The New Sudoku Players' Forum

[denis_berthier]

.
Still trying to illustrate new effective 3-digit patterns among eleven's impossible list of 630.
* effective = leading to eliminations.
In all the examples I've given until now, many more patterns appear, but they remain sterile in the resolution path.

Code: Select all

+-------+-------+-------+
! 1 . 3 ! . . 6 ! . . . !
! . . . ! 1 8 . ! . . . !
! . . . ! . 2 . ! 4 . . !
+-------+-------+-------+
! . 1 4 ! 5 7 . ! . 6 3 !
! 5 3 . ! . . . ! . . 7 !
! . . . ! 3 1 . ! 5 4 . !
+-------+-------+-------+
! . 6 . ! . . 7 ! . 5 . !
! . 7 1 ! . . . ! 3 . 4 !
! . . 5 ! . . 1 ! 6 7 . !
+-------+-------+-------+
1.3..6......18........2.4...1457..6353......7...31.54..6...7.5..71...3.4..5..167.;123;17552
SER = 11.7

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 1     24589 3     ! 479   459   6     ! 2789  289   2589  !
   ! 24679 2459  2679  ! 1     8     3459  ! 279   239   2569  !
   ! 6789  589   6789  ! 79    2     359   ! 4     1389  15689 !
   +-------------------+-------------------+-------------------+
   ! 289   1     4     ! 5     7     289   ! 289   6     3     !
   ! 5     3     289   ! 24689 469   2489  ! 1289  1289  7     !
   ! 26789 289   26789 ! 3     1     289   ! 5     4     289   !
   +-------------------+-------------------+-------------------+
   ! 23489 6     289   ! 2489  349   7     ! 1289  5     1289  !
   ! 289   7     1     ! 2689  569   2589  ! 3     289   4     !
   ! 23489 2489  5     ! 2489  349   1     ! 6     7     289   !
   +-------------------+-------------------+-------------------+
184 candidates.

[shye]

whole bunch of them in here! i used three different ones

Code: Select all

+-------+-------+-------+  +-------+-------+-------+  +-------+-------+-------+
| . . . | . . . | . . . |  | . . . | . . . | . . . |  | . . . | . . . | . . . |
| . . . | . . . | . . . |  | . . . | . . . | . . . |  | . . . | . . . | . . . |
| . . . | . . . | . . . |  | . . . | . . . | . . . |  | . . . | . . . | . . . |
+-------+-------+-------+  +-------+-------+-------+  +-------+-------+-------+
| # . . | . . # | . . . |  | # . . | . . . | # . . |  | # . . | . . # | # . . |
| . . . | . . . | . . . |  | . . # | . . . | . # . |  | . . # | . . . | . # . |
| . # . | . . # | . . # |  | . # . | . . . | . . # |  | . # . | . . # | . . # |
+-------+-------+-------+  +-------+-------+-------+  +-------+-------+-------+
| . . . | . . . | . . # |  | . . # | . . . | # . . |  | . . # | . . . | # . . |
| # . . | . . # | . # . |  | # . . | . . . | . # . |  | # . . | . . # | . # . |
| . . . | . . . | . . # |  | . # . | . . . | . . # |  | . . . | . . . | . . # |
+-------+-------+-------+  +-------+-------+-------+  +-------+-------+-------+
 Pattern A                  Pattern B (tridagon)       Pattern C

None of the above patterns can be limited to the same 3 candidates

Pattern A = 5r8c6 - 5r8c5 = 5r1c5 - 5r1c9 = 289 triple c9
=> -289r7c9

XSudo Input: Show

11 Truths = {5C5 48N1 6N2 468N6 8N8 169N9}
26 Links = {2r468 5r1 8r468 9r468 2c169 8c169 9c169 289b4 5b8 289b9}
3 Eliminations --> r7c9<>289

after singles Pattern B is immediately applicable
=> -289r9c2

XSudo Input: Show

11 Truths = {48N1 6N2 57N3 47N7 58N8 69N9}
48 Links = {2r456789 8r456789 9r456789 2c123789 8c123789 9c123789 2b4679 8b4679 9b4679}
3 Eliminations --> r9c2<>289

after singles Pattern C is immediately applicable
=> -289r8c6

XSudo Input: Show

13 Truths = {4N167 5N38 6N269 7N37 8N18 9N9}
39 Links = {2r4678 8r4678 9r4678 2c13689 8c13689 9c13689 2b4679 8b4679 9b4679}
3 Eliminations --> r8c6<>289

solves with a turbot fish

[denis_berthier]

None of the above patterns can be limited to the same 3 candidates

What do you mean? Your 3 patterns are based one the same 3 digits: 2, 8, 9

[shye]

None of the above patterns can be limited to the same 3 candidates

What do you mean? Your 3 patterns are based one the same 3 digits: 2, 8, 9

yes, the marked cells in each diagram cannot all be 289 only (but more generally, they cant all be the same set of any three digits)
these arent linked in any way, i just put them in the same code box to keep the message shorter

[denis_berthier]

.
OK, you meant each of your three 3-digit patterns A, B, C is contradictory. They require "guardians".

[denis_berthier]

.
Note that there may be different ways of using some of the 630-38 impossible patterns. Which ones are found first depends on the priorities they're given.
Reminder: in SudoRules, priorities for these patterns are for those with fewer cells.

Starting as usual from the resolution state after Singles and whips[1], a whole lot of patterns are found. I keep here only the 3 useful ones. Note that the OR3 Tridagon relation is immediately split into two OR2 relations:

Code: Select all

hidden-pairs-in-a-row: r6{n6 n7}{c1 c3} ==> r6c3≠9, r6c3≠8, r6c3≠2, r6c1≠9, r6c1≠8, r6c1≠2

   +-------------------+-------------------+-------------------+
   ! 1     24589 3     ! 479   459   6     ! 2789  289   2589  !
   ! 24679 2459  2679  ! 1     8     3459  ! 279   239   2569  !
   ! 6789  589   6789  ! 79    2     359   ! 4     1389  15689 !
   +-------------------+-------------------+-------------------+
   ! 289   1     4     ! 5     7     289   ! 289   6     3     !
   ! 5     3     289   ! 24689 469   2489  ! 1289  1289  7     !
   ! 67    289   67    ! 3     1     289   ! 5     4     289   !
   +-------------------+-------------------+-------------------+
   ! 23489 6     289   ! 2489  349   7     ! 1289  5     1289  !
   ! 289   7     1     ! 2689  569   2589  ! 3     289   4     !
   ! 23489 2489  5     ! 2489  349   1     ! 6     7     289   !
   +-------------------+-------------------+-------------------+

OR3-anti-tridagon[12] for digits 2, 8 and 9 in blocks:
        b4, with cells: r4c1, r5c3, r6c2
        b6, with cells: r4c7, r5c8, r6c9
        b7, with cells: r8c1, r7c3, r9c2
        b9, with cells: r8c8, r7c7, r9c9
with 3 guardians: n1r5c8 n1r7c7 n4r9c2

Trid-OR3-relation between candidates n1r5c8, n1r7c7 and n4r9c2
+ same valence for candidates n1r7c7 and n1r5c8 via c-chain[2]: n1r7c7,n1r5c7,n1r5c8
==> Trid-OR3-relation can be split into two Trid-OR2-relations with respective lists of guardians:
    n1r5c8 n4r9c2  and n1r7c7 n4r9c2 .

EL10c28-OR2-relation for digits: 2, 8 and 9
   in cells (marked #): (r4c6 r4c1 r6c9 r6c6 r6c2 r9c9 r7c9 r8c8 r8c6 r8c1)
   with 2 guardians (in cells marked @) : n1r7c9 n5r8c6
   +----------------------+----------------------+----------------------+
   ! 1      24589  3      ! 479    459    6      ! 2789   289    2589   !
   ! 24679  2459   2679   ! 1      8      3459   ! 279    239    2569   !
   ! 6789   589    6789   ! 79     2      359    ! 4      1389   15689  !
   +----------------------+----------------------+----------------------+
   ! 289#   1      4      ! 5      7      289#   ! 289    6      3      !
   ! 5      3      289    ! 24689  469    2489   ! 1289   1289   7      !
   ! 67     289#   67     ! 3      1      289#   ! 5      4      289#   !
   +----------------------+----------------------+----------------------+
   ! 23489  6      289    ! 2489   349    7      ! 1289   5      1289#@ !
   ! 289#   7      1      ! 2689   569    2589#@ ! 3      289#   4      !
   ! 23489  2489   5      ! 2489   349    1      ! 6      7      289#   !
   +----------------------+----------------------+----------------------+

EL15c97-OR6-relation for digits: 2, 8 and 9
   in cells (marked #): (r7c3 r7c7 r9c4 r9c9 r8c6 r8c1 r8c8 r4c1 r4c7 r5c4 r5c3 r5c8 r6c6 r6c2 r6c9)
   with 6 guardians (in cells marked @) : n1r7c7 n4r9c4 n5r8c6 n4r5c4 n6r5c4 n1r5c8
   +-------------------------+-------------------------+-------------------------+
   ! 1       24589   3       ! 479     459     6       ! 2789    289     2589    !
   ! 24679   2459    2679    ! 1       8       3459    ! 279     239     2569    !
   ! 6789    589     6789    ! 79      2       359     ! 4       1389    15689   !
   +-------------------------+-------------------------+-------------------------+
   ! 289#    1       4       ! 5       7       289     ! 289#    6       3       !
   ! 5       3       289#    ! 24689#@ 469     2489    ! 1289    1289#@  7       !
   ! 67      289#    67      ! 3       1       289#    ! 5       4       289#    !
   +-------------------------+-------------------------+-------------------------+
   ! 23489   6       289#    ! 2489    349     7       ! 1289#@  5       1289    !
   ! 289#    7       1       ! 2689    569     2589#@  ! 3       289#    4       !
   ! 23489   2489    5       ! 2489#@  349     1       ! 6       7       289#    !
   +-------------------------+-------------------------+-------------------------+

EL10c28-OR2-whip[3]: OR2{{n5r8c6 | n1r7c9}} - r3n1{c9 c8} - r3n3{c8 .} ==> r3c6≠5
EL10c28-OR2-whip[4]: OR2{{n1r7c9 | n5r8c6}} - c5n5{r8 r1} - c9n5{r1 r2} - c9n6{r2 .} ==> r3c9≠1
singles ==> r3c8=1, r2c8=3, r3c6=3, r5c7=1, r7c9=1

Code: Select all

   +-------------------+-------------------+-------------------+
   ! 1     24589 3     ! 479   459   6     ! 2789  289   2589  !
   ! 24679 2459  2679  ! 1     8     459   ! 279   3     2569  !
   ! 6789  589   6789  ! 79    2     3     ! 4     1     5689  !
   +-------------------+-------------------+-------------------+
   ! 289   1     4     ! 5     7     289   ! 289   6     3     !
   ! 5     3     289   ! 24689 469   2489  ! 1     289   7     !
   ! 67    289   67    ! 3     1     289   ! 5     4     289   !
   +-------------------+-------------------+-------------------+
   ! 23489 6     289   ! 2489  349   7     ! 289   5     1     !
   ! 289   7     1     ! 2689  569   2589  ! 3     289   4     !
   ! 23489 2489  5     ! 2489  349   1     ! 6     7     289   !
   +-------------------+-------------------+-------------------+

At least one candidate of a previous Trid-OR2-relation between candidates n1r7c7 n4r9c2 has just been eliminated.
There remains a Trid-OR1-relation between candidates: n4r9c2
Trid-ORk-relation with only one candidate => r9c2=4
singles ==> r2c1=4, r5c6=4

Code: Select all

   +----------------+----------------+----------------+
   ! 1    2589 3    ! 479  459  6    ! 2789 289  2589 !
   ! 4    259  2679 ! 1    8    59   ! 279  3    2569 !
   ! 6789 589  6789 ! 79   2    3    ! 4    1    5689 !
   +----------------+----------------+----------------+
   ! 289  1    4    ! 5    7    289  ! 289  6    3    !
   ! 5    3    289  ! 2689 69   4    ! 1    289  7    !
   ! 67   289  67   ! 3    1    289  ! 5    4    289  !
   +----------------+----------------+----------------+
   ! 2389 6    289  ! 2489 349  7    ! 289  5    1    !
   ! 289  7    1    ! 2689 569  2589 ! 3    289  4    !
   ! 2389 4    5    ! 289  39   1    ! 6    7    289  !
   +----------------+----------------+----------------+


At least one candidate of a previous EL15c97-OR6-relation between candidates n1r7c7 n4r9c4 n5r8c6 n4r5c4 n6r5c4 n1r5c8 has just been eliminated.
There remains an EL15c97-OR2-relation between candidates: n5r8c6 n6r5c4

hidden-pairs-in-a-column: c1{n6 n7}{r3 r6} ==> r3c1≠9, r3c1≠8
EL15c97-OR2-whip[2]: OR2{{n6r5c4 | n5r8c6}} - c6n8{r8 .} ==> r5c4≠8
whip[1]: c4n8{r9 .} ==> r8c6≠8
EL15c97-OR2-whip[2]: OR2{{n6r5c4 | n5r8c6}} - c6n2{r8 .} ==> r5c4≠2
whip[1]: c4n2{r9 .} ==> r8c6≠2
naked-pairs-in-a-column: c6{r2 r8}{n5 n9} ==> r6c6≠9, r4c6≠9
whip[1]: b5n9{r5c5 .} ==> r5c3≠9, r5c8≠9
finned-x-wing-in-columns: n9{c8 c6}{r8 r1} ==> r1c5≠9, r1c4≠9
finned-x-wing-in-rows: n9{r6 r1}{c2 c9} ==> r3c9≠9, r2c9≠9
finned-x-wing-in-columns: n9{c6 c8}{r8 r2} ==> r2c7≠9
whip[1]: b3n9{r1c9 .} ==> r1c2≠9
t-whip[2]: r4n9{c7 c1} - b7n9{r9c1 .} ==> r7c7≠9
EL15c97-OR2-whip[2]: OR2{{n5r8c6 | n6r5c4}} - r8n6{c4 .} ==> r8c5≠5
stte