Now that I have ORk-Forcing-Whips based on anti-tridagons, let me try the old puzzles.
- Code: Select all
Resolution state after Singles and whips[1]:
+----------------------+----------------------+----------------------+
! 4789 45689 4567 ! 236789 23789 6789 ! 45789 4789 1 !
! 4789 45689 2 ! 6789 789 1 ! 45789 3 789 !
! 1789 3 17 ! 789 4 5 ! 789 2 6 !
+----------------------+----------------------+----------------------+
! 14789 14589 1457 ! 14789 1789 2 ! 3 6 789 !
! 134789 1489 1347 ! 14789 6 789 ! 2789 5 2789 !
! 2 689 67 ! 789 5 3 ! 1 789 4 !
+----------------------+----------------------+----------------------+
! 34 7 8 ! 2369 239 69 ! 2469 1 5 !
! 5 14 9 ! 123678 12378 678 ! 24678 478 2378 !
! 6 2 13 ! 5 13789 4 ! 789 789 3789 !
+----------------------+----------------------+----------------------+
200 candidates.
- Code: Select all
hidden-pairs-in-a-row: r1{n2 n3}{c4 c5} ==> r1c5≠9, r1c5≠8, r1c5≠7, r1c4≠9, r1c4≠8, r1c4≠7, r1c4≠6
finned-x-wing-in-rows: n4{r7 r2}{c7 c1} ==> r1c1≠4
biv-chain[3]: r3n1{c1 c3} - r9c3{n1 n3} - b4n3{r5c3 r5c1} ==> r5c1≠1
z-chain[3]: b7n4{r7c1 r8c2} - c8n4{r8 r1} - c3n4{r1 .} ==> r4c1≠4, r5c1≠4
z-chain[4]: r7n4{c7 c1} - b7n3{r7c1 r9c3} - r9n1{c3 c5} - r9n9{c5 .} ==> r7c7≠9
whip[1]: b9n9{r9c9 .} ==> r9c5≠9
z-chain[5]: c7n6{r8 r7} - b9n2{r7c7 r8c9} - c9n3{r8 r9} - b7n3{r9c3 r7c1} - r7n4{c1 .} ==> r8c7≠4
z-chain[5]: c7n6{r8 r7} - b9n4{r7c7 r8c8} - r8c2{n4 n1} - r9n1{c3 c5} - r9n7{c5 .} ==> r8c7≠7
z-chain[5]: c7n6{r8 r7} - b9n4{r7c7 r8c8} - r8c2{n4 n1} - r9n1{c3 c5} - r9n8{c5 .} ==> r8c7≠8
t-whip[5]: r8c2{n1 n4} - r7c1{n4 n3} - c3n3{r9 r5} - r5n4{c3 c4} - r5n1{c4 .} ==> r4c2≠1
t-whip[5]: c9n3{r8 r9} - b7n3{r9c3 r7c1} - r7n4{c1 c7} - c7n6{r7 r8} - b9n2{r8c7 .} ==> r8c9≠7, r8c9≠8
t-whip[5]: r7n3{c5 c1} - r7n4{c1 c7} - c7n6{r7 r8} - b9n2{r8c7 r8c9} - c9n3{r8 .} ==> r9c5≠3
t-whip[5]: r2n6{c4 c2} - r2n5{c2 c7} - r2n4{c7 c1} - r7n4{c1 c7} - c7n6{r7 .} ==> r8c4≠6
whip[5]: r3c3{n7 n1} - r9c3{n1 n3} - c1n3{r7 r5} - c1n7{r5 r4} - c1n1{r4 .} ==> r1c3≠7
whip[6]: r2n5{c7 c2} - r2n4{c2 c1} - r7c1{n4 n3} - c3n3{r9 r5} - c3n4{r5 r4} - r4n5{c3 .} ==> r2c7≠7
whip[6]: r2n5{c7 c2} - r2n4{c2 c1} - r7c1{n4 n3} - c3n3{r9 r5} - c3n4{r5 r4} - r4n5{c3 .} ==> r2c7≠8
whip[6]: r2n5{c7 c2} - r2n4{c2 c1} - r7c1{n4 n3} - c3n3{r9 r5} - c3n4{r5 r4} - r4n5{c3 .} ==> r2c7≠9
whip[6]: c4n4{r5 r4} - b5n1{r4c4 r4c5} - r9n1{c5 c3} - c3n3{r9 r5} - r5n1{c3 c2} - r5n4{c2 .} ==> r5c4≠7
whip[6]: c4n4{r5 r4} - b5n1{r4c4 r4c5} - r9n1{c5 c3} - c3n3{r9 r5} - r5n1{c3 c2} - r5n4{c2 .} ==> r5c4≠8
whip[6]: c4n4{r5 r4} - b5n1{r4c4 r4c5} - r9n1{c5 c3} - c3n3{r9 r5} - r5n1{c3 c2} - r5n4{c2 .} ==> r5c4≠9
+-------------------+-------------------+-------------------+
! 789 45689 456 ! 23 23 6789 ! 45789 4789 1 !
! 4789 45689 2 ! 6789 789 1 ! 45 3 789 !
! 1789 3 17 ! 789 4 5 ! 789 2 6 !
+-------------------+-------------------+-------------------+
! 1789 4589 1457 ! 14789 1789 2 ! 3 6 789 !
! 3789 1489 1347 ! 14 6 789 ! 2789 5 2789 !
! 2 689 67 ! 789 5 3 ! 1 789 4 !
+-------------------+-------------------+-------------------+
! 34 7 8 ! 2369 239 69 ! 246 1 5 !
! 5 14 9 ! 12378 12378 678 ! 26 478 23 !
! 6 2 13 ! 5 178 4 ! 789 789 3789 !
+-------------------+-------------------+-------------------+
- Code: Select all
OR4-anti-tridagon[12] (type antidiag) for digits 7, 8 and 9 in blocks:
b2, with cells: r1c6, r2c5, r3c4
b3, with cells: r1c8, r2c9, r3c7
b5, with cells: r5c6, r4c5, r6c4
b6, with cells: r5c7, r4c9, r6c8
with 4 guardians: n6r1c6 n4r1c8 n1r4c5 n2r5c7
OR4-forcing-whip-elim[7] based on OR4-anti-tridagon[12] for n2r5c7, n4r1c8, n6r1c6 and n1r4c5:
|| n2r5c7 - partial-whip[1]: r8c7{n2 n6} -
|| n4r1c8 - partial-whip[1]: b9n4{r8c8 r7c7} -
|| n6r1c6 - partial-whip[1]: b8n6{r8c6 r7c4} -
|| n1r4c5 - partial-whip[3]: r9n1{c5 c3} - b7n3{r9c3 r7c1} - r7n4{c1 c7} -
==> r7c7≠6
hidden-single-in-a-block ==> r8c7=6
OR4-forcing-whip-elim[7] based on OR4-anti-tridagon[12] for n4r1c8, n6r1c6, n1r4c5 and n2r5c7:
|| n4r1c8 - partial-whip[1]: r8n4{c8 c2} -
|| n6r1c6 - partial-whip[1]: r2n6{c4 c2} -
|| n1r4c5 - partial-whip[2]: c4n1{r5 r8} - r8c2{n1 n4} -
|| n2r5c7 - partial-whip[2]: r7c7{n2 n4} - b7n4{r7c1 r8c2} -
==> r2c2≠4
x-wing-in-rows: n4{r2 r7}{c1 c7} ==> r1c7≠4
biv-chain[5]: b4n5{r4c3 r4c2} - r2n5{c2 c7} - b3n4{r2c7 r1c8} - r8n4{c8 c2} - c2n1{r8 r5} ==> r4c3≠1
biv-chain[6]: r4n5{c3 c2} - r2n5{c2 c7} - r2n4{c7 c1} - b7n4{r7c1 r8c2} - b7n1{r8c2 r9c3} - r3c3{n1 n7} ==> r4c3≠7
t-whip[6]: r2n5{c2 c7} - r2n4{c7 c1} - r7c1{n4 n3} - r5n3{c1 c3} - c3n4{r5 r4} - r4n5{c3 .} ==> r1c2≠5
OR4-forcing-whip-elim[7] based on OR4-anti-tridagon[12] for n4r1c8, n2r5c7, n1r4c5 and n6r1c6:
|| n4r1c8 -
|| n2r5c7 - partial-whip[1]: r7c7{n2 n4} -
|| n1r4c5 - partial-whip[2]: c4n1{r5 r8} - r8c2{n1 n4} -
|| n6r1c6 - partial-whip[3]: r2n6{c4 c2} - r2n5{c2 c7} - b3n4{r2c7 r1c8} -
==> r8c8≠4
singles ==> r7c7=4, r2c7=5, r7c1=3, r9c3=1, r3c3=7, r6c3=6, r8c2=4, r3c1=1, r5c2=1, r5c4=4, r5c3=3, r4c3=4, r1c3=5, r2c1=4, r1c8=4, r4c2=5, r9c9=3, r8c9=2, r5c7=2
naked-pairs-in-a-block: b8{r8c6 r9c5}{n7 n8} ==> r8c5≠8, r8c5≠7, r8c4≠8, r8c4≠7
finned-x-wing-in-rows: n7{r8 r6}{c8 c6} ==> r5c6≠7
finned-x-wing-in-columns: n7{c6 c7}{r1 r8} ==> r8c8≠7
stte
