Prelims
Only 39 Prelims in this, compared with 40 for the Twosomes, but I’ve listed them all because the cage pattern is so confusing and have given both cells for the same reason.
a) R1C1 + R7C7 = {18/27/36/45}, no 9
b) R15C2 = {29/38/47/56}, no 1
c) R1C3 + R4C6 = {17/26/35}, no 4,8,9
d) R1C49 = {19/28/37/46}, no 5
e) R1C5 + R3C7 = {69/78}
f) R15C6 = {19/28/37/46}, no 5
g) R16C7 = {15/24}
h) R1C8 + R7C2 = {59/68}
i) R29C1 = {29/38/47/56}, no 1
j) R2C25 = {29/38/47/56}, no 1
k) R2C3 + R7C8 = {19/28/37/46}, no 5
l) R2C4 + R5C7 = {14/23}
m) R27C6 = {19/28/37/46}, no 5
n) R24C7 = {15/24}
o) R2C8 + R5C5 = {16/25/34}, no 7,8,9
p) R28C9 = {69/78}
q) R3C19 = {29/38/47/56}, no 1
r) R3C2 + R8C7 = {19/28/37/46}, no 5
s) R38C3 = {29/38/47/56}, no 1
t) R37C4 = {69/78}
u) R3C58 = {16/25/34}, no 7,8,9
v) R39C6 = {16/25/34}, no 7,8,9
w) R4C13 = {39/48/57}, no 1,2,6
x) R4C49 = {19/28/37/46}, no 5
y) R4C58 = {49/58/67}, no 1,2,3
z) R57C1 = {16/25/34}, no 7,8,9
aa) R5C3 + R8C6 = {17/26/35}, no 4,8,9
bb) R58C4 = {18/27/36/45}, no 9
cc) R59C8 = {19/28/37/46}, no 5
dd) R5C9 + R9C5 = {49/58/67}, no 1,2,3
ee) R6C18 = {19/28/37/46}, no 5
ff) R6C29 = {15/24}
gg) R6C35 = {69/78}
hh) R6C6 + R9C9 = {29/38/47/56}, no 1
ii) R7C39 = {16/25/34}, no 7,8,9
jj) R7C5 + R9C3 = {19/28/37/46}, no 5
kk) R8C18 = {16/25/34}, no 7,8,9
ll) R8C25 = {18/27/36/45}, no 9
mm) R9C24 = {69/78}
1. Naked quad {1245} in R1246C7, locked for C7 -> R5C7 = 3 -> R2C4 = 2, clean-up: R1C1 = {123}, no 8 in R1C2, no 7 in R1C6, no 8 in R1C9, no 9 in R2C25, no 4 in R2C8, no 6,7,8,9 in R3C2, no 5 in R3C8, no 7 in R4C4, no 4 in R4C7, no 8 in R4C9, no 7 in R5C4, no 5 in R5C5, no 8 in R5C6, no 7 in R6C1, no 4 in R7C1, no 8 in R7C6, no 8 in R7C8, no 6,7 in R8C4, no 5 in R8C6, no 9 in R9C1, no 5 in R9C6, no 7 in R9C8
2. Naked quad {6789} in R789C7 + R8C9, locked for N9, clean-up: no 1,3,4 in R2C3, no 1,2,4 in R5C8, no 2,3,4,5 in R6C6, no 1 in R7C3, no 1 in R8C1
3. 7 in C8 only in R456C8, locked for N6, clean-up: no 3 in R4C4, no 6 in R9C5
4. Killer quad 6,7,8,9 in R6C18, R6C35 and R6C6, locked for R6
5. Min R9C7 = 6 -> max R4C2 + R6C4 = 8, no 8,9 in R4C2
6. 3 in R6 only in R6C14, CPE no 3 in R4C2
7. 45 rule on R4 3 innies R4C267 = 10 = {127/136/145/235}
7a. 3 of {136} must be in R4C6 -> no 6 in R4C6, clean-up: no 2 in R1C3
8. 45 rule on C6 3 innies R468C6 = 18 = {279/369/378/567} (cannot be {189} because 8,9 only in R6C6), no 1, clean-up: no 7 in R1C3, no 7 in R5C3
9. R15C6 = {19/46}/[82] (cannot be [37] which clashes with R468C6), no 3,7
10. R27C6 = {19/46}/[82] (cannot be {37} which clashes with R468C6), no 3,7
11. Using steps 9 and 10 combined cage R1257C6 = {1946/1982/4682}
11a. 7 in C6 only in R468C6 (step 8) = {378/567} (cannot be {279} which clashes with R1257C6), no 2,9, clean-up: no 6 in R1C3, no 6 in R5C3, no 2 in R9C9
11b. 9 in C6 only in R1257C6 = {1946/1982}, 1 locked for C6, clean-up: no 6 in R39C6
12. 2 in N5 only in R5C56, locked for R5, clean-up: no 9 in R1C2, no 5 in R7C1, no 6 in R8C6
13. R468C6 (step 11a) = {378/567}
13a. 6,8 only in R6C6 -> R6C6 = {68}, clean-up: no 4 in R9C9
14. Killer pair 6,8 in R6C35 and R6C6, locked for R6, clean-up: no 2,4 in R6C18
15. 2 in N4 only in R46C2, locked for C2, clean-up: no 9 in R5C2, no 7 in R8C5, no 8 in R8C7
16. 9 in C2 only in R79C2, locked for N7, clean-up: no 2 in R3C3, no 1 in R7C5
17. 2 in N1 only in R13C1, locked for C1, clean-up: no 9 in R2C1, no 5 in R5C1, no 5 in R8C8
18. 5 in N9 only in R79C9, locked for C9, clean-up: no 6 in R3C1, no 1 in R6C2, no 8 in R9C5
19. 3 in N4 only in R4C13 + R6C1
19a. R4C13 = {39} or R6C1 = 3 -> no 9 in R6C1, clean-up: no 1 in R6C8
20. Killer pair 1,3 in R57C1 and R6C1, locked for C1 -> R1C1 = 2 -> R7C7 = 7, clean-up: no 8 in R1C4, no 8 in R1C5, no 8 in R29C1, no 8 in R2C9, no 3 in R3C2, no 8 in R3C4, no 8,9 in R3C9, no 9 in R4C3, no 4 in R6C7, no 4 in R8C8, no 3 in R9C3
21. 4 in C7 only in R12C7, locked for N3, clean-up: no 6 in R1C4, no 7 in R3C1, no 3 in R3C5
22. 2 in C7 only in R46C7, locked for N6, clean-up: no 8 in R4C4, no 4 in R6C2
23. R34C1 = {89} (hidden pair in C1), clean-up: no 6,7 in R3C9, no 5,7,8 in R4C3
24. R4C267 (step 7) = {127/136/235} (cannot be {145} which clashes with R4C49), no 4
24a. 7 of {127} must be in R4C6 -> no 7 in R4C2
24b. 3 of {235} must be in R4C6 -> no 5 in R4C6, clean-up: no 3 in R1C3
25. Naked pair {37} in R48C6, locked for C6, clean-up: no 4 in R39C6
25a. R48C6 = {37} -> R6C6 = 8 (step 11a) -> R9C9 = 3, R3C6 = 5, R9C6 = 2, R3C9 = 2 -> R3C1 = 9, R4C1 = 8 -> R4C3 = 4, clean-up: no 3,7 in R1C2, no 7 in R1C4, no 6 in R1C5, no 6 in R2C2, no 7 in R2C3, no 7 in R3C3, no 6 in R4C49, no 5,9 in R4C58, no 7,8 in R5C8, no 7 in R6C35, no 3 in R7C1, no 5 in R7C3, no 6 in R7C4, no 6,8 in R7C5, no 1 in R7C8, no 4 in R8C1, no 7 in R8C2, no 2,6,7 in R8C3, no 1 in R8C4, no 8 in R9C3
26. Naked pair {67} in R4C58, locked for R4 -> R4C6 = 3 -> R1C3 = 5, R8C6 = 7, R5C3 = 1, R5C1 = 6, R6C1 = 3 -> R6C8 = 7, R7C1 = 1, R8C1 = 5 -> R8C8 = 2, R4C58 = [76], R6C35 = [96], R7C8 = 4 -> R2C3 = 6, R1C2 = 4 -> R5C2 = 7, R29C1 = [74], R1C7 = 1 -> R6C7 = 5, R24C7 = [42], R4C2 = 5, R6C2 = 2 -> R6C9 = 4, R1C5 = 9 -> R3C7 = 6
and the rest is naked singles.