.
The resolution path I find is quite typical of puzzles with a tridagon: mixing of ordinary whips and Trid-ORk-whips.
- Code: Select all
Resolution state after Singles and whips[1]:
+----------------------+----------------------+----------------------+
! 9 5 123 ! 123 8 4 ! 1236 167 2367 !
! 6 123 4 ! 12359 1239 7 ! 12389 158 2358 !
! 123 8 7 ! 6 1239 1235 ! 12349 15 2345 !
+----------------------+----------------------+----------------------+
! 123 7 8 ! 123 5 9 ! 1236 4 236 !
! 12345 123 9 ! 123478 12347 6 ! 1238 1578 23578 !
! 12345 6 123 ! 123478 12347 123 ! 1238 9 23578 !
+----------------------+----------------------+----------------------+
! 1238 4 5 ! 123 1236 123 ! 7 68 9 !
! 137 139 136 ! 13479 134679 8 ! 5 2 46 !
! 278 29 26 ! 24579 24679 25 ! 468 3 1 !
+----------------------+----------------------+----------------------+
199 candidates
hidden-pairs-in-a-column: c1{n4 n5}{r5 r6} ==> r6c1≠3, r6c1≠2, r6c1≠1, r5c1≠3, r5c1≠2, r5c1≠1
naked-triplets-in-a-column: c4{r1 r4 r7}{n3 n2 n1} ==> r9c4≠2, r8c4≠3, r8c4≠1, r6c4≠3, r6c4≠2, r6c4≠1, r5c4≠3, r5c4≠2, r5c4≠1, r2c4≠3, r2c4≠2, r2c4≠1
- Code: Select all
Trid-OR4-relation for digits 1, 2 and 3 in blocks:
b1, with cells (marked #): r1c3, r2c2, r3c1
b2, with cells (marked #): r1c4, r2c5, r3c6
b4, with cells (marked #): r6c3, r5c2, r4c1
b5, with cells (marked #): r6c6, r5c5, r4c4
with 4 guardians (in cells marked @): n9r2c5 n5r3c6 n4r5c5 n7r5c5
+-------------------------+-------------------------+-------------------------+
! 9 5 123# ! 123# 8 4 ! 1236 167 2367 !
! 6 123# 4 ! 59 1239#@ 7 ! 12389 158 2358 !
! 123# 8 7 ! 6 1239 1235#@ ! 12349 15 2345 !
+-------------------------+-------------------------+-------------------------+
! 123# 7 8 ! 123# 5 9 ! 1236 4 236 !
! 45 123# 9 ! 478 12347#@ 6 ! 1238 1578 23578 !
! 45 6 123# ! 478 12347 123# ! 1238 9 23578 !
+-------------------------+-------------------------+-------------------------+
! 1238 4 5 ! 123 1236 123 ! 7 68 9 !
! 137 139 136 ! 479 134679 8 ! 5 2 46 !
! 278 29 26 ! 4579 24679 25 ! 468 3 1 !
+-------------------------+-------------------------+-------------------------+
z-chain[4]: c7n4{r3 r9} - b9n8{r9c7 r7c8} - r2c8{n8 n5} - r3c8{n5 .} ==> r3c7≠1
z-chain[4]: r9c2{n9 n2} - r9c6{n2 n5} - c4n5{r9 r2} - c4n9{r2 .} ==> r9c5≠9
z-chain[5]: c7n9{r2 r3} - c7n4{r3 r9} - b9n8{r9c7 r7c8} - r2c8{n8 n5} - r3c8{n5 .} ==> r2c7≠1
z-chain[6]: r2c4{n5 n9} - r3n9{c5 c7} - c7n4{r3 r9} - b9n8{r9c7 r7c8} - r2c8{n8 n1} - r3c8{n1 .} ==> r2c9≠5
whip[8]: c8n7{r5 r1} - c9n7{r1 r6} - r6n5{c9 c1} - r5c1{n5 n4} - r5c4{n4 n8} - c9n8{r5 r2} - c8n8{r2 r7} - c8n6{r7 .} ==> r5c5≠7
At least one candidate of a previous Trid-OR4-relation between candidates n9r2c5 n5r3c6 n4r5c5 n7r5c5 has just been eliminated.
There remains a Trid-OR3-relation between candidates: n9r2c5 n5r3c6 n4r5c5
Trid-OR3-whip[4]: c7n4{r9 r3} - c7n9{r3 r2} - OR3{{n9r2c5 n4r5c5 | n5r3c6}} - r2c4{n5 .} ==> r9c5≠4t-whip[5]: r9n7{c5 c1} - r9n8{c1 c7} - r9n4{c7 c4} - c4n5{r9 r2} - c4n9{r2 .} ==> r8c4≠7
Trid-OR3-whip[5]: r3n4{c9 c7} - r3n9{c7 c5} - OR3{{n9r2c5 n5r3c6 | n4r5c5}} - r5c1{n4 n5} - c8n5{r5 .} ==> r3c9≠5whip[1]: c9n5{r6 .} ==> r5c8≠5
whip[7]: c8n7{r5 r1} - c8n6{r1 r7} - b9n8{r7c8 r9c7} - r9n4{c7 c4} - c4n7{r9 r6} - r6n8{c4 c9} - c9n5{r6 .} ==> r5c9≠7
whip[5]: b6n7{r5c8 r6c9} - c9n5{r6 r5} - c9n8{r5 r2} - r2c8{n8 n5} - r3c8{n5 .} ==> r5c8≠1
whip[1]: b6n1{r6c7 .} ==> r1c7≠1
Trid-OR3-whip[8]: r5c8{n7 n8} - b9n8{r7c8 r9c7} - c7n4{r9 r3} - c7n9{r3 r2} - r2c4{n9 n5} - OR3{{n5r3c6 n9r2c5 | n4r5c5}} - r5c1{n4 n5} - c9n5{r5 .} ==> r6c9≠7singles ==> r5c8=7, r1c9=7
Trid-OR3-whip[8]: c7n4{r9 r3} - c7n9{r3 r2} - r2c4{n9 n5} - OR3{{n5r3c6 n9r2c5 | n4r5c5}} - r5c4{n4 n8} - r6n8{c4 c9} - r6n5{c9 c1} - r6n4{c1 .} ==> r9c7≠8singles ==> r7c8=8, r9c1=8, r8c1=7, r1c8=6, r7c5=6
whip[7]: c7n6{r4 r9} - r9c3{n6 n2} - c1n2{r7 r3} - r1n2{c3 c4} - r1c7{n2 n3} - r3c9{n3 n4} - r8c9{n4 .} ==> r4c7≠2
Trid-OR3-ctr-whip[8]: r1n1{c3 c4} - b5n1{r4c4 r5c5} - c7n1{r5 r4} - c7n6{r4 r9} - c7n4{r9 r3} - r3n9{c7 c5} - r2c4{n9 n5} - OR3{{n9r2c5 n5r3c6 n4r5c5 | .}} ==> r6c3≠1z-chain[5]: c3n1{r1 r8} - c3n6{r8 r9} - c7n6{r9 r4} - r4n1{c7 c4} - r1n1{c4 .} ==> r3c1≠1
t-whip[3]: c1n1{r4 r7} - c3n1{r8 r1} - c4n1{r1 .} ==> r4c7≠1
biv-chain[4]: c9n4{r3 r8} - b9n6{r8c9 r9c7} - r4c7{n6 n3} - r1c7{n3 n2} ==> r3c9≠2
t-whip[6]: b1n1{r1c3 r2c2} - c8n1{r2 r3} - r3n5{c8 c6} - r9c6{n5 n2} - b7n2{r9c2 r7c1} - r3c1{n2 .} ==> r1c3≠3
z-chain[4]: r1n3{c7 c4} - r4n3{c4 c1} - b4n1{r4c1 r5c2} - c7n1{r5 .} ==> r6c7≠3
whip[5]: c9n4{r3 r8} - r8n6{c9 c3} - c3n3{r8 r6} - c1n3{r4 r7} - c6n3{r7 .} ==> r3c9≠3
singles ==> r3c9=4, r8c9=6, r9c7=4, r4c7=6, r9c3=6
biv-chain[3]: r3c1{n3 n2} - c3n2{r1 r6} - c3n3{r6 r8} ==> r7c1≠3
whip[1]: r7n3{c6 .} ==> r8c5≠3
biv-chain[3]: r7c1{n2 n1} - c3n1{r8 r1} - c3n2{r1 r6} ==> r4c1≠2
z-chain[3]: b4n2{r5c2 r6c3} - r1n2{c3 c4} - r4n2{c4 .} ==> r5c7≠2
z-chain[3]: b1n3{r2c2 r3c1} - r4n3{c1 c4} - r1n3{c4 .} ==> r2c9≠3
whip[1]: c9n3{r6 .} ==> r5c7≠3
t-whip[3]: c3n2{r6 r1} - c1n2{r3 r7} - c4n2{r7 .} ==> r6c6≠2, r6c5≠2
finned-x-wing-in-columns: n2{c1 c6}{r3 r7} ==> r7c4≠2
biv-chain[3]: r6c6{n3 n1} - r4n1{c4 c1} - c1n3{r4 r3} ==> r3c6≠3
biv-chain[4]: r3c1{n3 n2} - r7c1{n2 n1} - r7c4{n1 n3} - r1n3{c4 c7} ==> r3c7≠3
biv-chain[4]: c3n2{r6 r1} - r1n1{c3 c4} - r7c4{n1 n3} - c6n3{r7 r6} ==> r6c3≠3
singles ==> r6c3=2, r1c3=1, r8c3=3
whip[1]: c7n2{r3 .} ==> r2c9≠2
naked-single ==> r2c9=8
x-wing-in-columns: n1{c1 c4}{r4 r7} ==> r7c6≠1
biv-chain[2]: b4n3{r5c2 r4c1} - r3n3{c1 c5} ==> r5c5≠3
biv-chain[3]: r1c4{n2 n3} - r3n3{c5 c1} - b1n2{r3c1 r2c2} ==> r2c5≠2
biv-chain[3]: c4n1{r4 r7} - b8n3{r7c4 r7c6} - r6c6{n3 n1} ==> r5c5≠1, r6c5≠1
biv-chain[3]: r5c5{n4 n2} - r9c5{n2 n7} - r6n7{c5 c4} ==> r6c4≠4
biv-chain[4]: r5c4{n8 n4} - r8c4{n4 n9} - r8c2{n9 n1} - r5n1{c2 c7} ==> r5c7≠8
stte
by coloin » Tue Apr 29, 2025 11:10 pm 
