Here is one more example (#2 in mith 246-list http://forum.enjoysudoku.com/the-hardest-sudokus-new-thread-t6539-1190.html)
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+-------+-------+-------+
! . . . ! . . . ! . . 1 !
! . . . ! . . 2 ! . 3 . !
! . . . ! . 4 . ! 5 6 . !
+-------+-------+-------+
! . . . ! . . 7 ! . . . !
! . . 4 ! 8 1 . ! 2 . . !
! 1 9 . ! . 2 4 ! 8 . . !
+-------+-------+-------+
! . 8 9 ! . . 1 ! . . 7 !
! 4 2 . ! . 7 8 ! . . 9 !
! 7 . 1 ! . 9 . ! . . . !
+-------+-------+-------+
........1.....2.3.....4.56......7.....481.2..19..248...89..1..742..78..97.1.9....;28
- Code: Select all
Resolution state after Singles and whips[1]:
+----------------------+----------------------+----------------------+
! 235689 34567 235678 ! 35679 3568 3569 ! 479 2489 1 !
! 5689 14567 5678 ! 15679 568 2 ! 479 3 48 !
! 2389 137 2378 ! 1379 4 39 ! 5 6 28 !
+----------------------+----------------------+----------------------+
! 23568 356 23568 ! 3569 356 7 ! 13469 1459 3456 !
! 356 3567 4 ! 8 1 3569 ! 2 579 356 !
! 1 9 3567 ! 356 2 4 ! 8 57 356 !
+----------------------+----------------------+----------------------+
! 356 8 9 ! 23456 356 1 ! 346 245 7 !
! 4 2 356 ! 356 7 8 ! 136 15 9 !
! 7 356 1 ! 23456 9 356 ! 346 2458 234568 !
+----------------------+----------------------+----------------------+
196 candidates.
When whips are enabled, a full solution is obtained after an application of the tridagon elimination rule:
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hidden-pairs-in-a-column: c4{n2 n4}{r7 r9} ==> r9c4≠6, r9c4≠5, r9c4≠3, r7c4≠6, r7c4≠5, r7c4≠3
hidden-pairs-in-a-row: r4{n2 n8}{c1 c3} ==> r4c3≠6, r4c3≠5, r4c3≠3, r4c1≠6, r4c1≠5, r4c1≠3
t-whip[4]: c7n1{r4 r8} - r8c8{n1 n5} - r6c8{n5 n7} - r5c8{n7 .} ==> r4c7≠9
whip[1]: b6n9{r5c8 .} ==> r1c8≠9
hidden-pairs-in-a-block: b3{n7 n9}{r1c7 r2c7} ==> r2c7≠4, r1c7≠4
t-whip[5]: r5n7{c2 c8} - c8n9{r5 r4} - r4n1{c8 c7} - r4n4{c7 c9} - r2n4{c9 .} ==> r2c2≠7
t-whip[5]: r4n9{c4 c8} - r4n1{c8 c7} - r4n4{c7 c9} - r2n4{c9 c2} - r2n1{c2 .} ==> r2c4≠9
t-whip[6]: r5n7{c2 c8} - c8n9{r5 r4} - r4n1{c8 c7} - r4n4{c7 c9} - r2n4{c9 c2} - c2n1{r2 .} ==> r3c2≠7
t-whip[6]: r6n7{c8 c3} - r3n7{c3 c4} - r2n7{c4 c7} - r2n9{c7 c1} - r3n9{c1 c6} - r5n9{c6 .} ==> r5c8≠7
hidden-single-in-a-block ==> r6c8=7
hidden-single-in-a-block ==> r5c2=7
whip[4]: b5n9{r4c4 r5c6} - r5c8{n9 n5} - r8n5{c8 c3} - r6n5{c3 .} ==> r4c4≠5
whip[11]: b5n9{r4c4 r5c6} - r5c8{n9 n5} - b9n5{r7c8 r9c9} - c6n5{r9 r1} - c6n6{r1 r9} - b8n3{r9c6 r7c5} - c5n5{r7 r4} - c2n5{r4 r2} - r2n4{c2 c9} - c9n8{r2 r3} - c9n2{r3 .} ==> r4c4≠3
tridagon type diag for digits 3, 5 and 6 in blocks:
b5, with cells: r5c6 (target cell), r4c5, r6c4
b4, with cells: r5c1, r4c2, r6c3
b8, with cells: r9c6, r7c5, r8c4
b7, with cells: r9c2, r7c1, r8c3
==> r5c6≠3,5,6
stte
If only Subsets and tridagons are activated, no tridagon appears, but there is a tridagon-link:
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hidden-pairs-in-a-column: c4{n2 n4}{r7 r9} ==> r9c4≠6, r9c4≠5, r9c4≠3, r7c4≠6, r7c4≠5, r7c4≠3
hidden-pairs-in-a-row: r4{n2 n8}{c1 c3} ==> r4c3≠6, r4c3≠5, r4c3≠3, r4c1≠6, r4c1≠5, r4c1≠3
extended tridagon for digits 3, 5 and 6 in blocks:
b4, with cells: r6c3 (link cell), r5c1, r4c2
b5, with cells: r6c4, r5c6 (link cell), r4c5
b7, with cells: r8c3, r7c1, r9c2
b8, with cells: r8c4, r7c5, r9c6
==> tridagon-link(n7r6c3, n9r5c6)
With no other rule, nothing more can be deduced.
However, as mentioned by others in the "hardest" thread the tridagon link can be combined with chains in order to produce some eliminations.
I'll deal later with this situation.
What I wanted to show here is only an interesting case (IMO) where previous eliminations allow to reach a situation where the mere elimination rule applies.