c9, and that value (whichever it is) would be eliminated from all positions in b7
thats where the 7s come in

i like the jellyfish a lot actually, it was a welcome surprise to see hidden there in the puzzle after i'd finished up with it, only problem is it doesnt show the need for a 7 one of those corner cells :p

[denis_berthier]

slightly more longhand way of showing it: if r1c1 + r9c9 were limited to [89], r1c1 would be equal to r9c9 via r1c9, and that value (whichever it is) would be eliminated from all positions in b7
thats where the 7s come in

Actually, I thought your first step was about the elimination of n7r9c1; that's why I proposed the jellyfish instead.
If you want to eliminate 89 from r1c1 and r9c9, this can be done by chains like:
z-chain[6]: r7n8{c1 c8} - c9n8{r9 r2} - c9n5{r2 r6} - c9n7{r6 r9} - r8n7{c8 c1} - r7c1{n7 .} ==> r1c1≠8
but they are unrelated to your solution (and there are simpler ways to solve the puzzle).

Back to your description. The double hypothesis r1c1≠7 and r9c9≠7, leads to r1c1=r9c9=x=8or9, which impies no possible cell for x in b7. Therefore r1c1=7 or r9c9=7. And r1c9≠7.
I don't think there is a name for this.

i like the jellyfish a lot actually, it was a welcome surprise to see hidden there in the puzzle after i'd finished up with it, only problem is it doesnt show the need for a 7 one of those corner cells

Right, but using OR conditions (n7r1c1 or n7r9c9) is rarely easy.

[marek stefanik]

I don't think there is a name for it. It can probably be written as a loop with the almost ERs:
7r1c1 = (7–89r1c4) = ERs(89r1b7/r9c19) – (89=7)r9c9 – 7r9c123 = 7r78c1 – Loop
But that uses an unnecessary truth 7r1.

With six truths it's most likely the shortest solution to the puzzle (and it doesn't even require basics, neither at the start nor after the step).

The corresponding Xsudo input (even though the pattern is rank2 I only got it to work with 10 links):: Show

6 Truths = {789B7 1N19 9N9}
10 Links = {89r1 789r9 789c1 89c9}

[marek stefanik]

z-chain[6]: r7n8{c1 c8} - c9n8{r9 r2} - c9n5{r2 r6} - c9n7{r6 r9} - r8n7{c8 c1} - r7c1{n7 .} ==> r1c1≠8
Right, but using OR conditions (n7r1c1 or n7r9c9) is rarely easy.

Can't you just use it the same way you used for example the OR condition (n8r7c1 or n8r7c8) in your z-chain?
For example, let A{n7c1r1 n7c9r9} be the derived truth, then there should be a whip[1] eliminating n7r9c9 and some sort of grouped chains of lenght 2 for the other eliminations?
I don't understand your notation well enough to create an example, but maybe you can.

Edit: I gave it a go anyway, hopefully it's valid:
(I don't know what you'd call it)[2] A{n7c1r1 n7c9r9} – b7n7{r9c23 .} ==> r5c1≠7

[denis_berthier]

z-chain[6]: r7n8{c1 c8} - c9n8{r9 r2} - c9n5{r2 r6} - c9n7{r6 r9} - r8n7{c8 c1} - r7c1{n7 .} ==> r1c1≠8
Right, but using OR conditions (n7r1c1 or n7r9c9) is rarely easy.

Can't you just use it the same way you used for example the OR condition (n8r7c1 or n8r7c8) in your z-chain?

r7n8{c1 c8} is not an OR condition. It means that, in the context of the target and of the previous parts of the chain (here none), CSP-Variable r7n8 has only two (non-z and non-t) candidates, a left-linking (llc) one (n8r7c1) that is linked to the target (or in other cases to the previous right-linking one) and a right-linking (rlc) one (n8r7c8) that can possibly be linked to a next left-linking one. In the context of the target, the rlc is the only one that can be True.
But n7r1c1 and n7r9c9 belong to no common CSP-Variable (or 2D-cell if you prefer).
There's no chance that any of my chains can deal with such an OR between two candidates; they have no OR-branching.

[marek stefanik]

What I meant was that one of them can be the llc and the other the rlc. There is no OR-branching in my chain, either, since one of them is linked to the target.

[denis_berthier]

What I meant was that one of them can be the llc and the other the rlc.

That's impossible, because they are not candidates for any common CSP-Variable.

[Chrono]

After SSTS

Code: Select all

.--------------------.--------------------.------------------.
| 789    4      1    | 789     5     2    | 3     6      89  |
| 23     5789   5789 | 34789   347   6    | 129   12589  589 |
| 23     589    6    | 389     1     89   | 7     2589   4   |
:--------------------+--------------------+------------------:
| 4      56789  5789 | 5678    27    578  | 29    3      1   |
| 57     2      3    | 1457    9     1457 | 8     457    6   |
| 1      56789  5789 | 345678  2347  4578 | 249   24579  579 |
:--------------------+--------------------+------------------:
| 78     1      2    | 479     6     479  | 5     478    3   |
| 679    3      4    | 15      8     15   | 69    79     2   |
| 56789  5789   5789 | 2       47    3    | 1469  14789  789 |
'--------------------'--------------------'------------------'

Code: Select all

if R56C8=7 then R8C8<>7
and if R6C9=7 then R8C8<>7 because
   R2C9=5, R3C2=5
   XYZ-Wing: R7C1(78), R9C2(789), R9C9(89) => R9C13<>8
   Skyscraper: R7C1(8)-R1C1(8)=R1C9(8)-R9C9(8), R9C2<>8
   R7C1=8
   Empty Rectangle: R1C9(9)-R9C9(9)=R9C123(9)-R8C1(9), R1C1<>9
   R1C1=7, R5C1=5, R5C8=4, R7C8=7

STTE