- Code: Select all
Resolution state after Singles and whips[1]:
+----------------------+----------------------+----------------------+
! 12569 12356 39 ! 4 2569 23569 ! 7 8 269 !
! 4 2568 789 ! 1 256789 2569 ! 269 2569 3 !
! 2569 23568 3789 ! 2569 256789 23569 ! 1 2569 4 !
+----------------------+----------------------+----------------------+
! 269 4 1 ! 3 269 7 ! 8 269 5 !
! 2679 2367 5 ! 269 1 8 ! 23469 23469 269 !
! 269 2368 389 ! 2569 4 2569 ! 2369 1 7 !
+----------------------+----------------------+----------------------+
! 3 17 4 ! 269 269 1269 ! 5 2679 8 !
! 157 9 6 ! 8 25 1245 ! 234 2347 12 !
! 8 15 2 ! 7 3 14569 ! 469 469 169 !
+----------------------+----------------------+----------------------+
185 candidates.
After only Singles or after Singles + Subsets + Finned Fish, an anti-tridagon pattern with 6 guardians is found. This is currently too many guardians for SudoRules to deal with directly, so I had to allow some whips. As the puzzle will finally require whips[7], here's a direct solution found by activating W7+OR5FW7 since the start.
I chose this puzzle because:
- it has two short OR5 forcing whips;
- it has an OR5 forcing whip with five 0-length branches, i.e. a candidate directly linked to all the guardians. For 5 guardians, that must be quite rare.
- Code: Select all
hidden-pairs-in-a-column: c5{n7 n8}{r2 r3} ==> r3c5≠9, r3c5≠6, r3c5≠5, r3c5≠2, r2c5≠9, r2c5≠6, r2c5≠5, r2c5≠2
finned-x-wing-in-columns: n5{c5 c1}{r8 r1} ==> r1c2≠5
biv-chain[3]: r5n7{c2 c1} - r8n7{c1 c8} - c8n3{r8 r5} ==> r5c2≠3
whip[1]: r5n3{c8 .} ==> r6c7≠3
hidden-pairs-in-a-block: b6{n3 n4}{r5c7 r5c8} ==> r5c8≠9, r5c8≠6, r5c8≠2, r5c7≠9, r5c7≠6, r5c7≠2
hidden-pairs-in-a-row: r6{n3 n8}{c2 c3} ==> r6c3≠9, r6c2≠6, r6c2≠2
whip[1]: c3n9{r3 .} ==> r1c1≠9, r3c1≠9
z-chain[4]: c2n6{r3 r5} - c9n6{r5 r9} - c9n1{r9 r8} - c1n1{r8 .} ==> r1c1≠6
t-whip[4]: c6n4{r8 r9} - r9n5{c6 c2} - r9n1{c2 c9} - r8c9{n1 .} ==> r8c6≠2
t-whip[5]: r8c5{n5 n2} - r7n2{c6 c8} - c8n7{r7 r8} - r8n3{c8 c7} - r8n4{c7 .} ==> r8c6≠5
- Code: Select all
+-------------------+-------------------+-------------------+
! 125 1236 39 ! 4 2569 23569 ! 7 8 269 !
! 4 2568 789 ! 1 78 2569 ! 269 2569 3 !
! 256 23568 3789 ! 2569 78 23569 ! 1 2569 4 !
+-------------------+-------------------+-------------------+
! 269 4 1 ! 3 269 7 ! 8 269 5 !
! 2679 267 5 ! 269 1 8 ! 34 34 269 !
! 269 38 38 ! 2569 4 2569 ! 269 1 7 !
+-------------------+-------------------+-------------------+
! 3 17 4 ! 269 269 1269 ! 5 2679 8 !
! 157 9 6 ! 8 25 14 ! 234 2347 12 !
! 8 15 2 ! 7 3 14569 ! 469 469 169 !
+-------------------+-------------------+-------------------+
OR5-anti-tridagon[12] (type antidiag) for digits 2, 6 and 9 in blocks:
b2, with cells: r1c5, r2c6, r3c4
b3, with cells: r1c9, r2c7, r3c8
b5, with cells: r4c5, r6c6, r5c4
b6, with cells: r4c8, r6c7, r5c9
with 5 guardians: n5r1c5 n5r2c6 n5r3c4 n5r3c8 n5r6c6
OR5-forcing-whip-elim[1] based on OR5-anti-tridagon[12] for n5r1c5, n5r2c6, n5r3c4, n5r3c8 and n5r6c6:
|| n5r1c5 -
|| n5r2c6 -
|| n5r3c4 -
|| n5r3c8 -
|| n5r6c6 -
==> r3c6≠5
OR5-forcing-whip-elim[4] based on OR5-anti-tridagon[12] for n5r3c4, n5r3c8, n5r1c5, n5r2c6 and n5r6c6:
|| n5r3c4 -
|| n5r3c8 -
|| n5r1c5 - partial-whip[1]: r8n5{c5 c1} -
|| n5r2c6 - partial-whip[1]: c8n5{r2 r3} -
|| n5r6c6 - partial-whip[1]: c4n5{r6 r3} -
==> r3c1≠5
The end is like any puzzle in W7:
- Code: Select all
hidden-pairs-in-a-column: c1{n1 n5}{r1 r8} ==> r8c1≠7, r1c1≠2
singles ==> r7c2=7, r5c1=7, r7c6=1, r8c6=4, r8c8=7, r8c7=3, r5c7=4, r5c8=3, r9c8=4
x-wing-in-columns: n5{c1 c5}{r1 r8} ==> r1c6≠5
t-whip[6]: c2n1{r1 r9} - c9n1{r9 r8} - b9n2{r8c9 r7c8} - b8n2{r7c4 r8c5} - r4n2{c5 c1} - r3c1{n2 .} ==> r1c2≠6
z-chain[3]: r1n6{c6 c9} - r5n6{c9 c2} - b1n6{r2c2 .} ==> r3c4≠6
t-whip[7]: b2n6{r3c6 r1c5} - c5n5{r1 r8} - r8n2{c5 c9} - r1c9{n2 n9} - r5n9{c9 c4} - c5n9{r4 r7} - r9c6{n9 .} ==> r6c6≠6
whip[7]: c7n2{r2 r6} - c8n2{r4 r7} - b8n2{r7c4 r8c5} - r4n2{c5 c1} - c1n9{r4 r6} - r6c6{n9 n5} - b8n5{r9c6 .} ==> r1c9≠2
z-chain[5]: c7n2{r2 r6} - c9n2{r5 r8} - r8n1{c9 c1} - r1n1{c1 c2} - r1n2{c2 .} ==> r2c6≠2
whip[6]: r5n9{c4 c9} - r1c9{n9 n6} - r9c9{n6 n1} - r9n9{c9 c7} - r9n6{c7 c6} - b2n6{r1c6 .} ==> r7c4≠9
whip[5]: r7c4{n2 n6} - b5n6{r5c4 r4c5} - c5n9{r4 r1} - r1c9{n9 n6} - c8n6{r2 .} ==> r7c5≠2
biv-chain[2]: c9n2{r5 r8} - b8n2{r8c5 r7c4} ==> r5c4≠2
biv-chain[2]: c7n2{r2 r6} - r5n2{c9 c2} ==> r2c2≠2
whip[1]: r2n2{c8 .} ==> r3c8≠2
biv-chain[3]: b8n2{r7c4 r8c5} - c5n5{r8 r1} - c4n5{r3 r6} ==> r6c4≠2
biv-chain[3]: c4n2{r3 r7} - r8n2{c5 c9} - r5n2{c9 c2} ==> r3c2≠2
biv-chain[3]: b5n2{r6c6 r4c5} - r8n2{c5 c9} - r5n2{c9 c2} ==> r6c1≠2
biv-chain[2]: b5n2{r6c6 r4c5} - c1n2{r4 r3} ==> r3c6≠2
biv-chain[4]: c4n5{r6 r3} - b3n5{r3c8 r2c8} - b3n2{r2c8 r2c7} - r6n2{c7 c6} ==> r6c6≠5
hidden-single-in-a-block ==> r6c4=5
biv-chain[3]: r3c4{n9 n2} - r7c4{n2 n6} - r7c5{n6 n9} ==> r1c5≠9
biv-chain[3]: c4n6{r5 r7} - r7n2{c4 c8} - c9n2{r8 r5} ==> r5c9≠6
finned-x-wing-in-columns: n6{c9 c6}{r9 r1} ==> r1c5≠6
whip[1]: b2n6{r3c6 .} ==> r9c6≠6
whip[1]: r9n6{c9 .} ==> r7c8≠6
naked-pairs-in-a-column: c5{r1 r8}{n2 n5} ==> r4c5≠2
singles ==> r6c6=2, r2c7=2
naked-triplets-in-a-row: r1{c3 c6 c9}{n9 n3 n6} ==> r1c2≠3
finned-swordfish-in-columns: n9{c1 c7 c5}{r4 r6 r9} ==> r9c6≠9
stte
