diagonals+centres

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Re: diagonals+centres

Postby Leren » Wed Oct 28, 2020 8:47 am

For some reason in the second puzzle I found two Multifish in the same cells for a total of 27 eliminations. From the look of them I'll bet Phil's variant SK loop will apply. Leren
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Re: diagonals+centres

Postby denis_berthier » Wed Oct 28, 2020 8:49 am

Leren wrote:For some reason in the second puzzle I found two Multifish in the same cells for a total of 27 eliminations. From the look of them I'll bet Phil's variant SK loop will apply. Leren

Great. Could you write the 27 eliminations? I'll see what comes after.
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Re: diagonals+centres

Postby Ajò Dimonios » Wed Oct 28, 2020 9:07 am

Using contradiction chains it is possible to solve the puzzle in 4 steps.

1)27 eliminations by crossing the conjugate tracks T (1r4c8) and T (1r7c8) see post by Mauriès Robert
2) T (1r7c8) .T (8r1c3) => contracdiction
3) T (1r7c8) .T (8r1c7) => contracdiction => - 1r7c8
4) T (7r7c8) => contracdiction => - 7r7c8; stte.
Is it possible to write these chains of contradiction in AIC?

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Re: diagonals+centres

Postby Leren » Wed Oct 28, 2020 9:42 am

Code: Select all
*--------------------------------------------------------------------------------*
| 1       359     245      | 349     236     2479     | 257     679     8        |
| 239     7       289      | 1368    5       138      | 129     4       269      |
| 245     589     6        | 1489    128     2479     | 3       179     257      |
|--------------------------+--------------------------+--------------------------|
| 2359    138     12589    | 7       1348    6        | 14589   138     3459     |
| 3567    4       1578     | 138     9       138      | 1578    2       3567     |
| 379     1368    1789     | 2       1348    5        | 14789   1368    3479     |
|--------------------------+--------------------------+--------------------------|
| 457     159     3        | 14589   128     249      | 6       789     247      |
| 469     2       149      | 1368    7       138      | 489     5       349      |
| 8       569     457      | 3459    236     249      | 247     379     1        |
*--------------------------------------------------------------------------------*

This is the PM after a preliminary Swordfish and the 27 eliminations. Putting this into Hodoku it's first 5 moves are Brute Force and 4 forcing chains.

Leren
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Re: diagonals+centres

Postby denis_berthier » Wed Oct 28, 2020 10:41 am

Leren wrote:
Code: Select all
*--------------------------------------------------------------------------------*
| 1       359     245      | 349     236     2479     | 257     679     8        |
| 239     7       289      | 1368    5       138      | 129     4       269      |
| 245     589     6        | 1489    128     2479     | 3       179     257      |
|--------------------------+--------------------------+--------------------------|
| 2359    138     12589    | 7       1348    6        | 14589   138     3459     |
| 3567    4       1578     | 138     9       138      | 1578    2       3567     |
| 379     1368    1789     | 2       1348    5        | 14789   1368    3479     |
|--------------------------+--------------------------+--------------------------|
| 457     159     3        | 14589   128     249      | 6       789     247      |
| 469     2       149      | 1368    7       138      | 489     5       349      |
| 8       569     457      | 3459    236     249      | 247     379     1        |
*--------------------------------------------------------------------------------*

This is the PM after a preliminary Swordfish and the 27 eliminations. Putting this into Hodoku it's first 5 moves are Brute Force and 4 forcing chains.

Leren


It's interesting to notice that, after the 27 eliminations, the puzzle is still in T&E(2). However, it has moved down the BpB sub-hierarchy of T&E(2): the original puzzle was in B2B, it is now in B1B=gB, i.e. it can be solved by g-braids. (I need to learn how to use Sukaku Explainer in order to compute the SER of your PM.)

I don't know what Brute Force means in Hodoku (probably some kind of T&E). It may be the case that Hodoku doesn't have any grouped variant of forcing chains and that's why it has to use "Brute Force" at this point. But anyway, the second step should be a mere forcing chain.

As is generally the case for puzzles solvable by g-braids, it is also solvable by (much simpler) g-whips.
The first step is a long g-whip[13], with a single right-linking g-candidate: n9r9c456, in the third csp-variable:
g-whip[13]: r1n6{c8 c5} - r9n6{c5 c2} - r9n9{c2 c456} - r7n9{c6 c2} - r8c1{n9 n4} - c3n4{r9 r1} - r1c4{n4 n3} - r1c2{n3 n5} - r3c1{n5 n2} - b2n2{r3c6 r1c6} - c6n7{r1 r3} - r3n9{c6 c4} - r3n4{c4 .} ==> r1c8 ≠ 9

For the full solution, see here:
Code: Select all
(solve-sukaku-grid
   *--------------------------------------------------------------------------------*
   ! 1       359     245      ! 349     236     2479     ! 257     679     8        !
   ! 239     7       289      ! 1368    5       138      ! 129     4       269      !
   ! 245     589     6        ! 1489    128     2479     ! 3       179     257      !
   !--------------------------+--------------------------+--------------------------!
   ! 2359    138     12589    ! 7       1348    6        ! 14589   138     3459     !
   ! 3567    4       1578     ! 138     9       138      ! 1578    2       3567     !
   ! 379     1368    1789     ! 2       1348    5        ! 14789   1368    3479     !
   !--------------------------+--------------------------+--------------------------!
   ! 457     159     3        ! 14589   128     249      ! 6       789     247      !
   ! 469     2       149      ! 1368    7       138      ! 489     5       349      !
   ! 8       569     457      ! 3459    236     249      ! 247     379     1        !
   *--------------------------------------------------------------------------------*
)

Hidden Text: Show
***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = gW+SFin
*** Using CLIPS 6.32-r774
***********************************************************************************************
206 candidates, 1087 csp-links and 1087 links. Density = 5.15%
148 g-candidates, 888 csp-glinks and 516 non-csp glinks
g-whip[13]: r1n6{c8 c5} - r9n6{c5 c2} - r9n9{c2 c456} - r7n9{c6 c2} - r8c1{n9 n4} - c3n4{r9 r1} - r1c4{n4 n3} - r1c2{n3 n5} - r3c1{n5 n2} - b2n2{r3c6 r1c6} - c6n7{r1 r3} - r3n9{c6 c4} - r3n4{c4 .} ==> r1c8 ≠ 9
whip[7]: c5n6{r9 r1} - r1c8{n6 n7} - c6n7{r1 r3} - c6n2{r3 r1} - r1c7{n2 n5} - r3c9{n5 n2} - r7n2{c9 .} ==> r9c5 ≠ 2
biv-chain[4]: r5n6{c9 c1} - b7n6{r8c1 r9c2} - r9c5{n6 n3} - b9n3{r9c8 r8c9} ==> r5c9 ≠ 3
g-whip[6]: b6n3{r4c9 r6c789} - c2n3{r6 r1} - c5n3{r1 r9} - c8n3{r9 r6} - r6n6{c8 c2} - r9n6{c2 .} ==> r4c1 ≠ 3
whip[9]: c1n6{r8 r5} - r6n6{c2 c8} - r1n6{c8 c5} - r9c5{n6 n3} - c8n3{r9 r4} - c8n8{r4 r7} - r8c7{n8 n9} - r9c8{n9 n7} - r1c8{n7 .} ==> r8c1 ≠ 4
g-whip[5]: c1n4{r3 r7} - b7n7{r7c1 r9c3} - b7n5{r9c3 r789c2} - b1n5{r1c2 r1c3} - c3n4{r1 .} ==> r3c1 ≠ 2
whip[6]: r8c1{n9 n6} - c4n6{r8 r2} - r2n3{c4 c6} - r1c5{n3 n2} - b1n2{r1c3 r2c3} - r2n8{c3 .} ==> r2c1 ≠ 9
whip[7]: b1n8{r3c2 r2c3} - b1n9{r2c3 r1c2} - b1n3{r1c2 r2c1} - r2c6{n3 n1} - r2c4{n1 n6} - b8n6{r8c4 r9c5} - r9c2{n6 .} ==> r3c2 ≠ 5
g-whip[5]: b3n5{r3c9 r1c7} - b3n2{r1c7 r2c789} - b1n2{r2c3 r1c3} - b1n4{r1c3 r3c1} - r3n5{c1 .} ==> r3c9 ≠ 7
whip[5]: r3n7{c6 c8} - b3n1{r3c8 r2c7} - b3n9{r2c7 r2c9} - b3n2{r2c9 r1c7} - r9n2{c7 .} ==> r3c6 ≠ 2
whip[8]: r8c1{n9 n6} - r5n6{c1 c9} - r6n6{c8 c2} - r9c2{n6 n5} - r1c2{n5 n3} - r2c1{n3 n2} - r2c9{n2 n9} - b1n9{r2c3 .} ==> r7c2 ≠ 9
whip[8]: c1n7{r6 r7} - c9n7{r7 r5} - r5n6{c9 c1} - r8c1{n6 n9} - r6c1{n9 n3} - r2c1{n3 n2} - r4n2{c1 c3} - b4n9{r4c3 .} ==> r6c3 ≠ 7
z-chain[4]: c3n7{r5 r9} - c7n7{r9 r1} - r1c8{n7 n6} - b6n6{r6c8 .} ==> r5c9 ≠ 7
t-whip[5]: c1n9{r6 r8} - c1n6{r8 r5} - r5c9{n6 n5} - r3n5{c9 c1} - r4n5{c1 .} ==> r4c3 ≠ 9
whip[5]: r4n9{c9 c1} - r8c1{n9 n6} - c4n6{r8 r2} - r2c9{n6 n2} - c1n2{r2 .} ==> r6c9 ≠ 9
t-whip[6]: r2n6{c4 c9} - r5c9{n6 n5} - r3n5{c9 c1} - r4n5{c1 c3} - r4n2{c3 c1} - r2c1{n2 .} ==> r2c4 ≠ 3
whip[7]: r6n6{c2 c8} - r5c9{n6 n5} - r3n5{c9 c1} - r4n5{c1 c3} - c3n8{r4 r2} - c3n2{r2 r1} - b1n4{r1c3 .} ==> r6c2 ≠ 8
whip[8]: c1n2{r4 r2} - b1n3{r2c1 r1c2} - b1n5{r1c2 r1c3} - b3n5{r1c7 r3c9} - r5c9{n5 n6} - r2n6{c9 c4} - r1c5{n6 n2} - b3n2{r1c7 .} ==> r4c1 ≠ 5
whip[7]: r2n3{c1 c6} - r5n3{c6 c4} - b8n3{r8c4 r9c5} - r9n6{c5 c2} - r8c1{n6 n9} - r4c1{n9 n2} - r2c1{n2 .} ==> r6c1 ≠ 3
t-whip[5]: r6n6{c2 c8} - r1n6{c8 c5} - r9c5{n6 n3} - c8n3{r9 r4} - r6n3{c9 .} ==> r6c2 ≠ 1
whip[7]: r2n6{c4 c9} - r5c9{n6 n5} - r3c9{n5 n2} - r3c5{n2 n8} - r2c6{n8 n3} - c1n3{r2 r5} - r5n6{c1 .} ==> r2c4 ≠ 1
whip[7]: r2n6{c4 c9} - r5c9{n6 n5} - r3c9{n5 n2} - r3c5{n2 n1} - r2c6{n1 n3} - c1n3{r2 r5} - r5n6{c1 .} ==> r2c4 ≠ 8
singles ==> r2c4 = 6, r9c5 = 6, r8c1 = 6, r6c2 = 6, r5c9 = 6, r1c8 = 6
whip[1]: c1n9{r6 .} ==> r6c3 ≠ 9
biv-chain[3]: r1n7{c6 c7} - b3n5{r1c7 r3c9} - r3n2{c9 c5} ==> r1c6 ≠ 2
whip[1]: c6n2{r9 .} ==> r7c5 ≠ 2
naked-triplets-in-a-block: b8{r7c5 r8c4 r8c6}{n1 n8 n3} ==> r9c4 ≠ 3, r7c4 ≠ 8, r7c4 ≠ 1
hidden-single-in-a-row ==> r9c8 = 3
naked-pairs-in-a-block: b6{r4c8 r6c8}{n1 n8} ==> r6c7 ≠ 8, r6c7 ≠ 1, r5c7 ≠ 8, r5c7 ≠ 1, r4c7 ≠ 8, r4c7 ≠ 1
singles ==> r2c7 = 1, r8c7 = 8, r7c5 = 8, r7c2 = 1
whip[1]: b5n8{r5c6 .} ==> r5c3 ≠ 8
whip[1]: c7n9{r6 .} ==> r4c9 ≠ 9
naked-pairs-in-a-row: r6{c3 c8}{n1 n8} ==> r6c5 ≠ 1
swordfish-in-columns: n3{c2 c5 c9}{r4 r1 r6} ==> r1c4 ≠ 3
naked-triplets-in-a-block: b2{r1c4 r1c6 r3c6}{n4 n9 n7} ==> r3c4 ≠ 9, r3c4 ≠ 4
biv-chain-rc[3]: r8c4{n3 n1} - r3c4{n1 n8} - r2c6{n8 n3} ==> r8c6 ≠ 3
singles ==> r8c6 = 1, r8c4 = 3
biv-chain[3]: r8c9{n4 n9} - r2c9{n9 n2} - b9n2{r7c9 r9c7} ==> r9c7 ≠ 4
whip[1]: c7n4{r6 .} ==> r4c9 ≠ 4, r6c9 ≠ 4
hidden-pairs-in-a-block: b6{r4c7 r6c7}{n4 n9} ==> r6c7 ≠ 7, r4c7 ≠ 5
finned-x-wing-in-rows: n5{r3 r4}{c9 c1} ==> r5c1 ≠ 5
whip[1]: b4n5{r5c3 .} ==> r1c3 ≠ 5, r9c3 ≠ 5
hidden-pairs-in-a-column: c1{n4 n5}{r3 r7} ==> r7c1 ≠ 7
singles ==> r9c3 = 7, r9c7 = 2, r7c6 = 2
whip[1]: r9n4{c6 .} ==> r7c4 ≠ 4
biv-chain-rc[3]: r4c9{n3 n5} - r5c7{n5 n7} - r5c1{n7 n3} ==> r4c2 ≠ 3
stte
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Re: diagonals+centres

Postby SpAce » Wed Oct 28, 2020 12:44 pm

denis_berthier wrote:I don't know what Brute Force means in Hodoku (probably some kind of T&E).

I'm not sure, but I think it simply picks a useful placement from the DLX-precomputed solution if it can't progress logically.

It may be the case that Hodoku doesn't have any grouped variant of forcing chains and that's why it has to use "Brute Force" at this point. But anyway, the second step should be a mere forcing chain.

Hodoku would call it a forcing net contradiction (if it could find it), which is what your whip is. (Don't get started on that. You've said yourself that whips and braids are AND-nets, and of course they are. Any use of memories makes a net.)

That said, I don't know why Hodoku fails to find it as a contradiction net. (It's obvious that it can't find it as a verity, because it can't handle multi-krakens.) It can certainly use groups and subsets in its chains and nets (though it does have problems with groups in some contexts). Maybe the sheer number of z- and t-candidates (5+9) in this pattern overwhelms it, even though they don't add anything to the complexity according to you.

In any case, I count this as a failure for Hodoku, and a point for SudoRules.

The first step is a long g-whip[13], with a single right-linking g-candidate: n9r9c456, in the third csp-variable:
g-whip[13]: r1n6{c8 c5} - r9n6{c5 c2} - r9n9{c2 c456} - r7n9{c6 c2} - r8c1{n9 n4} - c3n4{r9 r1} - r1c4{n4 n3} - r1c2{n3 n5} - r3c1{n5 n2} - b2n2{r3c6 r1c6} - c6n7{r1 r3} - r3n9{c6 c4} - r3n4{c4 .} ==> r1c8 ≠ 9

As a matrix (without any group-breaking):

13x13 TM: Show
Code: Select all
 6r1c8 6r1c5
 . . . 6r9c5 6r9c2
 9r9c8 . . . 9r9c2 9r9c46
 9r7c8 . . . . . . 9r7c46  9r7c2
 . . . . . . 6r8c1 . . . . 9r8c1 4r8c1
 . . . . . . . . . . . . . . . . 4r89c3  4r1c3
 9r1c4 . . . . . . . . . . . . . . . . . 4r1c4 3r1c4
 9r2c1 . . . . . . . . . . . . . . . . . . . . 3r1c2 5r1c2
 . . . . . . . . . . . . . . . . 4r3c1 . . . . . . . 5r3c1 2r3c1
 . . . 2r1c5 . . . . . . . . . . . . . . . . . . . . . . . 2r3c56  2r1c6
 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7r1c6 7r3c6
 9r3c8 . . . . . . . . . . 9r3c2 . . . . . . . . . . . . . . . . . . . . 9r3c6 9r3c4
 . . . . . . . . . . . . . . . . 4r3c1 . . . . . . . . . . . . . . . . . 4r3c6 4r3c4
====================================================================================
-9r1c8

2-SIS: 3
3-SIS: 6
4-SIS: 4
z-candidates: 5
t-candidates: 9

Out of its thirteen SISs only three are binary.

--
Edit. I forgot to count the t-candidates from the left-linking group nodes. That's three more (6 --> 9).
Last edited by SpAce on Wed Oct 28, 2020 3:56 pm, edited 1 time in total.
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Re: diagonals+centres

Postby SpAce » Wed Oct 28, 2020 2:36 pm

denis_berthier wrote:
Leren wrote:This has 7 fewer candidates than the previous one. Pasting this into Hodoku, it's first move is a (very tedious) forcing chain:

Forcing Chain Contradiction in c3 => r3c9=2r3c9<>2 r3c9=4 r2c79<>4 r2c13=4 r1c3<>4r3c9<>2 r8c9=2 r8c9<>1 r8c4=1 r2c4<>1 r2c3=1 r2c3<>4r3c9<>2 r3c9=4 r3c5<>4 r9c5=4 r9c3<>4

Is this supposed to be a single chain (of length 9)?

No. Its length is 7 (one more than necessary), and it's actually not very tedious. It just looks that way, because Hodoku's notation is so horrible. (I never even attempt to read it; I just look at the pattern.) Furthermore, it forces a placement (+2r3c9) for no reason, which lengthens it by one unnecessarily, and uses a dumb routing. I don't know why Hodoku sometimes offers such inferior choices by default. Here's a better one with the same effect (found by Hodoku as a Forcing Chain Verity):

6x6 TM: Show
Code: Select all
 2r3c9 4r3c9
       4r3c56 4r1c6
       4r3c5        4r9c5
              4r1c3 4r9c3 4r2c3
                          1r2c3 1r2c4
 1r8c9                          1r8c4
=====================================
-2r8c9

That would be a very simple braid[6]. It's easy to write as an AIC:

(2=4)r3c9 - r3c56 = r1c6;r9c5 - r19c3 = (4-1)r2c3 = r2c4 - r8c4 = (1)r8c9 => -2 r8c9

Even easier as a kraken column:

Code: Select all
(4)r1c3 - r1c6 = r3c56 - (4=2)r3c9
||
(4-1)r2c3 = r2c4 - r8c4 = (1)r8c9
||
(4)r9c3 - r9c5 = r3c5 - (4=2)r3c9

=> -2 r8c9

Not tedious at all.

Added:

If so, Hodoku is pretty bad at this point, as it misses a much shorter chain (length 5):

whip[5]: b9n1{r7c8 r8c9} - c4n1{r8 r2} - r2n3{c4 c7} - b3n7{r2c7 r2c9} - r5c9{n7 .} ==> r7c8 ≠ 7

Well, Hodoku's move gets an immediate placement. That's what I would have aimed for. It finds the equivalent move to yours if asked (as a Forcing Chain Verity), but its slightly different routing makes it a z-chain[6].

5x5 TM; SudoRules whip(5): Show
Code: Select all
 1r7c8 1r8c9
 . . . 1r8c4 1r2c4
 . . . . . . 3r2c4 3r2c7
 7r3c8 . . . . . . 7r2c7 7r2c9
 . . . 1r5c9 . . . . . . 7r5c9
==============================
-7r7c8]

As an AIC: (1)r7c8 = r8c9 - [(1)r8c4 = (1-3)r2c4 = (3-7)r2c7 = r2c9 - (7=1)r5c9] = (7)r3c8 => -7 r7c8

6x6 TM; Hodoku z-chain(6): Show
Code: Select all
 1r7c8 1r7c5
 . . . 1r1c5 3r1c5
 . . . . . . 3r2c4 3r2c7
 7r3c8 . . . . . . 7r2c7 7r2c9
 . . . . . . . . . . . . 7r5c9 1r5c9
 1r7c8 . . . . . . . . . . . . 1r8c9
====================================
-7r7c8

As an AIC: (7)r3c8 = [(1)r7c8 = r7c5 - (1=3)r1c5 - r2c4 = (3-7)r2c7 = r2c9 - (7=1)r5c9 - r8c9 = (1)r7c8] => -7 r7c8

Notice that, after the first whip[5], none of the patterns depends on the target(s) and almost all of them are very simple bivalue-chains (basics AICs).

The same with Hodoku (after its own initial move), if only simple chains are allowed:

Code: Select all
biv (4) => -7 r79c8        (AIC)
biv (4) => -4 r2c1         (DNL)
biv (5) => -8 r13c8,r9c7   (AIC)
biv (3) => -8 r9c6         (W-Wing)
biv (6) => -9 r13c2,r8c3   (XY-Chain)
biv (6) => -6 r359c6       (XY-Chain)
biv (3) => -9 r1c6,r9c4    (XY-Wing)
biv (3) => -6 r6c2         (X-Chain)
biv (7) => -6 r3c2,r46c1   (XY-Chain); stte

Those are slightly longer than yours, but there's only 9 of them and 14 of yours. As a whole that's simpler, considering that a higher number of moves adds more overhead than longer chains do, all other things remaining equal.
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Re: diagonals+centres

Postby SpAce » Thu Oct 29, 2020 4:16 am

Leren wrote:For some reason in the second puzzle I found two Multifish in the same cells for a total of 27 eliminations. From the look of them I'll bet Phil's variant SK loop will apply. Leren

It's actually the plain old one. It also results in a perfect Jellyfish, which is kind of cool. (How rare are those, btw?)

1.......8.7..5..4...6...3.....7.6....4..9..2....2.5.....3...6...2..7..5.8.......1

Step 1. Swordfish/Loop (6) => 4 elims

Step 2. SK-Loop:

    (29/38)r2c13 - (38/59)r13c2 - (59/16)r79c2 - (16/49)r8c13 - (49/38)r8c79 - (38/79)r79c8 - (79/16)r13c8 - (16/29)r2c79 - SKLoop => 13 elims

    As a mutant Multifish:
Code: Select all
  \b1:38           \b7:16   \28n            \28n      \b3:16            \b9:38
          *1368                                               *1368
.-------------------------.-------------------------.--------------------------.
|  1^      359      2459  |  3469     236    23479  |  2579    679       8^    |
|  239     7        289   | \1368-9   5     \138-29 |  129     4         269   | *1368
|  2459    589      6^    |  1489     128    124789 |  3^      179       2579  |
:-------------------------+-------------------------+--------------------------:
|  2359   \138-59   12589 |  7        1348   6^     |  14589  \138-9     3459  | \n28
|  3567    4        1578  |  138      9      138    |  1578    2         3567  |
|  3679   \1368-9   1789  |  2        1348   5      |  14789  \1368-79   34679 | \n28
:-------------------------+-------------------------+--------------------------:
|  4579    159      3^    |  14589    128    12489  |  6^      789       2479  |
|  469     2        149   | \1368-49  7     \138-49 |  489     5         349   | *1368
|  8^      569      4579  |  34569    236    2349   |  2479    379       1^    |
'-------------------------'-------------------------'--------------------------'

    MF (1368 RC): 16x16 {1368R28 1368C28 \ 38b19 16b37 28n46 46n28} => 13 elims; NT (138) => 6 elims
Step 3. Perfect Jellyfish with perfectly symmetrical eliminations:

Code: Select all
.----------------------.-------------------.----------------------.
|  1      359    245-9 | 349    236   2479 |  257-9  679    8     |
| *239    7     *289   | 1368   5     138  | *129    4     *269   |
|  245-9  589    6     | 1489   128   2479 |  3      179    257-9 |
:----------------------+-------------------+----------------------:
| *2359   138   *12589 | 7      1348  6    | *14589  138   *3459  |
|  3567   4      1578  | 138    9     138  |  1578   2      3567  |
| *379    1368  *1789  | 2      1348  5    | *14789  1368  *3479  |
:----------------------+-------------------+----------------------:
|  457-9  159    3     | 14589  128   249  |  6      789    247-9 |
| *469    2     *149   | 1368   7     138  | *489    5     *349   |
|  8      569    457-9 | 3459   236   249  |  247-9  379    1     |
'----------------------'-------------------'----------------------'

(9)r2468\c1379 => 8 elims

Together the total of steps 2-3 is 27 eliminations (13+6+8), as with your pair of multifishes. (Would you mind showing them, btw?)

Variant Step 2. SK-Loop as a non-rectangular MSLS:

Code: Select all
  \b1:389          \b7:169                          \b3:169           \b9:389
          \5[9]                                             \7[9]
.-------------------------.-----------------------.--------------------------.
|  1^     *359      245-9 | 349      236   23479  |  257-9  *679       8^    |
| *239     7       *289   | 1368-9   5     138-29 | *129     4        *269   | \2[9]
|  245-9  *589      6^    | 1489     128   124789 |  3^     *179       257-9 |
:-------------------------+-----------------------+--------------------------:
|  2359    138-59   12589 | 7        1348  6^     |  14589   138-9     3459  |
|  3567    4        1578  | 138      9     138    |  1578    2         3567  |
|  379     1368-9   1789  | 2        1348  5      |  14789   1368-79   3479  |
:-------------------------+-----------------------+--------------------------:
|  457-9  *159      3^    | 14589    128   12489  |  6^     *789       247-9 |
| *469     2       *149   | 1368-49  7     138-49 | *489     5        *349   | \4[9]
|  8^     *569      457-9 | 3459     236   2349   |  247-9  *379       1^    |
'-------------------------'-----------------------'--------------------------'

    MSLS: 16x16 {1379N28 28N1379 \ 1b37 2r2 3b19 4r8 5c2 6b37 7c8 8b19 [9r28 9c28|9b1379]} => 21 elims; NT (138) => 6 elims
That gives the same 27 eliminations without needing the Jellyfish.
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Re: diagonals+centres

Postby StrmCkr » Thu Oct 29, 2020 6:03 am

Code: Select all
+---------------------------+------------------------------+--------------------------+
| 7        (159)     458-19 | 29-13      (13-24)   245-9   | 248-3   (39-8)    6      |
| (469)    2         (149)  | (13-679)   8         (679-4) | (37-4)  5         (479)  |
| 458-69   (569)     3      | 2679       (467-2)   24579-6 | 1       (789)     248-79 |
+---------------------------+------------------------------+--------------------------+
| 2689     (1679)    2789-1 | 5          (267)     3       | 4678    (1679-8)  4789-1 |
| 356-8    4         157-8  | (678)      9         (78-6)  | 3567-8  2         157-8  |
| 25689-3  (3679-5)  25789  | 4          (267)     1       | 5678-3  (3679-8)  5789   |
+---------------------------+------------------------------+--------------------------+
| 245-3    (37-5)    6      | 278-13     (13-247)  248-7   | 9       (178)     258-17 |
| (39-2)   8         (279)  | (13-2679)  5         (679-2) | (267)   4         (127)  |
| 1        (579)     245-79 | 26789      (467-2)   24789-6 | 258-67  (678)     3      |
+---------------------------+------------------------------+--------------------------+

    aals [21,246] 115 Candidates,
    32 Truths = {28N1 134679N2 28N3 258N4 134679N5 258N6 28N7 134679N8 28N9}
    52 Links = {9r1 134679r2 9r3 1r4 8r5 3r6 7r7 123679r8 7r9 1c4 2c5 3c4 4c5 5c2 6c2568 7c25689 8c8 9c2368 1b19 3b37 6b159 7b3579 9b137}
    54 Eliminations --> r5c1379<>8, r1379c5<>2, r8c4<>2679, r7c569<>7, r359c6<>6, r146c8<>8,
    r2c4<>679, r1c34<>1, r1c47<>3, r1c36<>9, r2c67<>4, r3c19<>9, r4c39<>1,
    r6c17<>3, r7c49<>1, r7c14<>3, r8c16<>2, r9c37<>7, r67c2<>5, r17c5<>4,
    r3c1<>6, r3c9<>7, r9c7<>6, r9c3<>9,

is the opening move i did before basics... {which includes the basics and a few extra eliminations}

reduces the grid to this
Code: Select all
+----------------------+---------------------+----------------------+
| 7      (159)   458   | 29     (13)   245   | 248    (39)    6     |
| (469)  2       (149) | (13)   8      (679) | (37)   5       (479) |
| 458    (569)   3     | 2679   (467)  24579 | 1      (789)   248   |
+----------------------+---------------------+----------------------+
| 2689   (1679)  2789  | 5      (267)  3     | 4678   (1679)  4789  |
| 356    4       157   | (678)  9      (78)  | 3567   2       157   |
| 25689  (3679)  25789 | 4      (267)  1     | 5678   (3679)  5789  |
+----------------------+---------------------+----------------------+
| 245    (37)    6     | 278    (13)   248   | 9      (178)   258   |
| (39)   8       (279) | (13)   5      (679) | (267)  4       (127) |
| 1      (579)   245   | 26789  (467)  24789 | 258    (678)   3     |
+----------------------+---------------------+----------------------+


aals 2rc rule
Code: Select all
+--------------------+------------------------+--------------------+
| 7      159   458   | (29)    13     245     | 248   (39)   6     |
| 469    2     149   | 13      8      (679)   | (37)  5      (479) |
| (458)  569   3     | (2679)  (467)  (24579) | 1     (789)  28-4  |
+--------------------+------------------------+--------------------+
| 2689   1679  2789  | 5       267    3       | 4678  1679   4789  |
| 356    4     157   | 678     9      78      | 3567  2      157   |
| 25689  3679  25789 | 4       267    1       | 5678  3679   5789  |
+--------------------+------------------------+--------------------+
| 245    37    6     | 278     13     248     | 9     178    258   |
| 39     8     279   | 13      5      679     | 267   4      127   |
| 1      579   245   | 26789   467    24789   | 258   678    3     |
+--------------------+------------------------+--------------------+


still needs ~4 more chains {maybe less but its getting easier at this point} as the chains are mostly just 2 digit short loops.
Some do, some teach, the rest look it up.
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Re: diagonals+centres

Postby denis_berthier » Thu Oct 29, 2020 7:49 am

Ajò Dimonios wrote:Using contradiction chains it is possible to solve the puzzle in 4 steps.
1)27 eliminations by crossing the conjugate tracks T (1r4c8) and T (1r7c8) see post by Mauriès Robert
2) T (1r7c8) .T (8r1c3) => contracdiction
3) T (1r7c8) .T (8r1c7) => contracdiction => - 1r7c8
4) T (7r7c8) => contracdiction => - 7r7c8; stte.


I think you can make it still shorter:
Code: Select all
ttte

ttte = tracks to the end
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Re: diagonals+centres

Postby Mauriès Robert » Thu Oct 29, 2020 9:28 am

Hi Denis,
denis_berthier wrote:
Ajò Dimonios wrote:Using contradiction chains it is possible to solve the puzzle in 4 steps.
1)27 eliminations by crossing the conjugate tracks T (1r4c8) and T (1r7c8) see post by Mauriès Robert
2) T (1r7c8) .T (8r1c3) => contracdiction
3) T (1r7c8) .T (8r1c7) => contracdiction => - 1r7c8
4) T (7r7c8) => contracdiction => - 7r7c8; stte.


I think you can make it still shorter:
Code: Select all
ttte

ttte = tracks to the end

Questionable humour!
I know that on this site the technique (TDP) that I defend, which Paolo is a user, is not well seen by many participants. I hope that you are not one of them.
Certainly, Paolo could have detailed it a little, but I understand his reluctance to waste time, because I see that on the remark we made on this thread of 27 eliminations by crossing two tracks, there was no intervention, neither from you nor from anyone else. However, I have given the details.
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Re: diagonals+centres

Postby denis_berthier » Thu Oct 29, 2020 10:02 am

Mauriès Robert wrote:Hi Denis,
denis_berthier wrote:
Ajò Dimonios wrote:Using contradiction chains it is possible to solve the puzzle in 4 steps.
1)27 eliminations by crossing the conjugate tracks T (1r4c8) and T (1r7c8) see post by Mauriès Robert
2) T (1r7c8) .T (8r1c3) => contracdiction
3) T (1r7c8) .T (8r1c7) => contracdiction => - 1r7c8
4) T (7r7c8) => contracdiction => - 7r7c8; stte.


I think you can make it still shorter:
Code: Select all
ttte

ttte = tracks to the end

Questionable humour!
I know that on this site the technique (TDP) that I defend, which Paolo is a user, is not well seen by many participants. I hope that you are not one of them.
Certainly, Paolo could have detailed it a little, but I understand his reluctance to waste time, because I see that on the remark we made on this thread of 27 eliminations by crossing two tracks, there was no intervention, neither from you nor from anyone else. However, I have given the details.
Robert


Glad you saw the humour in it. But I was serious also. There's an obvious abuse of notation and this solution from Paolo illustrates it very clearly.
I'm still in an undecided state about tracks.
About details, let's rather speak of them in the other thread, about a much simpler track.
BTW, do you have news of Defise?
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Re: diagonals+centres

Postby Ajò Dimonios » Thu Oct 29, 2020 12:08 pm

Hi Denis

After basic
Code: Select all
+--------------------+-------------------+-------------------+
| 7      159   14589 | 1239   13  2459   | 2348  389   6     |
| 469    2     149   | 13679  8   4679   | 347   5     479   |
| 45689  569   3     | 2679   467 245679 | 1     789   24789 |
+--------------------+-------------------+-------------------+
| 2689   1679  12789 | 5      267 3      | 4678  16789 14789 |
| 356    4     157   | 678    9   678    | 3567  2     157   |
| 235689 35679 25789 | 4      267 1      | 35678 36789 5789  |
+--------------------+-------------------+-------------------+
| 2345   357   6     | 12378  13  2478   | 9     178   12578 |
| 239    8     279   | 123679 5   2679   | 267   4     127   |
| 1      579   24579 | 26789  467 246789 | 25678 678   3     |
+--------------------+-------------------+-------------------+


In fact I think you are right.
A solution can be achieved in just three steps. The first 27 eliminations are superfluous as they are contained in track T (1r7c8).
Track T (1r7c8) leads to this result using only TB:
Code: Select all
+---------------+-----------------+----------------+
| 7    59  4589 | 29    1*  2459  | 248  3*   6    |
| 49   2   1*   | 3*    8   6*    | 47   5    479  |
| 4589 6*  3    | 279   47  24579 | 1    89   2489 |
+---------------+-----------------+----------------+
| 2689 1*  2789 | 5     267 3     | 478  6789 4789 |
| 56   4   57   | 678   9   78    | 3*   2    1*   |
| 2689 3*  2789 | 4     267 1     | 578  6789 5789 |
+---------------+-----------------+----------------+
| 245  57  6    | 278   3*  2478  | 9    1*   2578 |
| 3*   8   29   | 1*    5   279   | 6*   4    27   |
| 1    579 2459 | 26789 467 24789 | 2578 78   3    |
+---------------+-----------------+----------------+




It can be seen that in r1 there are only 2 candidates 8 in r1c3 and 8 in r1c7.
The extension of T (1r7c8) with T (8r1c3) and with T (8r1c7) produces the following two results:
Code: Select all
+--------------+----------------+---------------+
| 7    59  8   | 29    1*  259  | 4*   3   6    |
| 4*   2   1*  | 3*    8   6 *  | 7    5   79   |
| 59   6*  3   | 79    4* 579   | 1    8*  2*   |
+--------------+----------------+---------------+
| 2689 1*  279 | 5     267 3    | 78   679 4789 |
| 56   4   57  | 678   9   78   | 3*   2   1*   |
| 2689 3*  279 | 4     267 1    | 578  679 5789 |
+--------------+----------------+---------------+
| 25   57  6   | 278   3*  4*   | 9    1   578  |
| 3*   8   29  | 1*    5   279  | 6*   4   7    |
| 1    579 4*  | 26789 67  2789 | 2578 7   3    |
+--------------+----------------+---------------+


Code: Select all
+----------+--------+--------+
| 7  5 4   | 9 1  2 | 8 3 6  |
| 9  2 1   | 3 8  6 | 7 5 4  |
| 8  6 3   | 7 4  5 | 1 9 2  |
+----------+--------+--------+
| 2  1 789 | 5 2  3 | 4 6 89 |
| 5  4 .   | 8 9  7 | 3 2 1  |
| 26 3 789 | 4 26 1 | 5 7 89 |
+----------+--------+--------+
| 4  7 6   | 2 3  8 | 9 1 5  |
| 3  8 2   | 1 5  9 | 6 4 7  |
| 1  9 5   | 6 7  4 | 2 8 3  |
+----------+--------+--------+


Clearly the two sudokus are invalid 2 candidates 7 in b9 in the first extension and empty r5c3 in the second. At this point it is obvious that r7c8 ≠ 1.
The T (7r7c8) produces the following result after applying the TB:
Code: Select all
+------------+----------------+----------+
| 7  1*  589 | 29   3*  259   | 4*  89 6 |
| 6* 2   49  | 1*   8   49    | 3*  5  7*|
| 48 59  3   | 679  467 4579  | 1   89 2*|
+------------+----------------+----------+
| 28 679 289 | 5    267 3     | 678 1* 4*|
| 3* 4   1*  | 678  9   78    | 67  2  5*|
| 28 567 258 | 4    267 1     | 678 3* 9*|
+------------+----------------+----------+
| 5* 3*  6   | 2    1*  24    | 9   7* 8*|
| 9* 8   7*  | 3*   5   6*    | 2*  4  1*|
| 1  .   24  | 2789 47  24789 | 5*  6* 3 |
+------------+----------------+----------+




Also in this case the result is a contradiction r9c2 is empty, so r7c8≠7. At this point r7c8 = 8 which leads directly to the solution.
Surely to be clearer it is useful to use "*" instead of "." as a symbol for the boolean operator AND.

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Re: diagonals+centres

Postby mith » Thu Oct 29, 2020 11:38 pm

SpAce wrote:It also results in a perfect Jellyfish, which is kind of cool. (How rare are those, btw?)


I'm assuming by perfect jellyfish you mean the digit can appear in all 16 cells? If so... quite rare, in my experience. The first one in Tatooine Reflections is one (though the eliminations aren't symmetric), and The Final Countdown has two (with symmetric eliminations) on the same set of cells. (The harder consecutive puzzle I posted in variants has a pair on the same digit, with different eliminations... and four more almost perfect. :P)
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Re: diagonals+centres

Postby Leren » Fri Oct 30, 2020 12:54 am

For the avoidance of any doubt here is the Jellyfish in 9's r2468 / c1379 => - 9 r19c37, r37c19

Code: Select all
*---------------------------------------------------------*
| 1     359   245-9 | 349   236  2479 | 257-9 679   8     |
|*239   7    *289   | 1368  5    138  |*129   4    *269   |
| 245-9 589   6     | 1489  128  2479 | 3     179   257-9 |
|-------------------+-----------------+-------------------|
|*2359  138  *12589 | 7     1348 6    |*14589 138  *3459  |
| 3567  4     1578  | 138   9    138  | 1578  2     3567  |
|*379   1368 *1789  | 2     1348 5    |*14789 1368 *3479  |
|-------------------+-----------------+-------------------|
| 457-9 159   3     | 14589 128  249  | 6     789   247-9 |
|*469   2    *149   | 1368  7    138  |*489   5    *349   |
| 8     569   457-9 | 3459  236  249  | 247-9 379   1     |
*---------------------------------------------------------*

Leren

PS While on the subject of Jellyfish here is a perfect one from Hodoku that has 17 eliminations. Is that a record ?

.............1.....123.456...........27...38..36.5.42...........682.715..74...83.

Code: Select all
*---------------------------------------------------------------------*
| 345678-9 *4589 *359  | 568-9   2678-9 2568-9  |*279  *1479 123478-9 |
| 345678-9 *4589 *359  | 568-9   1      2568-9  |*279  *479  23478-9  |
| 789       1     2    | 3       789    4       | 5     6    789      |
|----------------------+------------------------+---------------------|
| 1458-9   *4589 *159  | 14678-9 23     23      |*679  *179  1567-9   |
| 1459      2     7    | 1469    469    169     | 3     8    1569     |
| 189       3     6    | 1789    5      189     | 4     2    179      |
|----------------------+------------------------+---------------------|
| 1235-9   *59   *1359 | 14568-9 3468-9 13568-9 |*2679 *479  2467-9   |
| 39        6     8    | 2       349    7       | 1     5    49       |
| 1259      7     4    | 1569    69     1569    | 8     3    269      |
*---------------------------------------------------------------------*

Jellyfish in 9's c2378 / r1247=> - 9 r17c14569, r2c1469, r4c149.

Leren
Leren
 
Posts: 5019
Joined: 03 June 2012

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