Here is now an example in which one of the eliminations based on the tridagon-link involves two short partial-whips (#147 in the same list):
- Code: Select all
+-------+-------+-------+
! . . . ! . . . ! . 1 2 !
! . . . ! . . . ! 3 . 4 !
! . . . ! . 1 5 ! 6 7 . !
+-------+-------+-------+
! . . 8 ! . 9 . ! . . 6 !
! . 5 1 ! . 7 6 ! . . . !
! 6 9 . ! . . 8 ! . . . !
+-------+-------+-------+
! . 7 5 ! . 8 9 ! . 6 . !
! 8 . . ! 6 5 . ! . 9 . !
! 9 . 6 ! 7 . 1 ! . . . !
+-------+-------+-------+
.......12......3.4....1567...8.9...6.51.76...69...8....75.89.6.8..65..9.9.67.1...;31
SER = 11.7
- Code: Select all
Resolution state after Singles and whips[1]:
+-------------------+-------------------+-------------------+
! 3457 3468 3479 ! 3489 346 347 ! 589 1 2 !
! 1257 1268 279 ! 289 26 27 ! 3 58 4 !
! 234 2348 2349 ! 23489 1 5 ! 6 7 89 !
+-------------------+-------------------+-------------------+
! 2347 234 8 ! 12345 9 234 ! 12457 2345 6 !
! 234 5 1 ! 234 7 6 ! 2489 2348 389 !
! 6 9 2347 ! 12345 234 8 ! 12457 2345 1357 !
+-------------------+-------------------+-------------------+
! 1234 7 5 ! 234 8 9 ! 124 6 13 !
! 8 1234 234 ! 6 5 234 ! 1247 9 137 !
! 9 234 6 ! 7 234 1 ! 2458 23458 358 !
+-------------------+-------------------+-------------------+
176 candidates
- Code: Select all
hidden-pairs-in-a-column: c4{n1 n5}{r4 r6} ==> r6c4≠4, r6c4≠3, r6c4≠2, r4c4≠4, r4c4≠3, r4c4≠2
extended tridagon for digits 2, 3 and 4 in blocks:
b7, with cells: r7c1 (link cell), r8c3, r9c2
b8, with cells: r7c4, r8c6, r9c5
b4, with cells: r5c1, r6c3 (link cell), r4c2
b5, with cells: r5c4, r6c5, r4c6
==> tridagon-link(n1r7c1, n7r6c3)
tridagon-forcing-whip-elim[14] based on tridagon-link(n7r6c3, n1r7c1)
....for n7r6c3: partial-whip[1]: c9n7{r6 r8} -
....for n1r7c1: partial-whip[1]: r7c9{n1 n3} -
==> r8c9≠3
tridagon-forcing-whip-elim[14] based on tridagon-link(n1r7c1, n7r6c3)
....for n1r7c1: -
....for n7r6c3: partial-whip[2]: c1n7{r4 r1} - c1n5{r1 r2} -
==> r2c1≠1
The end is in Z4:
- Code: Select all
singles ==> r2c2=1, r1c2=6, r3c2=8, r3c9=9, r5c7=9, r2c6=6, r7c1=1, r7c9=3, r5c9=8, r9c9=5
hidden-pairs-in-a-block: b9{n1 n7}{r8c7 r8c9} ==> r8c7≠4, r8c7≠2
hidden-pairs-in-a-block: b2{n8 n9}{r1c4 r2c4} ==> r2c4≠2, r1c4≠4, r1c4≠3
finned-x-wing-in-columns: n2{c6 c2}{r4 r8} ==> r8c3≠2
whip[1]: b7n2{r9c2 .} ==> r4c2≠2
z-chain[4]: r1c6{n3 n4} - r1c5{n4 n7} - b1n7{r1c1 r2c3} - c3n9{r2 .} ==> r1c3≠3
z-chain[2]: b1n3{r3c1 r3c3} - c4n3{r3 .} ==> r5c1≠3
z-chain[3]: c4n3{r5 r3} - c3n3{r3 r8} - b8n3{r8c6 .} ==> r6c5≠3
biv-chain[3]: r6c5{n4 n2} - c6n2{r4 r8} - b8n3{r8c6 r9c5} ==> r9c5≠4
biv-chain[3]: c5n4{r6 r1} - r1c6{n4 n3} - b5n3{r4c6 r5c4} ==> r5c4≠4
biv-chain[3]: r5c4{n3 n2} - r5c1{n2 n4} - r4c2{n4 n3} ==> r4c6≠3
hidden-single-in-a-block ==> r5c4=3
whip[1]: r3n3{c3 .} ==> r1c1≠3
biv-chain[3]: r2c1{n2 n5} - r1c1{n5 n7} - b2n7{r1c5 r2c5} ==> r2c5≠2
singles ==> r2c5=7, r3c4=2, r7c4=4, r7c7=2
whip[1]: b9n4{r9c8 .} ==> r9c2≠4
whip[1]: r3n4{c3 .} ==> r1c3≠4
naked-pairs-in-a-column: c3{r3 r8}{n3 n4} ==> r6c3≠4, r6c3≠3
hidden-single-in-a-row ==> r6c8=3
biv-chain[3]: c2n4{r4 r8} - r8n2{c2 c6} - r4c6{n2 n4} ==> r4c1≠4, r4c7≠4, r4c8≠4
biv-chain[3]: b6n2{r4c8 r5c8} - b6n4{r5c8 r6c7} - b5n4{r6c5 r4c6} ==> r4c6≠2
singles
Reducing a puzzle from SER = 11.7 to one in Z4 show how powerful the tridagon based rules are.