3x3:d:k:9216:3073:3330:3330:3330:6915:4868:4868:4868:9216:3073:3073:6915:6915:6915:3333:3333:4868:9216:9216:9216:9216:6915:6406:6406:6406:4868:4871:7944:7944:3337:3337:3337:6406:4627:4627:4871:4871:7944:7944:2572:2572:6406:4627:4627:5133:3086:7944:7944:2572:3855:3855:8976:8976:5133:3086:2833:2833:8210:3855:8976:8976:8976:5133:3086:7691:7691:8210:8210:8210:8210:8976:5133:5133:7691:7691:8210:3594:3594:3594:3594:

Preliminaries
Cage 13(2) n3 - cells do not use 123
Cage 11(2) n78 - cells do not use 1
Cage 10(3) n5 - cells do not use 89
Cage 19(3) n4 - cells do not use 1
Cage 30(4) n78 - cells ={6789}
Cage 14(4) n89 - cells do not use 9

1. "45" on n12: 1 innie r3c6 = 2
1a. "45" on n3: 2 outies r45c7 = 10 = {19/37/46}(no 5,8)

2. "45" on c1234: 4 innies r1c3 + r124c4 = 9
2a. min. r124c4 = 6 -> max r1c3 = 3
2b. max. r124c4 = 8 -> no 6,7,8,9, no 5 in r4c4

3. "45" on n1: 1 innie r1c3 + 3 = 1 outie r3c4 = [14/25/36]

First hard step
4. from step 2, r1c3 + r134c4 = 9 and from step 3, r1c3 + r3c4 = [14/25/36]
4a. -> r1c3 + r1234c4: [2]+[1..] blocked by can't reach 13(3)r1c345
4b. = [1][5142]/[2][4152]/[3][1362]
4c. r1c4 = (145), r2c4 = (13)
4d. r4c4 = 2, placed for d\
4e. -> r4c56 = 11 = {38/47/56}(no 1,9)
4f. and r1c345 = [157/247/319]
4g. -> r1c5 = (79)
4h. 1 must be in r12c4: locked for c4 and n2

5. "45" on r6789: 3 innies r6c345 = 11 (no 9)

6. "45" on n5: 3 innies r56c4 + r6c6 = 22 = {589/679}(no 1,3,4)

7. 10(3)n5 = {136/145}(no 7): if it has 4, also has 5
7a. r6c345 = 11 (step 5): but {245} as [254] only, blocked by 5 in 10(3) cage
7b. h11(3) = {128/137/146/236}(no 5)
7c. h22(3)n5 = {589/679} -> 8 in {589} must be in r6c4 -> no 8 in r5c4 nor r6c6

8. 10(3)n5 = {136/145}: if it has 3, also has 6
8a. h11(3)r6c345: but {236} as [263] only, blocked by 6 in 10(3)
8b. h11(3) = {128/137/146}
8c. must have 1: locked for r6
8d. can only have one of 6,7,8 -> no 6,7,8 in r6c35

This step was originally much more complicated but now manageable I hope.
9. "45" on n36: 3 innies r6c789 = 17: but {368} blocked by h11(3)r6 needing one of those (step 8b)
9a. = {269/278/359/458/467}(no eliminations yet)
9b. if 9 in r6c6 -> 15(3)r6c6 = [951/924] -> combined with h17(3)r6c789 -> r6c6789 = [95]{48}/[92]{78}
9c. ie, 9 in r6c6 must have 8 in r6c89
9d. h22(3)n5 = {589/679}: but [589] blocked by 8 in r6c89
9e. -> no 5 in r5c4

10. naked quad 6789 in r5689c4: all locked for c4
10a. no 3 in r1c3 (iodn1=-3)

11. 13(3)r1c3 = [157/247]
11a. r1c5 = 7, r1c4 = (45)

12. naked pair {45} in r13c4: both locked for n2 and c4
12a. r7c34 = [83], 8 placed for d/, r2c4 = 1

13. h22(3)n5 = {679} only: 6 & 7 both locked for n5

14. r4c56 = 11 = [83] only permutation, 3 placed for d/

15. h11(3)r6c345 = {137/146}(no 2)

16. 1 in n4 only in 31(6) = {135679} only (no 2,4)
16a. 3 & 5 locked for n4, no 9 in r5c12 since it sees all 9 in 31(6) (Common Peer Elimination CPE)

17. 5 in r6 only in n6 in h17(3) = {359/458}(no 2,6,7)

18. 2 in r6 only in n4: locked for n4

19. 2 in n47 only in two cages -> both must have 2
19a. -> 12(3)r6c2 = {129/246}(no 5,7,8)

20. 20(5)r6c1 must have 2 for n4/7 and 5 for n7
20a. = {12359/12458/23456}(no 7)

21. 7 in n7 only in r89c3: locked for c3 and 30(4)cage

22. 7 in c4 only in r56c4: locked for n5 and 31(6)

23. 7 in n4 only in 19(3) = {478} only: 4 and 8 locked for n4: 8 for r5

24. 8 in r6 only in r6c789 in h17(3) = {458} only: 4 locked for r6 and no 4,5 in r7c7 since it sees all of r6c789 (CPE), 4,5 locked for n6
24a. h11(3)r6c345 = [371], 7 placed for d/

25. naked pair {45} in r5c56: both locked for r5
25a. r4c1 = 4 (Hsingle n4)
25b. 7 in n4 only in r5c12: locked for r5

26. 2 and 4 in c3 only in n1: both locked for n1

27. r3c4 = (45) -> in n1, 12(3) must have at least one of 4 or 5
27a. {246} blocked by both 2 & 4 are only in r2c3
27b. = {147/156/345}(no 2,8,9)

28. hsingle 2 in n1 -> r1c3 = 2, r1c4 = 4 (cage sum), r3c4 = 5
28a. 36(6) = {16789/34789}[5]
28b. -> 7 locked for n1

29. r2c9 = 2 (hsingle n3), r5c8 = 2 (hsingle n6)

30. 2 on d/ only in n7: locked for n7

31. r7c5 = 2 (hsingle r7), r9c7 = 2 (hsingle n9), r8c2 = 2 (hsingle n7)
31a. -> r67c2 = 10 = [64/91]: note, has 6 in r6c2 or 1 in r7c2

32. 15(3)r6c6: {168} as [681] only, blocked by r67c2 (step 31a)
32a. = {159/456}(no 7,8)

33. 7 on d\ only in n9, locked for n9
33a. -> r7c7 = 7 (hsingle r7)

34. 7 in n6 only in 18(4) = {2367}: r5c9 = 3, 6 locked for n6 and r4

35. naked pair {19} in r45c7: both locked for c7 and not in r3c8

35. 2 innies n3 = 13 = [67] only: 6 placed for d/

36. r2c78 = [85/49]

37. 12(3)n1 = {156/345}
37a. 1 in {156} must be in r1c2 -> no 6 in r1c2

Last key step
38. 6 in r1 only in r1c16 -> no 6 in r6c6 (CPE)
38a. r6c6 = 9 (placed for d\), -> 15(3) = [951]

39. hsingle 4 on d/ -> r5c5 = 4: placed for d\

lots of naked stuff now.

This is a Killer-X.

Prelims

a) R2C78 = {49/58/67}, no 1,2,3
b) R7C34 = {29/38/47/56}, no 1
c) 19(3) cage at R4C1 = {289/379/469/478/568}, no 1
d) 10(3) cage at R5C5 = {127/136/145/235}, no 8,9
e) 30(4) cage at R8C3 = {6789}
f) 14(4) cage at R9C6 = {1238/1247/1256/1346/2345}, no 9

1a. 45 rule on N12 1 innie R3C6 = 2
1b. 45 rule on N3 2 innies R3C78 = 13 = {49/58/67}, no 1,3
1c. 45 rule on N3 2 remaining outies R45C7 = 10 = {19/37/46}, no 5,8

2. 45 rule on N47 5 outies R56789C4 = 33 = {36789/45789}, no 1,2, 7,8,9 locked for C4
2a. R4C4 = 2 (hidden single in C4), placed for D\
2b. 45 rule on N5 3 innie R56C4 + R6C6 = 22 = {589/679}, 9 locked for N5
2c. 10(3) cage at R5C5 = {136/145}, no 7, 1 locked for N5
2d. Killer pair 5,6 in R56C4 + R6C6 and 10(3) cage
2e. R4C4 = 2 -> R4C56 = 11 = {38/47}
2f. R56789C4 = {36789/45789} -> R7C4 = {34}, R7C3 = {78}
2g. 2 in C5 only in R789C5, locked for 32(6) cage at R7C5

3a. 45 rule on N1 1 outie R3C4 = 1 innie R1C3 + 3 -> R1C3 = {123}, R3C4 = {456}
3b. 45 rule on C1234 1 outie R1C5 = 1 remaining innie R2C4 + 6 -> R1C5 = {79}, R2C4 = {13}
3c. 1 in C4 only in R12C4, locked for N2
3d. Min R1C35 = 8 -> max R1C4 = 5
3e. 45 rule on N2 3 innies R1C45 + R3C4 = 16 = {169/457} (cannot be {349} which clashes with R7C4, cannot be {367} = [37]6 because 13(3) cage at R1C3 cannot be [337]), no 3

4. 45 rule on N457 4(1+3) innies R6C6 + R789C3 = 30
4a. Max R789C3 = 24 -> min R6C6 = 6
4b. Min R6C6 = 6 -> max R6C7 + R7C6 = 9, no 9 in R6C7 + R7C6

5. 45 rule on R6789 3 innies R6C345 = 11 = {128/137/146} (cannot be {236} = [263] which clashes with 10(3) cage = {136}, cannot be {245} = [254] which clashes with 10(3) cage = {145}), no 5,9, 1 locked for R6
5a. R6C4 = {678} -> no 6,7,8 in R6C35
5b. R56C4 + R6C6 (step 2b) = {589/679}
5c. 8 of {589} must be in R6C4 -> no 8 in R5C4 + R6C6

6. R56C4 + R6C6 (step 2b) = {589/679}
6a. R56C4 + R6C6 = {589} must be [589] when 15(3) cage at R6C6 = [924/951]
6b. 45 rule on N1236 3 innies R6C789 = 17 = {278/359/368/458/467} (cannot be {269} which clashes with R56C4 + R6C6)
6c. R6C789 = {278/359/368/458} (cannot be {467} because R56C4 + R6C6 = {589} + 15(3) cage = [924/951] doesn’t include 4,6,7 in R6C7 and {467} clashes with R56C4 + R6C6 = {679})
6d. R56C4 + R6C6 = {679} (cannot be {589} = [589] which clashes with R6C789), 6,7 locked for N5
6e. R4C56 (step 2e) = {38}, locked for R4, 3 locked for N5
6f. R5689C4 = {6789} -> R7C4 = 3 (step 2), R7C3 = 8, placed for D/, R4C6 = 3, placed for D/, R4C5 = 8, R2C4 = 1
6g. R13C4 = {45} (hidden pair in C4), locked for N2, R1C45 + R3C4 = 16 (step 3e) -> R1C5 = 7, R1C34 = 6 = [15/24]
6h. Naked pair {45} in R13C4, CPE no 4,5 in R1C1
6i. 8 in C4 only in R89C4, locked for N8
6j. R6C345 (step 5) = {137/146}, no 2
6k. R6C789 = {278/359/458} (cannot be {368} which clashes with R6C345), no 6
6l. Combined cages R6C345 + R6C789 = {137}{458}/{146}{278}/{146}{359}, 4 locked for R6
Clean-ups: no 5 in R2C7, no 5 in R3C8 (step 1b), no 7 in R5C7 (step 1c)

7a. 36(6) cage at R1C1 = {156789/246789/345789}, 7,8,9 locked for N1
7b. 12(3) cage at R1C2 = {156/246/345}

8. 31(6) cage at R4C2 = {135679/234679}, 3 locked for C3 and N4
8a. 3 in R6 only in combined cages R6C345 + R6C789 (step 6l) = {137}{458}/{146}{359}, no 2
8b. R6C789 = {359/458}, 5 locked for R6 and N6
8c. 2 in R6 only in R6C12, locked for R6 -> 31(6) cage = {135679}, no 4, 5 locked for N4
8d. 2,4 in C3 only in R123C3, locked for N1
8e. 12(3) cage at R1C2 (step 7b) = {156/345} (cannot be {246} because 2,4 only in R2C3), no 2
8f. R1C3 = 2 (hidden single in N1) -> R1C4 = 4 (cage sum), R3C4 = 5
8g. R3C78 (step 1b) = {49/67}, no 8
8h. R45C7 (step 1c) = {19}/[73] (cannot be {46} which clashes with R3C78), no 4,6
8i. 25(5) cage at R3C6 = 2{49}[73]/2{67}{49}, CPE no 7,9 in R12C7, clean-up: no 4,6 in R2C8
8j. R2C9 = 2 (hidden single in N3)
8k. R5C8 = 2 (hidden single in N6)
8l. R9C7 = 2 (hidden single in N9)
8m. R8C2 = 2 (hidden single on D/) -> R67C2 = 10 = [64/91]
8n. R6C1 = 2 (hidden single in C1)
8o. Naked triple {679} in R6C246, locked for R6
8p. R6C789 = {458}, 4 locked for R6, 4,8 locked for N6 -> R6C35 = [31], R6C4 = 7 (step 6j), placed for D/
8q. Naked pair {45} in R5C56, locked for R5
8r. R4C1 = 4 (hidden single in N4) -> R5C12 = {78} (hidden pair in N4), 7 locked for R5
8s. 30(4) cage at R8C2 = {6789}, 7 locked for C3 and N7
8t. Min R6C67 = 10 -> max R7C6 = 5
8u. 7 in R7 only in R7C789, locked for N9
8v. R2C1 = 7 (hidden single in R2) -> R5C12 = [87]
8w. R3C2 = 8 (hidden single in N1)
8x. R7C7 = 7 (hidden single on D\), R45C7 (step 8h) = {19}, locked for C7 and N6, 9 locked for 25(5) cage at R3C6) -> R3C78 (step 8g) = [67], 6 placed for D/, R4C8 = 6, R5C9 = 3
8y. R7C5 = 2 (hidden single in N8)
8z. Naked triple {689} in R126C6, 6,9 locked for C6

9a. R5C5 = 4 (hidden single on D/), placed for D\ -> R5C6 = 5
9b. 5 in C5 only in R89C5, locked for 32(6) cage at R7C5
9c. Naked triple {159} on D/, CPE no 1 in R1C1 + R9C9
9d. Naked pair {14} in R7C26, locked for R7
9e. 14(4) cage at R9C6 = {1238/2345} (cannot be {1247} because R9C9 only contains 5,6,8, cannot be {1256} which clashes with R7C78), no 6,7
9f. 14(4) cage at R9C6 = {1238/2345} -> R9C8 = 3
9g. R8C6 = 7 (hidden single in N8) -> R9C3 = 7 (hidden single in N7)
9h. 32(6) cage contains 2,5,7 = {125789/245678}, 8 locked for R8 and N9
9i. R9C9 = 5, placed for D\, R9C78 = [23] -> R9C6 = 4 (cage sum), R7C6 = 1, R7C2 = 4 -> R6C2 = 6 (cage sum), R6C6 = 9, placed for D\, R6C7 = 5 (cage sum), R7C89 = [96]
9j. Naked pair {19} in R9C12, locked for N7, 9 locked for R9
9k. R2C8 = 5 -> R2C7 = 8, R1C8 = 1, R1C9 = 9, placed for D/

and the rest is naked singles, without using the diagonals.

I'll rate my WT for A387 at Hard 1.25 for my hardest analysis step.

1. Innies n12 -> r3c6 = 2
Innies n3 -> r3c78 = +13(2)
-> r45c7 = +10(2)
-> r6c789 = +17(3)

2. IOD n1 -> r3c4 = r1c3 + 3
Innies c1234 = r1c3 + r124c4 = +9(4)
-> r1234c4 = +12(4) = {1236} or {1245}
-> r4c4 = 2

3. Innies n5 = +22(3) = {589} or {679}
30(4)r8c3 = {6789}
Innies r6789 = r6c345 = +11(3)

(Ed's way of removing one possibility (his Step 9 ) is better than mine!)

4. Trying r1234c4 = [{136}2] puts ...

r1c3 = 3 and r123c4 = [136]
HP r23c9 = [13] and 2 in n3 in r1
Also puts 1 in n1 in r3
puts HS 2 in n1 r2c3 = 2 (Since 36(6) cannot contain both 1 and 2, and 2 already on D\)

Also HS 4 in c4 puts 11(2)r7c3 = [74]
puts 7 in r89c4
puts H+22(3)n5 = {589}
puts 10(3)n5 = {136}

which leaves no solution for r6c345 = +11(3)

-> r123c4 = {145}

5. 13(3)r1 cannot contain both (12)
-> [r1c3][r123c4] from [1][514] or [2][415]
-> HS 3 in c4 -> 11(2)r7c3 = [83]
-> 8 in r89c4
-> Innies n5 = {679}
-> 10(3)n5 = {145}
-> 13(3)n5 = [283]

6. r6c345 = +11(3) from [371] or <164>
r6c789 = +17(3)
The only way 2 could be in there is if it is {278}
which puts r56c4 = [76]
which leaves no place for both (67) in n4
-> 2 in r6c12
-> 2 in c3 in r12c3

7. r6c126 = +17(3) and r6c6 from (679)
For r6c345 = [371] -> r6c126 = {269} -> 19(3)n4 = {478}
For r6c345 = <164> -> r6c126 = [{28}7] -> r5c4 = 9 -> 19(4) = {469}
Either way 4 in 19(3)n4
-> 4 in c3 in r123c4

8. -> For the case where r1c3,r123c4 = [1][514] -> No room for both (24) in n1
-> r1c3 = 2, r123c4 = [415]
-> r1c5 = 7
Also -> HS 2 in n3 r2c9 = 2
-> HS 2 in n6 r5c8 = 2
2 in n8 in r789c5
-> HS 2 in c7/n9 -> r9c7 = 2
-> HS 2 in D/ -> r8c2 = 2
-> HS 2 in n4 -> r6c1 = 2
-> HS 2 in n8 -> r7c5 = 2
Also r6c2 cannot be 8 -> r6c26 = {69}
-> r6c345 = [371]
-> r6c789 = {458}
Also r5c56 = {45}
-> 19(3)n4 = [4{78}]

9. This finishes it off
5 in r3c4 -> 5 in n1 in 12(3) = {156} or {345}
-> 7 in D\ in n9
r6c6 from (69) and r6c7 from (458} -> r7c6 cannot be 7
-> 7 in r7 in n9
-> r7c7 = 7

10. -> 35(6)r6c8 contains a 7 and not a 2
-> 35(6) = [{48}7{169}]
Also r45c7 = {19}
-> r3c78 = [67]
Also r6c7 = 5
-> r67c2 and r67c6 are between them [91] and [64]
-> r8c9 = 1
-> r1c8 = 1
-> HS 1 in D/ -> r9c1 = 1
-> 12(3)r6c2 = [642] and 15(3)r6c6 = [951]
Also HS 1 in D\ -> r3c3 = 1
Also 9 in r1 in r1c9
-> 13(2)r2c7 = [85]
etc.