Prelims:
a) 41(7) @ r3c4 – no 1,3
b) 4(2) r67c4 and r34c6 = {13} not elsewhere in c4, c6
-> NP {13} r6c4 + r4c6 not elsewhere in N5
c) 24(3) N3 = {789} not elsewhere in N3
d) 8(3) r12c7+r2c6 = {125/134} must have 1 in r12c7 not elsewhere in c7/N3
-> 9(3) N3 = {234} not elsewhere in N3
-> r12c7 = {15} not elsewhere in c7 -> r2c6 = 2 -> r3c9 = 6
-> r4c89 = {29/38/47}
-> 2 locked to r3c78 not elsewhere in r3
-> 2 locked to r45c4,r5c5 of 41(7) -> r46c5 <> 2
e) 19(3) r345c1 and r9c456 – no 1
f) 21(3) r89c3 + r8c4 – no 1,2,3
1. Outies c789: r28c6 = 6 -> r8c6 = 4 -> r89c7 = {27/36}
2. Outies c123: r28c4 = 12 = [48]/{57}
3. Innies r12: r2c258 = 13 = {19/46}3 / {18/36}4
4. Innies r89: r8c258 = 10 = {127/136/235}
5. O-I N9: r7c9 – r6c8 = 3 -> r7c9 = (45789), r6c8 = (12456)
6. Outies c1: r169c2 = 16
7. Outies c9: r149c8 = 24 = {789} not elsewhere in c8
-> r4c9 <> 7,8,9
-> 12(3) r9c8+r89c9 = [714], 8{13}, 9{12} -> r89c9 = (1234) ({723} would block both options for r89c7) -> 1 locked to r89c9, not elsewhere in c9/N9
8. Innies c5: r159c5 = 11 = {128/137/146/236/245}
If {128/137/146} r1c5 = 1 -> r1c5 <> 7, 8
If {137} r5c5 = 7 -> r9c5 <> 7
9. O-I N1: r2c4 + r4c2 - r3c1 = 4 -> r4c2 – r3c1 = 0 or -1 or -3
10. O-I c12: r37c3 – r5c2 = 3
11. O-I c89: r37c7 – r5c8 = 9
Max from r37c7 = 13 -> r5c8 is max 4 -> 6 locked to r678c8 of 21(4) -> r7c7 <> 6
r5c8 = (1234) -> r37c7 = 10, 11, 12, 13, r3c7 = (234) -> r7c7 is min 7
12. 21(3) r89c3 + r8c4 = [948]/{579/678}
13. 16(3) r12c3 + r2c4 = {39/57}4 / [29]/{38/47}5 / {18/36/45}7
14. Outies N14: r2c4+r7c1 = 8 = [44/53/71] -> r7c1 = (134)
15. 9 locked to r8c13, not elsewhere in N7 -> r8c3 <> 5.
16. 8 locked to r8c134 -> r9c3 <> 8
17. Killer Triple: Split 10(3) in r8 c258 = {127/136/235} (each option has 2 of 1,2,3), r8c9 = (123) -> r8c17 <> 1,2,3 -> r9c7 <> 6,7
18. 15(3) r1c456 = {168/348/357/456} ({159} blocked by r1c7)
15(3) contains one of 5,8 -> 17(3) r234c5 <> [854]
19. 21(4) r678c8+r7c7 must have 5 and 6 within r678c8
-> 21(4) = 56+{19/28/37} -> r67c8 <> 4 -> r7c9 <> 7 (step 5)
-> 4 locked to r79c9 not elsewhere in c9 -> r4c8 <> 7
20. 9 locked to r4569c4 -> r7c6 <> 9
9 also locked to r569c6
(Grouped x-wing) -> r7c5 <> 9, r9c8 <> 9 -> r89c9 <> 2
-> 2 locked to r456c9 not elsewhere in N6 -> r7c9 <> 5
-> 5 locked to r56c9 -> r6c8 <> 5 -> r7c9 <> 8
21. 16(3) r567c9 = {57}4 / {25}9 ({39}4 blocked by r89c9) -> r56c9 <> 3, 8, 9
-> 8 locked to r12c9 -> r1c8 <> 8
22. Looking at 3s to eliminate 3 in common peer cell r7c8
a) if 3 in r23c8 -> r7c8 <> 3
b) if 3 in r3c7 -> 3 locked to r12c5 -> r7c4 = 3 -> r7c8 <> 3
Either option r7c8 <> 3
23. Looking at 3s to eliminate 3 in common peer cell r8c8
a) if 3 in r23c8 -> r8c8 <> 3
b) if 3 in r3c7 -> r3c6 = 1 -> r4c6 = 3 -> r4c9 = 2 -> 16(3) = {57}4 -> r89c9 = {13} -> r8c8 <> 3
Either option r8c8 <> 3
24. Revisiting 21(4) options now: 56{19/28} -> r7c7 <> 7
25. Split (10)3 r8c258 can’t now be {136} – blocked by r8c9
Remaining options {127/235}
26. Looking at 6s to eliminate 6 in common peer cell r6c5
a) r6c8 = 6 -> r6c5 <> 6
b) r7c8 = 6 -> 6 locked to 41(7) within N5 -> r6c5 <> 6
Either option r6c5 <> 6
27. 17(3) r678c5 = {179/269/278/359/368/458/467}
If {359} r6c5 = 9; if {458} r6c5 = 4 -> r6c5 <> 5
28. 19(3) r9c456 must have 9. Options: {289/379} -> r9c456 <> 5,6
-> 5,6 locked to r9c123 not elsewhere in N7
-> r8c1 of 15(3) is min 7 -> r9c12 <> 7,8
-> HS r8c7 = 6 -> r9c7 = 3 -> r8c9 = 1 -> r9c9 = 4 -> r9c8 = 7
-> lots more singles and reasonably straightforward with cage combos and singles from here

