Prelims
a) R12C1 = {14/23}
b) R4C12 = {19/28/37/46}, no 5
c) R4C34 = {17/26/35}, no 4,8,9
d) R4C67 = {17/26/35}, no 4,8,9
e) R56C1 = {16/25/34}, no 7,8,9
f) R56C2 = {19/28/37/46}, no 5
g) R6C56 = {16/25/34}, no 7,8,9
h) R67C9 = {18/27/36/45}, no 9
i) R89C1 = {39/48/57}, no 1,2,6
j) R8C56 = {13}
k) R9C23 = {17/26/35}, no 4,8,9
l) 22(3) cage at R1C5 = {589/679}
m) 20(3) cage at R2C9 = {389/479/569/578}, no 1,2
n) 9(3) cage at R3C7 = {126/135/234}, no 7,8,9
o) 22(3) cage at R7C8 = {589/679}
Steps Resulting From Prelims
1a. Naked pair {13} in R8C56, locked for R8 and N8, clean-up: no 9 in R9C1
1b. 22(3) cage at R1C5 = {589/679}, 9 locked for R1
1c. 22(3) cage at R7C8 = {589/679}, 9 locked for N9
2a. R56C1 = {16/25} (cannot be {34} which clashes with R12C1), no 3,4
2b. Killer pair 1,2 in R12C1 and R56C1, locked for C1, clean-up: no 8,9 in R4C2
3a. 45 rule on N7 2 innies R78C3 = 9 = [18/36]/{27/45}, no 9, no 6,8 in R7C3
3b. 45 rule on N7 2 outies R89C4 = 11 = {29/47/56}, no 8
4. 45 rule on N9 3 innies R7C79 + R9C7 = 9 = {126/135/234}, no 7,8, clean-up: no 1,2 in R6C9
5. 45 rule on R4 3 innies R4C589 = 19 = {289/379/469/478/568}, no 1
5a. 2,3 of {289/379} must be in R4C8 -> no 2,3 in R4C5, no 3 in R4C9
5b. 4 in R4 only in R4C12 = {46} or in R4C589 -> R4C589 = {289/379/469/478} (cannot be {568}, locking-out cages, or maybe it’s blocking cages), no 5
[Alternatively variable hidden killer triple 5,6,7 in R4C34, R4C67 and R4C589 for R4, R4C34 and R4C67 each contain one of 5,6,7 -> R4C589 cannot contain more than one of 5,6,7 -> R4C589 = {289/379/469/478} (cannot be {568} which contains 5 and 6), no 5
5c. 5 in R4 only in R4C34 = {35} or R4C78 = {35} (locking cages), 3 locked for R4, clean-up: no 7 in R4C12
5d. 9(3) cage at R3C7 = {126/234}, (cannot be {135} because R4C8 only contains 2,4,6), no 5
5e. 9(3) cage = {126/234}, CPE no 2 in R12C8
6. 45 rule on N4 3 innies R456C3 = 18 = {189/279/369/378/459/468/567}
6a. Hidden killer pair 3,7 in R56C2 and R456C3 for N4, R56C2 contains both or neither of 3,7 -> R456C3 must contain both of neither of 3,7 -> R456C3 = {189/378/459/468} (cannot be {279/369/567} which only contain one of 3,7), no 2, clean-up: no 6 in R4C4
6b. 1,5,6 of {189/459/468} must be in R4C3 -> no 1,5,6 in R56C3
6c. Consider combinations for R456C3 = {189/378/459/468}
R456C3 = {189/378/468}, 8 locked for N4
or R456C3 = {459} => R56C2 = {37} (hidden pair in N4)
-> no 8 in R56C2, clean-up: no 2 in R56C2
[Ed suggested 3 in N4 only in R56C2 = {37} or R456C3 = {378} -> no 8 in R56C2 (locking out cages).
wellbeback used R56C1 = {16} => R4C12 = [82] or R56C1 = {25} -> no 2 in R56C2 (effectively combined cages).]
7. 45 rule on C1 3 innies R347C1 = 21 = {489/579/678}, no 3
8. 45 rule on N2 3(2+1) outies R12C7 + R4C5 = 22
8a. Max R12C7 = 17 -> no 4 in R4C5
8b. Max R1C7 + R4C5 = 18 -> min R2C7 = 4
9. 45 rule on C12 2 outies R39C3 = 1 innie R1C2 + 3, IOU no 3 in R9C3, clean-up: no 5 in R9C2
10. 45 rule on C1234 2 outies R57C5 = 8 = [17/26/35/62], no 4,8,9, no 5,7 in R5C5
11. 45 rule on R89 2 outies R7C38 = 1 innies R8C2 + 6, IOU no 6 in R7C8
[After slow going, this step achieved much more than I expected.]
12. Consider combinations for R12C1 = {14/23}
R12C1 = {14} => R56C1 = {25} => R89C1 = [93] => R4C12 = [64]
or R12C1 = {23}, R56C1 = {16} => R4C12 = [82]
-> R4C12 = [64/82]
12a. R4C589 (step 5b) = {289/469} (cannot be {478} which clashes with R4C12), no 7
12b. Hidden quad 1,3,5,7 in R4C3467 -> R4C34 = {17/35}, R4C67 = {17/35}
12c. R347C1 (step 7) = {489/678} (cannot be {579} because R4C1 only contains 6,8), no 5, 8 locked for C1, clean-up: no 4 in R89C1
12d. Killer pair 2,6 in R4C12 and R56C1, locked for N4, clean-up: no 4 in R56C2
12e. 6 in N4 only in R456C1, locked for C1
12f. R9C23 = {17/26} (cannot be [35] which clashes with R89C1), no 3,5
12g. R78C3 (step 3a) = [18/36]/{45} (cannot be {27} which clashes with R9C23), no 2,7
12h. R89C1 = {57}/[93], R9C23 = {17/26} -> combined cage R89C1 + R9C23 = {57}{26}/[93]{17}/[93]{26}
12i. R78C3 = [18]/{45} (cannot be [36] which clashes with combined cage R89C1 + R9C23), no 3,6
12j. R456C3 (step 6c) = {189/378/459}, R78C3 = [18]/{45} -> combined cage R45678C3 = {189}{45}/{378}{45}/{459}[18], 4,5,8 locked for C3
13. 45 rule on R5 3 outies R6C128 = 14 = {158/167/239/257/356} (cannot be {248} because 4,8 only in R6C8, cannot be {347} because no 3,4,7 in R6C1, cannot be {149} because [194] clashes with R56C2 = [19], CCC), no 4 in R6C8
14. R456C3 (step 6c) = {189/378/459}
14a. Consider combinations for R78C3 (step 12i) = [18]/{45}
R78C3 = [18] => R456C3 = {459} => R56C2 = {37} (hidden pair in N4), locked for C2
or R78C3 = {45}, locked for N7 => R89C1 = [93]
-> no 3 in R7C2
14b. R9C1 = 3 (hidden single in N7) -> R8C1 = 9, clean-up: no 2 in R12C1
14c. Naked pair {14} in R12C1, locked for C1 and N1, clean-up: no 6 in R56C1
14d. Naked pair {25} in R56C1, locked for N4, R4C2 = 4 -> R4C1 = 6, R4C8 = 2
14e. 4 in C3 only in R78C3 = {45}, locked for N7 and 20(4) cage at R7C3, clean-up: no 3 in R4C4, no 6,7 in R89C4 (step 3b)
14f. R89C4 = [29], clean-up: no 6 in R5C5 (step 10)
14g. R7C8 = 9 (hidden single in N9)
14h. 16(3) cage at R9C5 = {178/268/457}
14i. 2 of {268} must be in R9C7 -> no 6 in R9C7
14j. Killer pair 2,7 in R9C23 and 16(3) cage, locked for R9
14k. 2 in N9 only in R7C79 + R9C7 (step 4) = {126/234}, no 5
14l. 16(3) cage at R9C5 = {178/268/457}
14m. 4 of {457} must be in R9C7 -> no 4 in R9C56
14n. 4 in N8 only in R7C46, locked for R7 -> R78C3 = [54], clean-up: no 3 in R5C5 (step 10)
14o. R6C56 = {16/34} (cannot be {25} which clashes with R6C1), no 2,5
14p. 15(3) cage at R1C2 = {267/357} (cannot be {258} because 5,8 only in R1C2), no 8,9, 7 locked for N1
14q. R37C1 = [87], R7C5 = 6, R5C5 = 2 (step 10), R56C1 = [52], clean-up: no 1 in R6C6, no 1 in R9C23
14r. Naked pair {26} in R9C23, locked for R9 and N7 -> R78C2 = [18], clean-up: no 9 in R56C2
14s. Naked pair {37} in R56C2, locked for C2 and N4 -> R4C3 = 1, R4C4 = 7
14t. R9C56 = {57} (hidden pair in N8), 5 locked for R9, R9C7 = 4 (cage sum)
14u. R9C89 = {18}, R8C9 = 5 (cage sum)
14v. R5C5 = 2 -> R5C34 = 14 = [86], R6C3 = 9, clean-up: no 1 in R6C5
14w. Naked pair {34} in R6C56, locked for R6 and N5 -> R4C67 = [53], R56C2 = [37], R7C7 = 2, R7C9 = 3 -> R6C9 = 6, R9C56 = [57]
14x. 20(3) cage at R2C9 = {479} (only remaining combination) -> R4C9 = 9, R23C9 = {47}, locked for C9 and N3 -> R5C6789 = [9741], R9C89 = [18], R8C78 = [67], R3C7 = 1, R3C8 = 6 (cage sum), R4C5 = 8
14y. R1C9 = 2 -> R12C8 = 11 = {38}, locked for C8 and N3 -> R6C78 = [85], R7C6 = 4, R6C45 = [43], R67C4 = [18], R8C56 = [31]
14z. R123C6 = [862] -> R1C57 = 14 = [95]
and the rest is naked singles.