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PostPosted: Mon Jan 20, 2020 5:51 am 
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MR 0,1,2,4,5,6,7


I'm not sure if these puzzles are interesting enough to continue with so I've created a batch for your views.

When a Restrained Killer Sudoku is created in JSudoku you can invariably solve it with very little use of the constraint. In Vanilla's that is not the case. I'm not sure if this is a killer point or Jean-Christophe's coding (Tarek your thoughts?). Hence I thought why apply the constraint everywhere, why not just apply it to a few cells, perhaps unknown.

Where you choose a cell that choice may not be unique but the solution is. For those where I have given placement they obviously can be solved without knowing them. In this case I believe the solution is unique but do not have the tools to prove it without heavy labour.

If you attempt these without the placement I would be grateful for demonstration of multiple solutions or proof of uniqueness.

Number 3 is vanilla and I still have not finished creating it, so I am taking a different approach see snowflakes next week.


MR 0 NC 1-cell
This is an easy one to start find one cell that is NC.

Image

MR 1 AkN-3
Find the three cells that are Anti-kNight (AN).

Image

MR 2 AkN 6 8 8
The position of two AN cells is given so find the third one.

Image

MR 4 NC 7-cell
The position of the seven NC cells is given. Alternatively find the cells knowing that they are 2236789.

Image

MR 5 NC 1-Cell
Find one NC cell to solve it.

Image

MR 6 NC 2-Cell
Find two NC cells to solve it

Image


MR 7 NC 1-Cell
Find one NC cell to solve it

Image


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PostPosted: Tue Jan 21, 2020 5:41 pm 
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I haven't looked closely at these yet Maurice. The declared NC or Anti-Chess cells are a concept which I can see. Finding a hidden cell that is NC or anti-chess is a bit more tricky and may depend on the solution path as you progress.

tarek


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PostPosted: Tue Jan 28, 2020 11:45 pm 
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As HATMAN said the first one is very easy. Just routine killer steps, easier than the earliest Assassins, to reach
Selecting the NC cell:
Attachment:
Minimum Constraints 0 NC 1-cell.jpg
Minimum Constraints 0 NC 1-cell.jpg [ 73.6 KiB | Viewed 7738 times ]

Naked pairs {17} in R23C6 and R23C7 -> R3C5 = 6 must be the NC cell -> R23C6 = [71], R23C7 = [17]

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


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PostPosted: Thu Jan 30, 2020 6:56 pm 
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I got stuck with Minimum Constraints 1 Anti-Knight 3. Maybe it's because I don't have enough experience with Anti-Knight puzzles.

I reached the following position which I hope is correct
After normal killer steps:
Attachment:
Minimum Constraints 1 Anti-Knight 3 (1).jpg
Minimum Constraints 1 Anti-Knight 3 (1).jpg [ 76.21 KiB | Viewed 7724 times ]

After applying two Anti-Knight Steps:
There seem to be three separate chains of values. I used 2 in R7C3 to remove 2 from R5C2 + R6C1 and 1 in R7C7 to remove 1 from R9C6. This left the following position where there is clearly one chain. I think R147C9 needs to become [187] but I can't see an Anti-Knight to immediately force this except for a Toroidal one, for example 7 in R8C1 removing 7 from R7C8, but I think that would be against the rules.
Attachment:
Minimum Constraints 1 Anti-Knight 3 (2).jpg
Minimum Constraints 1 Anti-Knight 3 (2).jpg [ 74.45 KiB | Viewed 7724 times ]


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PostPosted: Sat Feb 01, 2020 10:53 am 
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Andrew

OKish

Clue: look through the other end of the telescope


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PostPosted: Sun Feb 02, 2020 6:37 am 
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Thanks HATMAN for the hint.:
There's only one cell to which it can apply. R4C8 = 1 (cannot be 4,8 because of R2C7 = 8 and R2C9 = 4, or I could have chosen a different 4 but I spotted that 8,4 pair first). Like a double-barrelled shotgun; potentially any AN cell can be surrounded by 8 different values.
As I said I don't have enough experience with Anti-kNight puzzles.

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


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PostPosted: Sun Feb 02, 2020 10:30 pm 
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The early killer steps for Minimum Restraints 5 NC 1-cell weren't much harder than for the first one, maybe a bit closer to the very earliest Assassins.

My Key Steps Were:
45 rule on N1 2(1+1) outies R3C4 + R4C1 = 5
45 rule on C12 2 outies R19C3 = 1 innie R6C2 + 15 after eliminating 8 from R9C3
and 45 rule on C6789 4 innies R1489C6 = 14 which usefully eliminated 9 from R89C6

Position immediately after using one NC:
Attachment:
Minimum Constraints 5 NC 1-cell.jpg
Minimum Constraints 5 NC 1-cell.jpg [ 75.69 KiB | Viewed 7680 times ]

R6C9 = 4, no 5 in R6C8 (NC) -> R6C8 = 7

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


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PostPosted: Wed Feb 05, 2020 9:40 pm 
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Unless I missed something easier, the early killer steps of Minimum Restraints 2 Anti-Knight 6 8 8 were moderate Assassin level. Then the third AN cell was obvious.

My walkthrough for Minimum Restraints 2 Anti-Knight 6 8 8:
The positions of two Anti-kNight (AN) cells R3C3 and R7C7 are given, so find the third one.

Prelims

a) R12C3 = {18/27/36/45}, no 9
b) R1C67 = {29/38/47/56}, no 1
c) R23C5 = {49/58/67}, no 1,2,3
d) R3C12 = {19/28/37/46}, no 5
e) R34C9 = {18/27/36/45}, no 9
f) R5C23 = {16/25/34}, no 7,8,9
g) R5C78 = {17/26/35}, no 4,8,9
h) R67C1 = {19/28/37/46}, no 5
i) R78C5 = {29/38/47/56}, no 1
j) R7C89 = {14/23}
k) R89C7 = {39/48/57}, no 1,2,6
l) R9C34 = {69/78}
m) 11(3) cage = {128/137/146/236/245}, no 9
n) 7(3) cage at R8C6 = {124}

1a. Naked triple {124} in 7(3) cage at R8C6, locked for N8, clean-up: no 7,9 in R78C5
1b. 45 rule on N1 1 innie R3C3 = 8, clean-up: no 1 in R12C3, no 2 in R3C12, no 1 in R4C9, no 7 in R9C4
1c. R3C3 = 8 -> no 8 in R1C4 + R2C5 + R4C15 + R5C4 (AN), clean-up: no 5 in R23C5
1d. R3C3 = 8 -> R3C4 + R4C3 = 8 = {17/26/35}, no 4,9
1e. 45 rule on N9 1 innie R7C7 = 6, clean-up: no 5 in R1C6, no 4 in R6C1
1f. R7C7 = 6 -> no 6 in R5C68 + R6C59 + R8C5 (AN), clean-up: no 2 in R5C78, no 5 in R78C5
1g. Naked pair {38} in R78C5, locked for C5 and N8, clean-up: no 7 in R9C3
1h. R7C7 = 6 -> R6C7 + R7C6 = 8 = [17/35]
1i. Naked pair {69} in R9C34, locked for R9, clean-up: no 3 in R8C7
1j. 6,9 in N8 only in R789C4, locked for C4, clean-up: no 2 in R4C3
1k. Killer pair 1,3 in R5C78 and R6C7, locked for N6, clean-up: no 6 in R3C9
1l. 45 rule on N7 2(1+1) outies R6C1 + R9C4 = 15 = {69} -> R7C1 = {14}
1m. R7C89 = {23} (cannot be {14} which clashes with R7C1), locked for R7 and N9 -> R78C5 = [83], clean-up: no 9 in R8C7
1n. 9 in N9 only in R8C89, locked for R8
1o. 17(3) cage at R7C2 = {179/467} (cannot be {269} which clashes with R9C3), no 2,5
1p. 18(4) cage at R8C1 = {2358} (hidden quad in N7)
1q. 6 in N7 only in R89C3, locked for C3, clean-up: no 3 in R12C3, no 2 in R3C4, no 1 in R5C2
1r. 45 rule on N3 2 innies R1C7 + R3C9 = 8 = [35/53/71] -> R1C6 = {468}, R4C9 = {468}
1s. 45 rule on N5 2 innies R4C6 + R6C4 = 10, no 1,4,5 in R4C6, no 5 in R6C4
1t. 3 in C3 only in R456C3, locked for N4, clean-up: no 4 in R5C3
1u. 1,4 in R7 only in R7C123, locked for N7
1v. 5 in R7 only in R7C46, locked for N8
1w. Naked pair {67} in R8C34, 7 locked for R8, clean-up: no 5 in R9C7
1x. 11(3) cage = {128/137/236/245} (cannot be {146} which clashes with R23C5)

2a. 45 rule on R12 3 innies R2C567 = 19 = {289/379/469/478/568}, no 1
2b. 45 rule on C12 3 innies R567C2 = 18 = {279/459/468/567} (cannot be {189} because R5C2 only contains 2,4,5,6), no 1
2c. 2 of {279} must be in R5C2 -> no 2 in R6C2
2d. 17(3) cage at R7C2 (step 1o) = {179/467}
2e. 1 of {179} only in R7C3 -> no 9 in R7C3

3a. R6C1 + R9C4 (step 1l) = {69}
3b. Consider placement for 9 in C3
R6C3 = 9
or R9C3 = 9, R9C4 = 6 => R6C1 = 9
-> 9 in R6C13, locked for R6 and N4

4a. R567C2 (step 2b) = {279/459/468/567}, 17(3) cage at R7C2 (step 1o) = {179/467}
4b. Consider combinations for R12C3 = {27/45}
R12C3 = {27}, 7 locked for C3 => R8C3 = 6, R7C23 = [74] => no 9 in R7C2
or R12C3 = {45} => no 2 in R5C2
-> R567C2 = {459/468/567}, no 2, clean-up: no 5 in R5C3
Also 4 in R12C3 + R7C3, locked for C3
4c. 7 of {567} must be in R7C2 -> no 7 in R6C2

5a. 6,9 in C4 only in R789C4
5b. 45 rule on C123 5 outies R36789C4 = 29 = {15689/25679/34679} (cannot be {24689} because 2,4,8 only in R6C4)
5c. R36789C4 = 29 = {25679/34679} (cannot be {15689} = [18569] because R678C4 = [856] = 19 when R6C23 cannot total 9 because 2,7 only in R7C3), no 1,8, 7 locked for C4, clean-up: no 7 in R4C3 (step 1d)
5d. 2,4 of {25679/34679} only in R6C4 -> R6C4 = {24}, R4C6 = {68} (step 1s)
5e. 9 in C34 only in 28(5) cage at R6C2 and R9C34 -> both must contain 9 -> 28(5) cage = {14689/23689/24679/34579} (cannot be {13789/15679} because R6C4 only contains 2,4, cannot be {24589} because R8C4 only contains 6,7)
5f. 28(5) cage = {24679/34579} (cannot be {14689/23689} = [81496/83296] which clash with R9C4), no 1,8, 4 locked for R6
5g. 28(5) cage = {24679} (cannot be {34579} = [53497] which clashes with R6C7 + R7C6 (step1h) = [17/35]), no 3,5, 2 locked for R6
5h. Naked triple {679} in R789C4, 7 locked for C4 and N8 -> R7C6 = 5, R6C7 = 3 (cage sum), clean-up: no 8 in R1C6, no 1 in R4C3 (step 1d), no 5 in R3C9 (step 1r), no 4 in R4C9, no 5 in R5C78
5i. Naked pair {68} in R4C69, locked for R4
5j. Naked pair {17} in R5C78, locked for R5, 7 locked for N6, clean-up: no 6 in R5C2

6a. R7C3 = 1 (hidden single in C3) -> R7C2 + R8C3 = 16 = [97], R9C34 = [69], R78C4 = [76], R6C234 = [492], R67C1 = [64], R5C2 = 5, R45C3 = [32], R3C4 = 5, R5C1 = 8, clean-up: no 6 in R3C2
6b. R2C4 = 8 (hidden single in C4) -> R1C45 = 3 = [12], R45C4 = [43], R5C56 = [69], R4C6 = 8, R4C9 = 6 -> R3C9 = 3, R7C89 = [32], R5C9 = 4, clean-up: no 7 in R23C5, no 7 in R3C12
6c. R3C12 = [91], R23C5 = [94], R1C6 = 6 -> R1C7 = 5, R12C3 = [45], R236C6 = [371], R4C12 = [17], R46C5 = [57], R1C12 = [73], R2C12 = [26], R89C1 = [53], R9C5 = 1
6d. R3C78 = [26], R2C7 = 7 (cage sum), R2C89 = [41], R4C78 = [92], R5C78 = [17]
6e. R8C89 = [19] (hidden pair in R8), R1C89 = [98], R6C89 = [85], R9C89 = [57]

7a. R8C7 = 4 (no 8 in R8C7, AN from R6C8 = 8 and R7C5 = 8) -> R89C6 = [24], R89C2 = [82], R9C7 = 8
[That third AN fits in with the puzzle title Anti-Knight 6 8 8]

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


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PostPosted: Wed Feb 26, 2020 9:52 pm 
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Minimum Restraints 7 NC 1-cell was like the first one, just routine killer steps to reach

Selecting an NC cell:
Attachment:
Minimum Restraints 7 NC 1-cell.jpg
Minimum Restraints 7 NC 1-cell.jpg [ 74.25 KiB | Viewed 7560 times ]

Then a choice of R5C1 = 7 -> no 8 in R5C2 (NC), R6C3 = 6 -> no 5 in R6C2 (NC) or R6C6 = 7 -> no 8 in R6C7 (NC)

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


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PostPosted: Sun Mar 01, 2020 4:15 am 
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Minimum Restraints 6 NC 2-cell was another for which the killer steps were of moderate Assassin level.

Here is my walkthrough for Minimum Restraints 6 NC 2-cell:
Find 2 cells which are NC.

Prelims

a) R1C45 = {18/27/36/45}, no 9
b) R1C67 = {39/48/57}, no 1,2,6
c) R1C89 = {15/24}
d) R3C34 = {39/48/57}, no 1,2,6
e) R45C3 = {39/48/57}, no 1,2,6
f) R56C7 = {39/48/57}, no 1,2,6
g) R7C67 = {19/28/37/46}, no 5
h) R9C12 = {49/58/67}, no 1,2,3
i) R9C34 = {18/27/36/45}, no 9
j) R9C56 = {17/26/35}, no 4,8,9
k) 20(3) cage at R1C1 = {389/479/569/578}, no 1,2
l) 11(3) cage at R1C3 = {128/137/146/236/245}, no 9
m) 10(3) cage at R2C1 = {127/136/145/235}, no 8,9
n) 10(3) cage at R7C2 = {127/136/145/235}, no 8,9

1a. 45 rule on N1 2 outies R23C4 = 8 = [17/35/53], R3C3 = {579}
1b. 45 rule on N12 2 innies R13C6 = 6 = {39/48} (cannot be {57} which clashes with R23C4), clean-up: no 5,7 in R1C7
1c. 45 rule on N9 2 outies R78C6 = 15 = {69/78}, R7C7 = {1234}
1d. Killer pair 8,9 in R13C6 and R78C6, locked for C6
1e. 45 rule on N89 2 innies R79C4 = 8 = {17/26/35}, no 4,8,9
1f. R9C4 = {123567} -> R9C3 = {234678}
1g. Killer triple 5,6,7 in R79C4, R78C6 and R9C56, locked for N8
1h. 4 in N8 only in 14(3) cage at R7C5 = {149/248}, no 3
1i. 45 rule on N4 3 innies R6C123 = 11 = {128/137/146/236/245}, no 9
1j. 45 rule on R1 3 innies R1C123 = 18 = {279/369/468/567} (cannot be {189/378} which clash with R1C67, cannot be {459} which clashes with R1C89), no 1
1k. 45 rule on R1 1 outies R2C2 = 1 innie R1C3 + 2, no 8 in R1C3, no 3 in R2C2
1l. 45 rule on R9 1 outie R8C8 = 1 innie R9C7 + 1, no 1 in R8C8, no 9 in R9C7
1m. R1C45 = {18/27/36} (cannot be {45} which clashes with R1C89), no 4,5
1n. 12(3) cage at R2C8 = {138/156/237/246} (cannot be {129/147/345} which clash with R1C89), no 9
1o. Killer pair 1,2 in R1C89 and 12(3) cage, locked for N3
1p. 45 rule on N6 3 innies R4C789 = 12 = {129/138/147/156/237/246} (cannot be {345} which clashes with R56C7)
1q. 45 rule on N9 3 innies R789C7 = 12 = {129/138/147/156/237/246} (cannot be {345} which clashes with R56C7)
1r. 45 rule on N6 1 outie R3C9 = 1 innie R4C7 + 6, R3C9 = {789}, R4C7 = {123}
1s. 45 rule on N4 1 outie R7C1 = 1 innie R6C3 + 4, R6C3 = {12345}, R7C1 = {56789}
1t. 45 rule on N1 3 innies R123C3 = 15 = {249/258/267/456} (cannot be {168/348} because R3C3 only contains 5,7,9, cannot be {159} = [519] because 11(3) cage at R1C3 cannot contain both of 1,5, cannot be {357} which clashes with 10(3) cage at R2C1), no 1,3, clean-up: no 5 in R2C2
1u. R3C3 = {579} -> no 5,7 in R12C3, clean-up: no 7,9 in R2C2
1v. 1 in C3 only in R678C3, locked for 27(6) cage at R6C3, clean-up: no 7 in R9C4, no 2 in R9C3

2a. R1C45 (step 1m) = {18/27/36}, R23C4 (step 1a) = [17]/{35} -> combined cage R1C45 + R23C4 = {18}{35}/{27}/{35}/{36}[17], 3 locked for N2, clean-up: no 9 in R13C6 (step 1b), no 3,9 in R1C7
2b. Naked pair {48} in R1C67, locked for R1, clean-up: no 1 in R1C45, no 2 in R1C89, no 6 in R2C2 (step 1k)
2c. Naked pair {48} in R13C6, locked for C6 and N2, clean-up: no 7 in R78C6 (step 1c), no 2,3 in R7C7
2d. Naked pair {15} in R1C89, locked for N3, 5 locked for R1
2e. Naked pair {69} in R78C6, locked for N8, 6 locked for C6, clean-up: no 2 in R79C4 (step 1e), no 2 in R9C56, no 3,7 in R9C4
2f. Naked quad 1,3,5,7 in R2379C4, locked for C4, clean-up: no 2,6 in R1C5
2g. Naked pair {26} in R1C34, 6 locked for R1
2h. 9 in R1 only in R1C12, locked for N1, clean-up: no 3 in R3C4, no 5 in R2C4 (step 1a)
2i. Naked pair {57} in R3C34, locked for R3, clean-up: no 1 in R4C7 (step 1r)
2j. 1 in C7 only in R789C7, locked for N9
2k. R789C7 (step 1q) = {129/138/147} (cannot be {156} = 1{56} because 17(3) cage at R8C6 cannot contain both of 5,6), no 5,6
2l. 6 in C7 only in R23C7, locked for N3 and 29(6) cage at R2C7
2m. 2 in N3 only in 12(3) cage at R2C8 = {237}, 3,7 locked for N3, 7 locked for R2
2n. 4 in N3 only in R123C7, locked for C7 -> R7C7 = 1, R7C6 = 9, R8C6 = 6, clean-up: no 8 in R56C7
2o. R8C6 = 6 -> R89C7 = 11 = {29/38}, no 7
2p. R56C7 = {57} (hidden pair in C7), locked for N6
2q. 1 in N1 only in 10(3) cage at R2C1 = {136/145}, no 2
2r. 5 of {145} must be in R2C1 -> no 4 in R2C1
2s. 2 in N1 only in R12C3, locked for C3
2t. 11(3) cage at R1C3 = {128/236}, no 4
2u. 9 in C4 only in R456C4, locked for N5
2v. 18(3) cage at R3C9 = {189/468} (cannot be {369} = 9{36} which clashes with R3C9 + R4C7 = [93], step 1r), no 2,3
2w. 18(3) cage = {189/468}, CPE no 8 in R56C9
2x. 1 in R9 only in R9C456, locked for N8
2y. 2 in R9 only in R9C789, locked for N9, clean-up: no 9 in R9C7
2z. R45C3 = {39/48} (cannot be {57} which clashes with R3C3), no 5,7

3a. 17(3) cage at R7C8 = {368/458/467} (cannot be {359} which clashes with R89C7), no 9
3b. 16(3) cage at R8C8 = {259/358/367/457} (cannot be {268/349} which clash with R89C7)

4. Consider placement for 2 in R3
R3C5 = 2 => R1C4 = 6, R1C5 = 3, R1C12 = {79} => R2C2 = 4 (cage total)
or R3C8 = 2, R2C89 = {37}, 3 locked for R2 => R2C4 = 1, R12C3 = 10 = [28] => R2C2 = 4
-> R2C2 = 4, R1C12 = 16 = {79}, 7 locked for R1 and N1, R1C5 = 3, R1C4 = 6, R1C3 = 2, R2C4 = 1, R2C3 = 8 (cage sum), R3C34 = [57], clean-up: no 4 in R45C3, no 9 in R9C1
4a. Naked pair {35} in R79C4, locked for N8
4b. Naked pair {17} in R9C56, 7 locked for R9, clean-up: no 6 in R9C12
4c. Naked pair {39} in R45C3, locked for C3 and N4
4d. 7 in C3 only in R78C3, locked for N7 and 27(6) cage at R6C3
4e. 2,3 in N7 only in 10(3) cage at R7C2 = {235}, 5 locked for N7, clean-up: no 8 in R9C12
4f. R9C12 = [49], R1C12 = [97], R9C3 = 6 -> R9C4 = 3, R7C4 = 5, R678C3 = [471], clean-up: no 8 in R8C7 (step 2o)
4g. R678C3 = [471], R7C4 = 5 -> R6C45 = 10 = {28}, locked for R6 and N5
4h. R7C1 = 8 -> R6C12 = 7 = {16}, locked for R6 and N4
4i. Naked pair {39} in R6C89, locked for N6, 3 locked for R6
4j. R4C7 = 2, R9C7 = 8, R8C7 = 3 (cage sum)
4k. Naked pair {46} in R7C89, 4 locked for R7 and N9, R8C9 = 7 (cage sum), R7C25 = [32], R6C45 = [28], R8C45 = [84], R23C5 = [59], R2C6 = 2, R2C89 = [73], R3C8 = 2, R2C1 = 6, R3C12 = [31], R6C12 = [16], R6C89 = [39], R9C89 = [52], R8C8 = 9, R1C89 = [15], R123C7 = [496], R13C6 = [84],
4l. 45 rule on N5 2 remaining innies R4C56 = 8 = {17}, locked for R4 and N5 -> R4C12 = [58], R5C12 = [72], R8C12 = [25], R56C6 = [35], R45C3 = [39], R45C4 = [94], R56C7 = [57], R5C5 = 6, R5C89 = [81], R3C9 = 8

5a. R6C8 = 3 -> no 4 in R7C8 (NC), R7C8 = 6 -> R4C89 = [46], R7C9 = 6
5b. A choice of R4C7 = 2 -> no 1 in R4C6 (NC), R5C5 = 6 -> no 7 in R4C5 (NC), R8C6 = 6 -> no 7 in R9C6 (NC) or R9C7 = 8 -> no 7 in R9C6 (NC)
-> R4C56 = [17], R9C56 = [71]

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


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