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 Post subject: Ordered NC 4, 4H and 5
PostPosted: Sat Mar 07, 2020 5:36 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Ordered NC Killer 3

Non-consecutive but ordered so 89 is not allowed while 98 is allowed.

This is for Andrew as he suffered through the Vanilla one.

When you solve them please give your views on difficulty as it helps me to calibrate future puzzles.


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Ordered NC Killer 4

This is the easiest - just paper solvable

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Ordered NC Killer 4H

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Ordered NC Killer 5

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PostPosted: Mon Apr 06, 2020 2:54 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Ordered NC Killer 4 is straightforward, so I won't post my walkthrough.

Solution:
6 4 8 7 1 9 5 3 2
9 7 3 2 5 8 1 6 4
1 5 2 6 4 3 9 8 7
5 9 7 1 8 2 6 4 3
3 6 4 9 7 5 8 2 1
2 8 1 3 6 4 7 9 5
4 1 6 8 3 7 2 5 9
8 3 9 5 2 1 4 7 6
7 2 5 4 9 6 3 1 8


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PostPosted: Mon Apr 06, 2020 11:08 pm 
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Grand Master
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Location: Lethbridge, Alberta, Canada
Thanks HATMAN for that amusing comment! While Vanilla Sudokus aren't my favourites, they're occasionally useful when learning how to solve new variants.

Ordered NC Killer 3 was a fairly hard one, so I'd taken a break to do number 4 yesterday and came back to it today.

Here is my walkthrough for Ordered NC Killer 3:
NC increasing (ONC), 89 not allowed, 98 allowed.

Prelims

a) R23C2 = {16/25}/[43] (ONC)
b) R23C8 = [98] (ONC)
c) R45C3 = [98] (ONC)
d) R67C5 = {49/58}/[76] (ONC)
e) R8C12 = {19/28/37/46}, no 5
f) 13(4) cage at R4C1 = {1237/1246/1345}, no 8,9
g) 12(4) cage at R7C8 = {1236/1245}, no 7,8,9

1a. 13(4) cage at R4C1 = {1237/1246/1345}, 1 locked for N4
1b. 12(4) cage at R7C8 = {1236/1245}, 1,2 locked for N9
1c. R3C8 = 8 -> no 7 in R3C7 (ONC)
1d. R5C3 = 8 -> no 7 in R5C2, no 9 in R5C4 (ONC)
1e. 8,9 in C9 only in R456C9, locked for N6
1f. Hidden killer pair 8,9 for R45C9 and R6C9, R45C9 cannot be [89] (ONC) -> R45C9 must contain only one of 8,9 and R6C9 = {89}
1g. 18(3) cage at R3C3 = {279/369/459/567}, no 1

2a. 45 rule on N1 3 innies R123C3 = 14 = {167/257/347} (cannot be {356} which clashes with R23C2), 7 locked for C3 and N1
2b. 45 rule on C12345 2 innies R12C5 = 8 = {17/26/35}
2c. 45 rule on C12 2 innies R9C12 = 13 = {49/58}/[76] (ONC)
2d. R9C12 = 13 -> R89C3 = 8 = {26/35}
2e. 45 rule on N47 2 innies R67C3 = 6 = [24/42/51]
2f. R67C3 = 6 -> R67C4 = 9 = {18/27/36} (cannot be {45} which clashes with R67C3), no 4,5,9
2g. Killer pair 2,5 in R67C3 and R89C3, locked for C3
2h. Combined cage R67C3 + R89C3 = [2435/4253/5162] (ONC), no 2 in R8C3, no 6 in R9C3
2i. 45 rule on N4 3 innies R6C123 = 15 = {267/357/456}
2j. 2 of {267} must be in R6C3 -> no 2 in R6C12
2k. 5 of {357} must be in R6C3, {456} = [465/654] (ONC) -> no 5 in R6C1, no 4 in R6C2
2l. 45 rule on C67 2 innies R3C67 = 12 = [57/75/93]
2m. 18(3) cage at R3C3 (step 1g) = {279/369/459/567}
2n. 4 of {459} must be in R3C3 -> no 4 in R3C45
2o. 7 of {279} must be in R3C3, {567} = [657/765] (ONC) -> no 7 in R3C4

3a. 45 rule on N7 3 innies R7C123 = 14 -> max R7C12 = 13
3b. Hidden killer triple 7,8,9 in R7C12, R8C12 and R9C12 for N7, none of them can contain more than one of 7,8,9 -> each must contain one of 7,8,9 -> R8C12 = {19/28/37}, no 4,6
3c. R7C123 = {149/158/248/347} (cannot be {239/257/356} which clash with R89C3, cannot be {167} = [761] which clashes with R6C12), no 6
3d. R67C3 = 6 (step 2e), R6C123 (step 2i) = {267/357/456} = [762/375/735/465/654] -> R7C123 = {149/158/248} (cannot be {347} = {37}4 which clashes with R6C123 = [762]), no 3,7
3e. Consider placement for 6 in N7
R8C3 = 6 => R9C3 = 2 (step 2d)
or R9C2 = 6 => R6C123 = [375/735/654]
-> no 2 in R6C3 -> R67C3 + R89C3 (step 2h) = [4253/5162]
3f. R6C123 = {357/456}, 5 locked for R6 and N4, clean-up: no 8 in R7C5
3g. 2 in C3 only in R79C3, locked for N7, clean-up: no 8 in R8C12
3h. R7C123 = {149/158/248}
3i. 1 of {149/158} must be in R7C3 -> no 1 in R7C12
3j. R7C3 = {12} -> no 2 in R7C4 (ONC), clean-up: no 7 in R6C4 (step 2f)
3k. R8C3 = {56} -> no 6 in R8C4 (ONC)
3l. R9C3 = {23} -> no 3 in R9C4 (ONC)

4a. 45 rule on R123 4 innies R12C5 + R3C67 = 16, R12C5 = 8 (step 2b) -> R3C67 = 8 = {26/35}/[71], no 4,9, no 1 in R3C6
4b. R3C67 = 8 -> R4C67 = 11 = {47}/[65/83] (cannot be [56], ONC), no 1,2, no 3,5 in R4C6, no 6 in R4C7
4c. 18(3) cage at R3C3 (step 1g) = {279/369/459} (cannot be {567} which clashes with R3C67), 9 locked for R3 and N2
4d. 7 of {279} must be in R3C3 -> no 7 in R3C5
4e. 4 of {459} must be in R3C3 -> no 5 in R3C4 (ONC)
4f. 9 in R1 only in R1C12 -> no 8 in R1C1 (ONC)
4g. R23C2 = {16/25} (cannot be [43] because R23C2 = [43] + 18(3) cage = 7{29} clashes with R3C67), no 3,4
[With hindsight that was my key step. Looks like it’s now time for another forcing chain.]
4h. Consider combinations for R23C2
R23C2 = {16}, locked for N1 => R123C3 = {347}
or R23C2 = {25}, locked for C2 => R6C123 (step 3d) = [375/735/465] => R6C3 = 5 => R789C3 (step 3e) = [162]
-> R123C3 = {347}, 3,4 locked for C3 and N1, R6789C3 = [5162], clean-up: no 8 in R67C4 (step 2f), no 9 in R8C12
4i. Naked pair {37} in R8C12, locked for R8, 7 locked for N7
4j. R6C12 = {37} (cannot be [46] because 23(4) cage at R6C1 = [4685], ONC clashes with R23C2), locked for R6 and N4, clean-up: no 6 in R7C4 (step 2f), no 6 in R7C5
4k. 12(4) cage at R7C8 = {1236} (cannot be {1245} which clashes with R8C8), 3,6 locked for N9, 1 locked for C9
4l. R6C3 = 5 -> R6C4 = 2 (ONC), R7C4 = 7 (step 2f)
4m. 18(3) cage = {279/369/459}
4n. 3 of {369} must be in R3C3 -> no 3 in R3C45
4o. R6C4 = 2 -> no 1 in R5C4 (ONC)

5a. 45 rule on R89 4(2+2) innies R89C89 = 15 = [4173/5271] -> R9C8 = 7, R9C9 = {13}
5b. R89C9 = [13/21] -> R7C89 = {26/36}
5c. 45 rule on R67 4 (2+2) innies R67C89 = 19 = [19]{36} -> R6C89 = [19], R7C89 = {36}, locked for R7, 3 locked for N9 -> R89C9 = [21], R8C8 = 5, clean-up: no 4 in R7C5
[Cracked.]
5d. Naked triple R789C7 = {489}, 4 locked for C7
5e. R6C7 = 6, R7C6 = 2 (hidden single in N8) -> R6C6 + R7C7 = 12 = {48}
5f. Naked pair {48} in R6C56, locked for N5
5g. 45 rule on N5 2 remaining innies R45C6 = 15 = [69] -> R5C7 = 3 (step 2l), no 4 in R5C8 (ONC)
5h. R45C8 = [42], R4C9 = 8 (hidden single in N6) -> R5C9 = 7 (cage sum), R5C45 = [51], R4C45 = [37]
5i. R4C67 = [65] = 11 -> R3C67 = 8 = [71], no 6 in R3C5 (ONC), clean-up: no 6 in R2C2
5j. R12C7 = {27} = 9 -> R12C6 = 7 = [43] (ONC) -> R6C6 + R7C7 = [84], R89C6 = [15], R67C5 = [49], R8C45 = [48], R89C7 = [98], R9C45 = [63]
5k. R3C4 = 9 -> R3C35 = 9 = [45], R12C3 = [37], R12C4 = [81] (ONC), R12C5 = [26] (ONC)
5l. R2C7 = 2, R2C2 = 5 -> R3C2 = 2
5m. R7C12 = [58] -> R6C12 = [73] (ONC), R8C12 = [37] -> R9C12 = [94] (ONC)

and the rest is naked singles without using ordered NC.

Solution:
1 9 3 8 2 4 7 6 5
8 5 7 1 6 3 2 9 4
6 2 4 9 5 7 1 8 3
2 1 9 3 7 6 5 4 8
4 6 8 5 1 9 3 2 7
7 3 5 2 4 8 6 1 9
5 8 1 7 9 2 4 3 6
3 7 6 4 8 1 9 5 2
9 4 2 6 3 5 8 7 1


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PostPosted: Sat Apr 11, 2020 2:24 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
I enjoyed Ordered NC Killer 4H; an excellent puzzle about moderate Assassin level.

Same solution as Ordered NC Killer 4.

I used:
MinMax, which is something I rarely use for Assassins, and a short forcing chain to finally crack the puzzle.

Here is my walkthrough for Ordered NC Killer 4H:
NC increasing (ONC), 89 not allowed, 98 allowed.

Prelims

a) R9C89 = {18/27/36}/[54] (ONC), no 9
b) 26(4) cage at R1C1 = {2789/3689/4589/4679/5678}, no 1
c) 27(4) cage at R7C8 = {3789/4689/5679}, no 1,2
d) 14(4) cage at R8C6 = {1238/1247/1256/1346/2345}, no 9

1a. 45 rule on R12 2 innies R12C9 = 6 = {15/24}
1b. 45 rule on C89 using R12C9 = 6, 2 outies R12C7 = 6 = {15/24}
1c. Naked quad {1245} in R12C79, locked for N3
1d. R12C7 = 6 -> R12C8 = 9 = {36}, locked for C8 and N3, clean-up: no 3,6 in R9C9
1e. Naked triple {789} in R3C789, locked for R3
1f. 45 rule on N9 3 innies R789C7 = {135/234} (cannot be {126} which clashes with R12C7), 3 locked for N9
1g. Naked quint {12345} in R12789C7, locked for C7
1h. 27(4) cage at R7C8 = {4689/5679}
1i. R9C89 = {18/27} (cannot be [54] which clashes with 27(4) cage), no 4,5
1h. 6 in C7 only in R456C7, locked for N6
1i. Min R3C89 = 15 -> max R4C89 = 7, no 7,8,9
1j. Min R34C7 = 13 = [76] -> max R34C6 = 7 but cannot be {16}, no 6,7,8,9

2a. 45 rule of C6789 using R12C9 = 6, 3 outies R127C5 = 9 = {126/135/234}
2b. 45 rule of C5 using R127C5 = 9, 2 innies R89C5 = 11 = {29/38/47}/[65] (ONC), no 1
2c. R89C5 = 11 -> R89C4 = 9 = {18/27/36}/[54] (ONC), no 9
2d. 45 rule of C6789 using R12C9 = 6, 2 innies R12C6 = 1 outie R7C5 + 14
2e. Min R12C6 = 15 = {69/79}/[87/98] (ONC)
2f. Max R12C6 = 17 -> max R7C5 = 3
2g. R127C5 = {126} can only be [621] (because [261] clashes with R12C6 = [87], ONC), no 6 in R2C5
2h. R12C6 = {79}/[87/98] (cannot be {69} because R7C5 = 1, R12C5 = {35} and 23(4) cage at R1C5 = [3659/5936] (ONC) clashes with one of R12C8), no 6
2i. 25(4) cage at R3C5 = {1789/2689/3589/3679/4579/4678}
2j. 1 of {1789} must be in R3C5 -> no 1 in R456C5
2k. Max R7C57 = [35] = 8 -> min R7C6 = 5 (because {345} must be [354], ONC)

3a. 45 rule on R89 4(3+1) innies R8C789 + R9C1 = 28, max R8C789 = 24 -> min R9C1 = 4
3b. 45 rule on R89 4(2+2) innies R89C1 + R8C89 = 28, max R8C89 = 17 -> min R89C1 = 11, no 1 in R8C1

[I ought to have spotted this earlier; I never used it when solving the simpler version.]
4a. 45 rule on N89 1 innie R8C4 = 8, clean-up: no 1 in R89C4 (step 2c), no 3 in R89C5 (step 2b)
4b. R8C4 = 8 = R7C34 + R8C3 = 10 (127/136/145/235}, no 9, no 7 in R7C4 + R8C3 (ONC)
4c. 8 in N2 only in R12C6 = [87/98] (ONC) = 15,17 -> R7C5 = {13} (step 2d)
4d. 12(3) cage at R7C5 = {129/147/156/237}/[354] (cannot be {246} because R7C5 only contains 1,3)
4e. R7C5 = {13} -> no 1,3 in R7C7
4f. 3 in N9 only in R89C7, locked for 14(4) cage at R8C6
4g. R89C4 + R89C5 cannot be {27}[65] which clashes with R127C5 = {35}1/[621] and with 12(3) cage at R7C5 = [354/372] -> no 2,7 in R89C4
4h. R89C5 = {29/47} (cannot be [65] which clashes with R89C4), no 5,6
4i. 12(3) cage = {129/147/156/237} (cannot be [354] which clashes with R89C4)
4j. 14(4) cage at R8C6 contains 3 = {1346/2345}, no 7
4k. 1 of {1346} must be in R89C6 (R89C6 cannot be {46} which clashes with R89C4), no 1 in R89C7
4l. 1 in C7 only in R12C7 (step 1b) = {15}, locked for N3, 5 locked for C7
4m. Naked pair {24} in R12C9, locked for C9
4n. Naked triple {234} in R789C7, 2,4 locked for N9, clean-up: no 7 in R9C89
4o. Naked pair {18} in R9C89, locked for R9, 8 locked for N9
4p. 12(3) cage = {129/147/237} (cannot be {156} because 5,6 only in R7C6) -> R7C6 = {79}
4q. Killer pair 7,9 in R12C6 and R7C6, locked for C6
4r. R12C6 + R7C5 (step 2d) = [871/983] -> 12(3) cage = [192/372] (cannot be [174] which clashes with R12C6 + R7C5) -> R7C7 = 2, R89C7 = [43] (ONC), no 2 in R9C6 (ONC) -> R89C6 = 7 = [16/25], clean-up: no 6 in R8C4 (step 2c), no 7 in R9C5 (step 2b), no 5 in R8C7 (ONC)
4s. 7 in R9 only in R9C123, locked for N7
4t. R127C5 (step 2a) = {126/135} (cannot be {234} which clashes with R89C5), no 4, 1 locked for C5
4u. 2 of {126} must be in R2C5 -> no 2 in R1C5
4v. 4,6 in N8 only in R9C456, locked for R9

5a. 45 rule on C34 using R89C4 = 9 (step 2c) 4(2+2) innies R5C34 + R89C3 = 27, max R5C34 = 16 (cannot be [89], ONC) -> min R89C3 = 11, no 1
5b. Min R89C3 = 11 -> max R89C2 = 8, no 8,9
5c. Min R89C2 = 5 (cannot be [12], ONC) -> max R89C3 = 14 -> min R5C34 = 13, no 1,2,3

6a. R89C1 + R8C89 = 28 (step 3b), min R8C89 = {79} = 16 -> max R89C1 = 12, no 2
6b. 2 in N7 only in 19(4) cage at R8C2 = {1279/2359} (cannot be {2368} because 3,6,8 only in R8C23), no 6,8, 9 locked for C3 and N7
6c. R8C1 = 8 (hidden single for N7)
6d. R8C9 = 6 (hidden single in R8) -> no 5 in R7C9 (ONC)
6e. R7C8 = 5 (hidden single in N9) -> no 4 in R6C8 (ONC)

[With hindsight, if I’d spotted step 9a next, step 8 and particularly 8a would have been simpler.]

7a. Variable hidden killer pair 4,6 in R7C12 and R7C3 for R7 -> R7C12 must contain at least one of 4,6
7b. 15(4) cage at R6C1 = {1248/1347/2346} (cannot be {1239/1257/1356} which don’t contain 4 or 6), no 5,9

8a. 22(4) cage at R3C8 = [7915/8725/8743] (cannot be {79}{24} because 2,4 only in R4C8, cannot be [9823] (ONC), cannot be [9715] because R89C8 cannot be [78] (ONC), cannot be [9841] which clashes with R9C9), no 7 in R3C7, no 9 in R3C8, no 8 in R3C9, no 1 in R4C9
8b. 7 in C7 only in R456C7, locked for N7
8c. R3C89 = [79]
or R3C89 = [87] => R7C9 = 9
-> no 9 in R56C9
8d. 17(4) cage at R5C8 = {1259/1349/2348} (cannot be {1358} which clashes with R4C9)
8e. 1,3,5 of {1259/1349} must be in R56C9, 3,8 of {2348} must be in R56C9 -> no 1,8 in R56C8
8f. {2348} must be [4328] (ONC) -> no 8 in R5C9
8g. Min R34C6 = 4 (cannot be [21] which clashes with R8C6) -> max R34C7 = 16, no 8,9 in R4C7
8h. Min R34C7 = 14 -> max R34C6 = 6 = {13/14/24}/[32] (ONC) (cannot be {15} which clashes with R89C6), no 5
8i. Killer pair 1,2 in R34C6 and R8C6, locked for C6

9a. Consider combinations for 19(4) cage at R8C2 (step 6b) = {1279/2359}
19(4) cage = {1279} => R9C1 = 5 (hidden single in N7)
or 19(4) cage = {2359}, 3 locked for R8 => R8C4 = 5
-> R9C6 = 6, R8C6 = 1 (cage sum), R7C5 = 3 -> R7C6 = 7 (cage sum)
9b. R12C6 = [98] = 17 -> R12C5 = 6 = {15}, locked for N2, 5 locked for C5
9c. R7C9 = 9, R8C8 = 7, R3C789 = [987], R9C89 = [18]
9d. R89C4 = [54]
9e. Naked pair {29} in R89C5, locked for C5
9f. 4 in N2 only in R3C56, 4 locked for R3
9g. 7 in N2 only in R12C4, locked for C4 and 20(4) cage at R1C3
9h. 19(4) cage = {2359}, 5 locked for N7 -> R9C1 = 7
9i. 1,5 in R3 only in R3C123, locked for N1
9j. 15(4) cage at R6C1 (step 7b) = {1248/1347/2346}, R7C12 = {14/46} -> R6C12 = [28/37/32] (ONC) -> R6C1 = {23}, R6C2 = {278}

10a. R5C34 + R89C3 (step 5a) = 27
10b. R5C4 = {69} -> R589C3 must contain 9 in R89C3 = 18,21 = {279/369/459/579}
10c. 4,6,7 only in R5C3 -> R5C3 = {467}

11a. 18(4) cage at R6C3 = {136}8/{145}8 (cannot be {235}8 because R7C3 only contains 1,4,6, cannot be [7218] which clashes with R6C12), no 2,7
11b. 18(4) cage = {13}[68]/[5148] (cannot be {36}[18] which clashes with 15(4) cage at R6C1), 1 locked for R6, no 1 in R7C3
11c. 1 in R7 only in 15(4) cage at R6C1 (step 7b) = {1248/1347} -> R7C12 = {14}, R7C3 = 6, R6C34 = {13}, 3 locked for R6, R6C12 = [28], R6C89 = [95] = 14 -> R5C89 = 3 = [21], R4C89 = [43]
11d. R6C6 = 4, R5C6 = 5 (hidden single in C6) -> R56C7 = 15 = [87] -> R3456C5 = [4876], 20(4) cage at R3C6 = [3926], R456C4 = [193], R56C3 = [41]
11e. R4C3 = 7 (hidden single in C3), R4C4 = 1 -> R3C34 = 8 = [26], R2C3 = 6, R2C8 = 6 -> R2C7 = 1 (ONC), R1C8 = 3 -> R1C9 = 2 (ONC)

and the rest is naked singles without using ordered NC.


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PostPosted: Sun Apr 12, 2020 7:24 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Ordered NC Killer 5 was my least favourite of these four puzzles.

After an easy start which gave quite a lot of placements:
and reduced some of the square cages to single combinations, I had to use heavy interactions between the 23(4) cage and each of the 15(4) cages in R12.

Here is my walkthrough for Ordered NC Killer 5:
NC increasing (ONC), 89 not allowed, 98 allowed.

Prelims

a) R23C1 = {19/28/37/46}, no 5
b) R45C1 = {17/26/35}, no 4,8,9
c) R67C1 = {15/24}
d) R9C34 = {18/27/36}/[54] (ONC), no 9
e) R9C56 = {69/78}
f) R9C78 = {13}
g) 14(4) cage at R7C6 = {1238/1247/1256/1346/2345}, no 9
h) 27(4) cage at R7C8 = {3789/4689/5679}, no 1,2

1a. Naked pair {13} in R9C78, locked for R9 and N9, clean-up: no 6,8 in R9C34
1b. 27(4) cage at R7C8 = {4689/5679}, 6,9 locked for N9

2a. 45 rule on C1 3 innies R189C1 = 21 = {489/579/678}
2b. Hidden killer triple 1,2,3 in R23C1, R45C1 and R67C1 for C1, R45C1 and R67C1 each contains one of 1,2,3 -> R23C1 must contain one of 1,2,3 = {19/28/37}, no 4,6
2c. Killer triple 7,8,9 in R189C1 and R23C1, locked for C1, clean-up: no 1 in R45C1
2d. Killer pair 2,5 in R45C1 and R67C1, locked for C1, clean-up: no 8 in R23C1
2e. 45 rule on R123456 2 innies R16C1 = 8 = [62/71], clean-up: no 1,2 in R7C1
2f. R189C1 = {678} (only remaining combination)
2g. R7C1 = 4 (hidden single in C1) -> R6C1 = 2 -> R1C1 = 6
2h. Naked pair {35} in R45C1, locked for N4, 3 locked for C1
2i. R89C1 = [87] (ONC), clean-up: no 2 in R9C34, no 8 in R9C56
2j. Naked pair {19} in R23C1, locked for N1
2k. R9C34 = [54]
2l. R9C29 = [28] (hidden pair in R9)
2m. 27(4) cage at R7C8 = {5679}, 5,7 locked for N9
2n. 45 rule on C45 1 remaining innie R9C5 = 9 -> R9C6 = 6
2o. 45 rule on C67 1 remaining innie R9C7 = 3 -> R9C8 = 1
2p. R7C78 = [24] = 6, no 3,5 in R8C6 (ONC) -> R78C6 = 8 = [71] (ONC)
2q. 45 rule on N1 2 remaining innies R3C23 = 7 = [43/52] (ONC) -> R4C23 = 16 = {79}, locked for R4 and N4
ONC clean-ups: no 7 in R1C2, no 2 in R2C3, no 3 in R3C4, no 1 in R6C7, no 9 in R8C2, no 3 in R8C4, no 5 in R8C8, no 7 in R8C9
2r. R8C8 = 7 (hidden single in N9), no 6 in R7C8 (ONC)
2s. R7C8 + R78C9 = [596/965], 9 locked for R7, 6 locked for C9
2t. R8C3 = 9 (hidden single in N7) -> R4C23 = [97], no 8 in R4C4, no 8 in R5C3 (ONC)
2u. 45 rule on R12 1 remaining innie R2C1 = 9 -> R3C1 = 1
2v. 45 rule on R34 1 remaining innies R4C1 = 5 -> R5C1 = 3, no 4 in R5C2 (ONC)

3a. R2C2 = 7 (hidden single in N1) -> no 8 in R2C3 (ONC)
3b. R3C23 (step 2q) = [52] (cannot be [43] which clashes with R2C3)
3c. 8 in N1 only in R1C23, locked for R1
3d. R8C45 = {25}/[53] (cannot be [23], ONC), 5 locked for R8 and N8 -> R8C9 = 6, R7C89 = [59] (ONC), R8C2 = 3, no 4 in R6C8 (ONC)
3e. R1C23 + R2C3 = {48}3 (cannot be [834] ONC) -> R1C23 = {48}, 4 locked for R1, R2C3 = 3

4a. 1 in N2 only in 15(4) cage at R1C4 -> 15(4) cage at R1C4 = {1239/1248/1257/1347/1356}
4b. 23(4) cage at R1C6 = {1589/2489/2579/2678/3578} (cannot be {1679} because 1,6,7 on in R12C7, cannot be {3479} because R2C7 only contains 1,5,6,8, cannot be {3569} = [3956] ONC, cannot be {4568} because 4,6,8 only in R2C67)
4c. 5 in N3 only in R12C7 and 15(4) cage at R1C8
4d. 23(4) cage = {1589/2489/2579/3578} (cannot be {2678} = [2786] which clashes with 15(4) cage in R1C8 = {1257/1356}), no 6
4e. 2 in N2 only in 15(4) cage at R1C4 and R12C6
4f. 23(4) cage = {1589/2489/2579} (cannot be {3578} = [3785] (not [3758] ONC) which clashes with 15(4) cage in R1C4 = {1239/1248/1257}), no 3, 9 locked for R1
4g. 23(4) cage = {1589/2579} (cannot be {2489} = [2948] + R1C8 = 3 clashes with 15(4) cage at R1C4), no 4
4h. {2579} must be [9725] -> no 2 in R1C6
4i. 15(4) cage at R1C4 = {1257/1356} (cannot be {1248} which clashes with 23(4) cage, cannot be {1347} which clashes with [9725] and because 15(4) cage must contain 2 when 23(4) cage = {1589}), no 4,8, 5 locked for N2 -> R1C6 = 9
4j. 23(4) cage = {1589/2579} = [9581/9725] (cannot be [9185] which clashes with 15(4) cage at R1C8 = {2346} = [3264] ONC) -> R1C7 = {57}, R2C7 = {15}
4k. R1C8 = {23} -> no 3 in R1C9 (ONC)
4l. 15(4) cage at R1C8 = {1248/2346} (cannot be {1257/1356} which clash with R2C7, cannot be {1347} = [3741] ONC), no 5,7
4m. 6,8 of {1248} only in R2C8 -> R2C8 = {68}, R2C9 = 4, R1C89 = [21/32], 2 locked for R1
4n. 5 in C6 only in R56C6, locked for N5 and 24(4) cage at R5C6

5a. 5 in N6 only in 17(4) cage at R5C8 = {1259/1358/2456} (cannot be {1457} because 1,5,7 only in R56C9, cannot be {2357} = [2537/2735] ONC), no 7
5b. 7 in N6 only in R56C7, locked for C7 -> R12C7 = [51], R2C6 = 8 (cage sum), R1C89 = [32], R2C8 = 6, R3C49 = [67]
5c. 17(4) cage = {1259} (cannot be {1358} which clashes with R4C9, cannot be {2456} because 2,4 only in R5C8) -> R56C8 = [29]
5d. R2C89 + R3C8 = [874] = 19 -> R3C9 = 3 (cage sum)
5e. R3C7 + R4C6 = [92] = 11 -> R3C6 + R4C7 = 9 = [36]

and the rest is naked singles with using ordered NC.

Solution:
6 4 8 7 1 9 5 3 2
9 7 3 2 5 8 1 6 4
1 5 2 6 4 3 9 8 7
5 9 7 1 8 2 6 4 3
3 6 4 9 7 5 8 2 1
2 8 1 3 6 4 7 9 5
4 1 6 8 3 7 2 5 9
8 3 9 5 2 1 4 7 6
7 2 5 4 9 6 3 1 8


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