Prelims
a) R1C56 = {29/38/47/56}
b) R1C78 = {59/68}
c) R23C1 = {18/27/36/45}, no 9
d) R34C2 = {18/27/36/45}, no 9
e) R45C1 = {69/78}
f) R56C9 = {79}
g) R67C4 = {17/26/35}, no 4,8,9
h) R67C8 = {17/26/35}, no 4,8,9
i) R78C9 = {18/27/36/45}, no 9
j) R8C34 = {19/28/37/46}, no 5
k) R9C23 = {18/27/36/45}, no 9
l) R9C45 = {49/58/67}, no 1,2,3
m) 38(8) cage at R1C9 = {12345689}, no 7
1a. Naked pair {79} in R56C9, locked for C9 and N6, clean-up: no 1 in R7C8, no 2 in R78C9
1b. R1C56 = {29/38/47} (cannot be {56} which clashes with R1C78), no 5,6
1c. 7 in N3 only in R3C78, locked for R3 and 29(6) cage at R3C7, clean-up: no 2 in R2C1, no 2 in R4C2
2a. 45 rule on N7 3 innies R7C23 + R8C3 = 21 = {489/579/678}, no 1,2,3, clean-up: no 7,8,9 in R8C4
2b. 45 rule on N9 2 outies R7C56 = 1 innie R7C8 + 2, IOU no 2 in R7C56
2c. Max R7C8 = 7 -> max R7C56 = 9, no 9 in R7C56
2d. 15(4) cage at R7C5 = {1248/1257/1347/1356/2346} (cannot be {1239} = {13}{29} which clashes with R7C8 = 2, step 2b), no 9
2e. 9 in R7 only in R7C123, locked for N7, clean-up: no 1 in R8C4
2f. 45 rule on N9 3 innies R7C78 + R8C7 = 13 = {157/238/247/256/346} (cannot be {148} because no 1,4,8 in R7C8)
2g. 45 rule on R9 2 innies R9C16 = 1 outie R8C8
2h. Min R9C16 = 3 -> min R8C8 = 3
2i. Max R8C8 = 9 -> max R9C16 = 9, no 9 in R9C6
2j. 45 rule on N89 3 innies R78C4 + R7C8 = 14
2k. R78C4 cannot total 12 -> no 2 in R7C8, clean-up: no 6 in R6C8
2l. R78C4 cannot total 8 (which clashes with R67C4, CCC) -> no 6 in R7C8, clean-up: no 2 in R6C8
2m. R7C8 = {357} -> R7C56 = 5,7,9 must contain one even number -> 15(4) cage = {1248/1347/1356/2346} (cannot be {1257} because 2 only in R78C7)
2n. 45 rule on N47 2 outies R48C4 = 1 innie R4C2 + 4, IOU no 4 in R8C4, clean-up: no 6 in R8C3
3a. 45 rule on N1 2 outies R3C45 = 1 innie R3C2 + 3, IOU no 3 in R3C45
3b. 45 rule on N2 4 innies R2C6 + R3C456 = 17 = {1259/1268/1358/2456} (cannot be {1349/2348} which clash with R1C56)
3c. 17(3) cage at R1C4 = {179/269/359/368/458/467} (cannot be {278} which clashes with R1C56)
3d. 45 rule on R89 2 outies R7C19 = 1 innie R8C7 + 5, IOU no 5 in R7C1
4a. 12(3) cage at R4C8 = {138/156/246/345}
4b. R45C8 cannot be {13} which clashes with R67C8 -> no 8 in R4C9
[Odds and evens in N8]
5a. R7C8 is odd -> R7C56 must be odd (step 2b)
5b. R7C8 is odd -> R78C4 must be odd (step 2j)
5c. R7C56, R78C4 and R9C45 are all odd so must each contain one even number -> 16(3) cage at R8C5 must contain only one even number = {169/178/259/349/358/367} (cannot be {268} with three even numbers, cannot be {457} which clashes with R9C45)
[Unfortunately not particularly useful (and unnecessary after step 6c) unlike wellbeback’s powerful odds and evens step in Assassin 413.]
6a. 45 rule on N89 2 innies R7C48 = 1 outie R8C3 + 4
6b. R8C3 = {478} -> R7C48 = 8,11,12 = [17]/{35/57} (cannot be {26} because no 2,6 in R7C8, cannot be [65] because R7C48 + R8C3 = [657] clashes with R7C23 + R8C3, step 2a), no 2,6 in R7C4, clean-up: no 2,6 in R6C4
6c. R7C48 = [17]/{35/57} = 8,12 -> no 7 in R8C3, clean-up: no 3 in R8C4
6d. R7C48 + R8C3 (step 2a) = {489/678} (cannot be {579} because R8C3 only contains 4,8), no 5
6e. R7C48 + R8C3 = {489} (cannot be {678} = {67}8 which clashes with R7C48 + R8C3 = {57}8), locked for N7, 9 locked for 30(6) cage at R4C4, clean-up: no 1,5 in R9C23
6f. R7C48 + R8C3 = {489}, CPE no 4,8 in R456C3
6g. R9C45 = {49/58} (cannot be {67} which clashes with R9C23), no 6,7
7a. 16(3) cage at R8C5 (step 5c) = {169/178/349/358/367} (cannot be {259} which clashes with R9C45), no 2
7b. R8C4 = 2 (hidden single in N8) -> R8C3 = 8, clean-up: no 1 in R7C9
7c. Naked pair {49} in R7C23, 4 locked for R7 and 30(6) cage at R4C4, clean-up: no 5 in R8C9
7d. 45 rule on N47 1 remaining outie R4C4 = 1 innie R4C2 + 2, no 7,8 in R4C2, no 1 in R4C4, clean-up: no 1,2 in R3C2
7e. R8C3 = 8 -> R7C48 = 12 (step 6a) = {57}, locked for R7, clean-up: no 5,7 in R6C4, no 5 in R6C8, no 4 in R8C9
7f. Naked pair {13} in R6C48, locked for R6
7g. 15(4) cage at R7C5 (step 2m) = {1248/1356/2346} (cannot be {1347} because 4,7 only in R8C7), no 7
7h. 4,5 of 15(4) cage only in R8C7 -> R8C7 = {45}
7i. 2 of {1248} must be in R7C7 -> no 8 in R7C7
7j. R7C78 + R8C7 (step 2f) = {157/247} (cannot be {256/346} because no 2,3,6 in R7C8 + R8C7) -> R7C8 = 7, R78C7 = [15/24], R6C8 = 1, R67C4 = [35], clean-up: no 1,3 in R4C2 (step 7d), no 6,8 in R3C2, no 8 in R9C45
7k. Naked pair {49} in R9C45, locked for R9 and N8
7l. R8C78 = [49] (hidden pair in N9) -> R7C7 = 2, clean-up: no 5 in R1C7
7m. 2,4 in N6 only in 12(3) cage at R4C8 = {246}, 6 locked for N6
7n. Naked triple {358} in R456C7, locked for C7 and 29(6) cage at R3C8, clean-up: no 6 in R1C8
7o. R1C7 = 7 (hidden single in N3), R456C7 = {358} = 16 -> R3C8 + R6C6 = 6 = {24}
7p. Naked pair {24} in R3C8 + R6C6, CPE no 2,4 in R3C6
7q. Caged X-Wing for 2,4 in R3C8 + R6C6 and 38(8) cage at R1C9 in C6 and N3 -> 2,4 in R246C6, locked for C6, clean-up: no 7,9 in R1C5
7r. Naked triple {246} in R345C8, locked for C8, 6 locked for N6
7s. 5 in N9 only in R9C89, locked for R9
7t. 45 rule on N1 3 innies R2C3 + R3C23 = 18 = {369/459/567} (cannot be {189/279} because R3C2 only contains 3,4,5), no 1,2
7u. 3,4 of {369/459} must be in R3C2 (R23C3 cannot be {49} which clashes with R7C3 -> no 3,4 in R23C3
7v. R3C45 = R3C2 + 3 (step 3a)
7w. Max R3C2 = 5 -> max R3C45 = 8, no 8,9 in R3C45
7x. R3C2 = {345} -> R3C45 = 6,7,8 = [15]/{16}/[62] (cannot be {24} which clashes with R3C8, cannot be {25} because 2,5 only in R3C5), no 4
8a. R4C4 = R4C2 + 2 (step 7d) -> R4C24 = [46/57/68]
8b. R7C23 = {49} = 13 -> R456C3 + R4C4 = 17 = {1358/1367} (cannot be {1268/2357} which clash with R4C24, CCC) -> R456C3 = {135/136/137}, no 2
[Reworked from here; I’d overlooked that {1367} can be either {136}7 or {137}6]
8c. R6C3 = {567} -> R45C3 = {13}, locked for C3 and N4, clean-up: no 6 in R9C2
8d. 2 in N4 only in 15(3) cage at R5C2 = {249/258} (cannot be {267} which clashes with R45C1), no 6,7
8e. 45 rule on N5 3 remaining innies R4C46 +R6C6 = 17 = [764/782/854] (cannot be [692] because R4C4 + R4C89 = {246} clashes with R4C24, CCC)
8f. R4C4 = {78} -> R4C2 = {56}, R3C2 = {34}, R6C3 = {56}
[Then continuing as previously, with sub-steps renumbered]
8g. Naked pair {56} in R4C2 + R6C3, locked for N4, clean-up: no 9 in R45C1
8h. Naked pair {78} in R45C1, locked for C1, 8 locked for N4, clean-up: no 1,2 in R23C1
8i. Naked triple {249} in R567C2, locked for C2, 2 locked for N4
8j. R3C2 = 3 -> R4C2 = 6, R4C4 = 8, R45C1 = [78], R6C3 = 5, R9C2 = 7 -> R9C3 = 2, clean-up: no 6 in R23C1
8k. Naked pair {45} in R23C1, locked for C1 and N1 -> R6C1 = 9, R56C9 = [97]
8l. 45 rule on N1 2 remaining innies R23C3 = 15 = {69}, locked for N1, 9 locked for C3
8m. R23C3 = 15 -> R3C45 = 6 = [15], R23C1= [54], R3C8 = 2, R6C6 = 4
8n. R1C3 = 7, clean-up: no 4 in R1C5
9a. 45 rule on N5 1 remaining innie R4C6 = 5
9b. R1C8 = 5 (hidden single in N3) -> R1C7 = 9, clean-up: no 2 in R1C5
9c. 38(8) cage at R1C9 = {12345689} -> R23C6 = [29]
9d. R3C39 = [68], clean-up: no 1 in R8C9
9e. Naked pair {36} in R78C9, locked for C9 and N9
9f. R78C7 = [24] -> R7C56 = 9 = {18} (cannot be {36} which clashes with R7C9), locked for N8, 1 locked for R7
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