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Ed
 Post subject: Assassin 427
PostPosted: Wed Feb 15, 2023 9:16 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
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a427.png
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Note the broken 23(4)r5c1

Assassin 427
I had a lot of trouble finding the weak area of this puzzle and kept feeling I'd missed something important. Perfect! Lots of crannies to explore otherwise. SudokuSolver gives it 1.50 and JSudoku finds it pretty easy.
triple click code:
3x3::k:5632:7425:7425:7682:7682:4611:4611:2564:2564:5632:2309:7425:7425:7682:4611:9990:1031:1031:5632:2309:7425:7682:2312:4611:9990:9990:9990:5632:4361:7425:2312:2312:4618:9990:9990:5899:5900:4361:5900:5900:4618:8205:8205:3342:5899:4361:4361:5900:4618:8205:8205:8205:3342:5899:4361:3599:3599:3599:7696:2321:8205:3342:5899:4882:4882:4882:4882:7696:2321:2321:3347:5899:4372:4372:4372:7696:7696:7696:1813:1813:3347:
solution: 
+-------+-------+-------+
| 1 3 5 | 7 9 4 | 6 2 8 |
| 8 7 9 | 2 6 5 | 4 3 1 |
| 4 2 6 | 8 1 3 | 5 7 9 |
+-------+-------+-------+
| 9 1 4 | 5 3 7 | 8 6 2 |
| 7 5 8 | 6 2 1 | 9 4 3 |
| 3 6 2 | 9 4 8 | 7 1 5 |
+-------+-------+-------+
| 2 9 1 | 4 5 6 | 3 8 7 |
| 5 4 7 | 3 8 2 | 1 9 6 |
| 6 8 3 | 1 7 9 | 2 5 4 |
+-------+-------+-------+
Cheers
Ed
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wellbeback
 Post subject: Re: Assassin 427
PostPosted: Sat Feb 18, 2023 8:03 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 282
Location: California, out of London
Likewise! I went round in circles for a while on this one. Very nice! I expect quite different paths here.
Assassin 427 WT:
1. 30(4)n2 = {6789}
-> Max r123c6 = {345} = +12
-> Min r1c7 = 6
39(6)n36 = {456789}
-> r1c7 = r4c8 (from 6789)

2. 4(2)n3 = {13}
-> (HS 2 in n3) 12(2)n3 = {28}
-> (HS 8 in 39(6)) r4c7 = 8

3. r1c7 cannot be 7 since that would put r123c6 = {245} leaving no place for both (13) in n2
-> r1c7 and r4c8 from (69)
-> Either r1c7 = 6 and r123c6 = {345}
or r1c7 = 9 and r123c6 = {135} or {234}
-> 3 locked in n2/c6 in r13c6

4. NQ r1c1236 = {1345}
Since at least one of (45) in r1c123 -> 9(2)n1 cannot be {45}

5. Remaining Outies c89 = r239c7 = +11(3)
-> r239c7 = [{45}2] or [{46}1]
I.e., 4 locked in r23c7 and 7(2)n9 = [25] or [16]

6. 7 in c7 only in r567c7
-> 7 in c6 only in r49c6

7! Innies r1234 = r4c269 = +10(3)
-> Max r4c6 = 7
IOD c6789 -> r6c5 + 12 = r49c6
-> r49c6 is Min +13(2)
Since one of r49c6 is 7 -> other must be from (689)
Since r4c6 is max 7 -> r4c6 from (67)
But Innies r1234 = r4c269 = +10(3) cannot be <163> since that leaves no solution for 9(3)r3c5
-> r4c269 = <172>

8. -> 9(3)r3c5 = [1{35} or [2{34}]
I.e., 3 locked in r4c45

9. Min r12378c6 = +15(5) -> Max r18c7 = +12(2)
r1c7 from (69) -> Max r8c7 = 5
But 3 in r123c6 -> r8c7 cannot be 5 (Since 9(3)r7c6 cannot be [{13}5]
Also 4 already in c7 in r23c7
-> Max r8c7 = 3
IOD n78 -> r7c1 = r8c7 + 1
-> r8c7 from (123) and r7c1 from (234)

10! r2c4 from (245)
Outies n1 = r2c4,r4c1,r4c3 = +15(3)
(A) r2c4 = 2 -> r4c13 = {49}
(B) r2c4 = 4 -> r4c13 = {56}
(C) r2c4 = 5 -> r4c13 = {46}
-> 4 in outies of n1
If 4 in r2c4 or r4c3 -> 4 in n1 in c1
-> In all cases 4 in c1 in r1234c1
-> r7c1 from (23)

11! -> r8c7 from (12)
-> r89c7 = {12} and 3 in c7 in r567c7
-> 9(3)r7c6 = [{16}2] or [{26}1]
-> (IOD c6789) [r6c5,r9c7] = [49] (Only remaining solution)
-> 9(3)r3c5 = [1{35}]

12. Finishing up
Also -> 32(6)r5c6 = {134789} with r6c5 = 4, r56c6 = {18}, r567c7 = {379}
-> 9(3)r7c6 = [{62}1]
-> r123c6 = {345} and r1c7 = 6
-> r4c8 = 6
Also 7(2)n9 = [25]
-> r23c7 = {45} and r3c89 = {79}
Also r2c4 = 2 and r4c13 = {49}
Also (IOD n78) r7c1 = 2
-> 17(5)n47 = [1{356}2] and r4c9 = 2
Also 18(3)n5 = [729]
-> 23(4)r5c1 = [{78}62]
Also 10(2)n3 = [28]
-> (HS 8 in c8) 13(3)c8 = [418]
etc.
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Ed
 Post subject: Re: Assassin 427
PostPosted: Fri Feb 24, 2023 8:52 am 
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Joined: Wed Apr 16, 2008 1:16 am
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I missed wellbeback's really nice step 4 so never had a chance for the neat step 10. Instead, I veered off at the end of step 8. Boring way really by comparison.
alt middle from wellbeback's end step 8 with candidate diagram:
end step 8 here. Paste into A427 in SudokuSolver. Thanks to Andrew for some clarifications and corrections.
.-------------------------------.-------------------------------.-------------------------------.
| 1345      1345      1345      | 679       679       1345      | 69        28        28        |
| 2456789   2678      2456789   | 245       6789      245       | 456       13        13        |
| 123456789 1237      123456789 | 6789      12        12345     | 456       5679      5679      |
:-------------------------------+-------------------------------+-------------------------------:
| 4569      12        4569      | 345       345       7         | 8         69        12        |
| 123456789 1234567   123456789 | 1245689   1245689   1245689   | 1235679   12345679  12345679  |
| 1234567   1234567   123456789 | 1245689   124       1245689   | 1235679   12345679  12345679  |
:-------------------------------+-------------------------------+-------------------------------:
| 1234567   123456789 123456789 | 123456789 123456789 12456     | 1235679   123456789 123456789 |
| 123456789 123456789 123456789 | 123456789 123456789 12456     | 12356     456789    123456789 |
| 123456789 123456789 123456789 | 123456789 123456789 689       | 12        56        456789    |
'-------------------------------.-------------------------------.-------------------------------'

9. "45" on c9: 4 innies r1239c9 = 22 and must have 2/8 for r1c9 and 1/3 for r2c9
9a. = {1489/1678/2389/3478/3568}
9b. 8 locked for c9

10. h22(4)c9 = {1489/1678/2389/3478/3568}
10b. the only permutation possible for 8 in r9c9 = [2398]
10c. 8 in r9c9 forces combined cage 20(4)n9 = [5168]. But with 9 in r3c9 -> r4c8 = 6: ie, two 6 in c8
[edit: or [98] in r39c9 -> r48c8 = [65] which is blocked by r9c8 = (56)]
10d. -> no 8 in r9c9
10c. -> r1c89 = [28] (hsingle 8 c9)

11. h22(4)c9 = [8]{149/167/347/356}
11a. {149} must have 4 in r9c9 -> no 9 in r9c9
11b. -> no 4,5 in r8c8

12. 4 in c8 only in 13(3)r5c8
12a. = {148/346}(no 579)

13. variable hidden killer pair 5,7 in c8 since they are only in r3c8 OR at least one in combined 20(4) n9: ie r8c8 = 7 and/or r9c8 = 5
13a.
il In that combined cage, if r8c8 = 7 -> r9c789 = [256]
ii. or r9c8 = 5
13b. -> r3c8 <> 5
13c. -> r9c8 = 5, r9c7 = 2
13d. -> no 8 in r8c8

14. r7c8 = 8 (hsingle n9)
14a. -> r56c8 = {14} only: both locked for n6, 1 for c8
14b. r2c89 = [31]
14b. r4c29 = [12]

15. 23(5)r4c9 = [2]{3459/3567}
15a. 5 locked for c9 & n6

16. "45" on c6789: 1 outie r6c5 + 5 = 1 remaining innie r9c6 = [16/49]

17. 8 in c6 only in 32(6) = {125789/134789/145678}
17a. 8 locked for n5
17b. but both {45} in n5 is blocked by r4c45 = {345}
17c. 32(6) = {125789/134789} = 4/5 in n5

18. killer pair 4,5 in r4c45 + 32(6): both locked for n5

19. r5c5 + r6c4 = 11 = {29} only: both locked for n5

20. 32(6) = {134789} only (no 5,6)
20a. -> {148} in n5: 4 locked for n5
20b. -> {379} in r567c7: 3 and 9 locked for c7
20c. -> r18c7 = [61]

Much easier now
Cheers
Ed
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Andrew
 Post subject: Re: Assassin 427
PostPosted: Mon Mar 06, 2023 8:49 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
My solving path was very long so I feel that I must have missed something. Even after I found my step 6 the puzzle still resisted right to the end.

Another busy week ahead so it may be a while until I can see how wellbeback and Ed solved it. However, from a quick glance at wellbeback's step 4, I can see that wasn't relevant to my solving path.

A425 and A427 had fairly low SS scores but were both hard, A426 had a high score but was fairly easy; I wonder what A428, another high score, will be like.

Here's how I solved Assassin 427:
Prelims

a) R1C89 = {19/28/37/46}, no 5
b) R23C2 = {18/27/36/45}, no 9
c) R2C89 = {13}
d) 13(2) cage at R8C8 = {49/58/67}, no 1,2,3
e) R9C89 = {16/26/34}, no 7,8,9
f) 9(3) cage at R3C5 = {126/135/234}, no 7,8,9
g) 9(3) cage at R7C6 = {126/135/234}, no 7,8,9
h) 30(4) cage at R1C4 = {6789}
i) 17(5) cage at R4C2 = {12347/12356}, no 8,9
j) 39(6) cage at R2C7 = {456789}, no 1,2,3

1a. Naked quad {6789} in 30(4) cage at R1C4, locked for N2
1b. Naked pair {13} in R2C89, locked for R2 and N3, clean-up: no 7,9 in R1C89, no 6,8 in R3C2
1c. Max R123C6 = 12 -> min R1C6 = 6
1d. 2 in N3 only in R1C89 = {28}, locked for R1, 8 locked for N3
1e. 45 rule on N3 2 outies R4C78 = 1 innie R1C7 + 8 -> no 8 in R4C8 (IOU)
1f. 39(6) cage at R2C7 = {456789} -> R4C7 = 8
1g. 45 rule on N3 1 remaining outie R4C8 = 1 innie R1C7 -> R4C8 = {679}
1h. Naked triple {679} in R1C457, locked for R1
1i. 9 in C2 only in R789C2, locked for N7
1j. 17(5) cage at R4C2 = {12347/12356}, CPE no 1,2,3 in R45C1
1k. 13(3) cage at R5C8 = {148/157/247/256/346} (cannot be {139} which clashes with R2C8, cannot be {238} which clashes with R1C8), no 9

2a. 45 rule on R1234 3 innies R4C269 = 10 = {127/136/145/235}, no 9
2b. Max R4C6 = 7 -> min R5C5 + R6C4 = 11, no 1 in R5C5 + R6C6
2c. 45 rule on N78 1 innie R7C1 = 1 outie R8C7 + 1, no 1 in R7C1
2d. 17(5) cage at R4C2 = {12347/12356}, 1 locked for N4
2e. 45 rule on N7 2 outies R78C4 = 1 innie R7C1 + 5, no 5 in R8C4 (IOU)
2f. 45 rule on N8 2 innies R78C4 = 1 outie R8C7 + 6, no 6 in R7C4 (IOU)
2g. 45 rule on R9 2 outies R78C5 = 1 innie R9C9 + 9
2h. Min R9C9 = 4 -> min R78C5 = 13, no 1,2,3 in R78C5
2i. Max R89C5 = 17 -> max R9C9 = 8, clean-up: no 4 in R8C8
2j. 45 rule on N14 3(2+1) outies R25C4 + R7C1 = 10
2k. Min R2C4 + R7C1 = 4 -> max R5C4 = 6
2l. R25C4 cannot total 4 -> no 6 in R7C1, clean-up: no 5 in R8C7
2m. 18(4) cage at R1C6 = {1359/2349/3456} (cannot be {1269/1467/2367} because 6,7,9 only in R1C7, cannot be {2457} which clashes with R2C4), no 7, 3 locked for C6 and N2, clean-up: no 7 in R4C8 (step 1g)
2n. 9(3) cage at R7C6 = {126/135/234}
2o. {126} cannot be {12}6 which clashes with 18(4) cage -> no 6 in R8C7, clean-up: no 7 in R7C1
2p. 3 of {234} must be in R8C7 -> no 4 in R8C7, clean-up: no 5 in R7C1
2q. 7 in R1 only in R1C45, locked for N2
2r. Max R7C1 = 4 -> max R78C4 = 9, no 9 in R78C4
2s. 9(3) cage at R3C5 = {126/135/234}
2t. {135} must be 1{35} (cannot be 5{13} which clashes with R4C269), no 5 in R3C5

3a. 45 rule on C6789 2 innies R49C6 = 1 outie R6C5 + 12
3b. Max R49C6 = 16 -> max R6C5 = 4
3c. Min R49C6 = 13, no 1,2 in R4C6
3d. Max R4C6 = 7 -> min R9C6 = 6
3e. R4C269 = 10 (step 2a), min R4C6 = 4 -> max R4C29 = 6, no 6,7 in R4C29

4a. 45 rule on N1 3(1+2) outies R2C4 + R4C13 = 15
4b. 8 in N4 only in 23(4) disjoint cage at R5C1 = {1589/2489/2678/3578/4568}
4c. 18(4) cage at R1C6 (step 2m) = {1359/2349/3456}, R1C7 = R4C8 (step 1g), R25C4 + R7C1 = 10 (step 2j), R4C269 (step 2a) = {127/136/145/235}
4d. Consider placements for R2C4 = {245}
R2C4 = 2 => R4C13 = 13 = {49} (cannot be {67} which clashes with 17(5) cage at R5C2)
or R2C4 = 4 => 18(4) cage = {1359} => R4C8 = 9 => 8,9 in N4 both in 23(4) disjoint cage = {2489} = {489}2 (cannot be {1589} = {589}1 because R25C4 + R7C1 = 10), 4 locked for N4 => R4C13 = 11 = {56}
or R2C4 = 5 => R4C13 = 10 = {46}/[73]
-> R4C13 = {46/49/56}/[73], no 2,7 in R4C3
[Continuing with a separate forcing chain to avoid making step 4d too heavy.]
4e. Now consider combinations for R4C13
R4C13 = {46/49/56} => R4C6 = 7 (hidden single in R4), R4C29 = {12}
or R4C13 = [73] => R2C4 = 5, 18(4) cage = {2349}, 4 locked for C6, R4C269 = {145} => R4C6 = 5, R4C29 = {14}
-> R4C29 = {12/14}, 1 locked for R4, R4C6 = {57}
4f. R49C6 = R6C5 + 12 (step 3a)
4g. Consider combinations for 9(3) cage at R3C5 = 1{26}/1{35}/{234}
9(3) cage = 1{26}, 2 locked for N5 => min R6C5 = 3 => min R49C6 = 15, no 5 in R4C6
or 9(3) cage = 1{35}/{234}, 3 locked for R4 => R4C13 = {46/49/56} => R4C6 = 7 (hidden single in R4)
-> R4C6 = 7, R4C13 = {46/49/56}, no 3
4h. R49C6 = 13,15,16 -> R6C5 = {134}
4i. Killer pair 6,9 in R4C13 and R4C8, locked for R4
4j. 9(3) cage = 1{35}/{234}, 3 locked for N5
4k. R6C5 = {14} -> R49C6 = 13,16 = 7{69}, no 8
4l. R4C6 = 7 -> R5C5 + R6C6 = 11 = {29/56}, no 4,8
4m. R4C6 = 7 -> R4C29 = {12}, locked for R4
4n. 9(3) cage = 1{35}/2{34}, no 4 in R3C5
4o. R2C4 + R4C13 = 2{49}/4{56}/5{46}, CPE no 4 in R4C4
4p. Killer pair 1,4 in 9(3) cage and R6C5, locked for C5 and 4 locked for N5
4q. R25C4 + R7C1 = 10 = [262/424/514] (cannot be [253] which clashes with 9(3) cage = 1{35}), no 5 in R5C4, no 3 in R7C1, clean-up: no 2 in R8C7 (step 2c)
4r. 17(5) cage at R4C2 = {12347/12356}, 3 locked for N4
4s. Consider placements for R2C4
R2C4 = 2 => R5C4 = 6
or R2C4 = 4 => R4C13 = {56}, locked for N4
or R2C5 = 5 => R4C13 = {46}, locked for N4
-> no 6 in R5C13 + R6C3
4t. 23(4) disjoint cage = {278}6/{489}2/{589}1
4u. Consider placements for R2C4
R2C4 = 2 => R4C13 = {49}, locked for N4
or R2C4 = 4 => R5C4 = 2 => 23(4) disjoint cage = {489}2, 4 locked for N4
or R2C5 = 5 => R4C13 = {46}, locked for N4
-> no 4 in R5C2 + R6C12

5a. 9(3) cage at R7C6 = {15}3/{24}3/{26}1
5b. 9 in N8 only in 30(5) cage R7C5 = {15789/24789/34689/35679} (cannot be {25689} which clashes with 9(3) cage)

6a. Hidden killer pair 1,4 in R123C6 and R5678C6 for C6, R123C6 must contain one of 1,4 -> R5678C6 must contain one of 1,4
6b. Hidden killer pair 6,9 in R5678C6 and R9C6 for C6, R9C6 = {69} -> R5678C6 must contain one of 6,9
6c. 45 rule on N69 5(1+4/3+2) outies R6C5 + R5678C6 = 1 remaining innie R4C8 + 15
6d. R6C5 = {14}, R5678C6 must contain 8 for C6, one of 1,4 and one of 6,9
6e. 1 in N2 only in R13C6 or R3C5 -> R6C5 + R5678C6 cannot contain two 1s so it must contain either both of 1,4 or two 4s
6f. R4C8 = {69} -> R6C5 + R5678C6 = 21,24 = {12468/12489/14568/24468} = 1{68}{24}/4{18}{26}/1{89}{24}/4{68}{15}/4{68}{24} (cannot be 4{68}{12}/4{89}{12}/1{68}{45}/1{58}{46} because R78C6 cannot total 3, 9 or 10)
6g. 32(6) cage at R5C6 must contain 8 for C6 = {125789/134789/135689/234689/245678}
6h. 9(3) cage at R7C6 = {15}3/{24}3/{26}1
6i. Consider placements for R9C6 = {69}
R9C6 = 6 => 9(3) cage = {15/24}3 => R9C78 = {25} => 32(6) cage cannot be {189}{257} which clashes with R9C7, cannot be {189}{347/356} which clash with R8C7) => R6C5 + R56C6 cannot be 1{89}
or R9C6 = 9
-> {12468/14568/24468}, no 9
6j. 9 in N5 only in 18(3) cage at R4C6 = 7{29}, 2 locked for N5
6k. R25C4 + R7C1 (step 4q) = [262/514], no 4 in R2C4
6l. 4 in N2 only in 18(4) cage at R1C6 = {2349/3456}, no 1, 4 locked for C6
6m. R3C5 = 1 (hidden single in N2) -> R6C5 = 4, R4C45 = {35}, 5 locked for R4 and N5, clean-up: no 8 in R2C2
6n. 4 in R4 only in R4C13, locked for N4
6o. 8 in C6 only in 32(6) cage at R5C6 = {134789/234689/245678}, R6C5 = 4, R56C6 = {18/68} -> R567C7 = {239/257/379}, no 1,6
6p. 1 in C7 only in R89C7, locked for N9, clean-up: no 6 in R9C7

7a. R9C6 = 9 (hidden single in C6)
7b. Max R78C5 = 15 -> max R9C9 = 6 (step 2g), clean-up: no 5,6 in R8C8
7c. 17(3) cage at R9C1 = {278/368/458/467}, no 1
7d. Variable killer triple 4,5,6 in 17(3) cage, R9C78 and R9C9 for R9, R9C78 and R9C9 each contain one of 4,5,6 -> 17(3) cage cannot contain more than one of 4,5,6 = {278/368} (cannot be {458/467}, no 4,5, 8 locked for R9 and N7
7e. Variable killer quad 2,4,5,6 in 17(3) cage, R9C45, R9C78 and R9C9, 17(3) cage contains one of 2,6, R9C78 and R9C9 each contain one of 4,5,6 -> R9C45 cannot contain more than one of 2,4,5,6 -> 30(5) cage at R7C5 (step 5b) = {15789/34689/35679} (cannot be {24789} = {78}[429]), no 2
7f. R5C5 = 2 (hidden single in C5) -> R6C4 = 9 (cage sum)
7g. 9(3) cage at R7C6 = {15}3/{26}1
7h. 30(5) cage = {15789/34689} (cannot be {35679} which clashes with 9(3) cage), 8 locked for C5 and N8
7i. 1,4 only in R9C7 -> R9C7 = {14}
7j. Killer pair 5,6 in 30(5) cage and 9(3) cage, locked for N8
7k. R78C4 = R7C1 + 5 (step 2e)
7l. R7C1 = 2,4 -> R78C4 = 7,9 = {27/34}, no 1
7m. R3C4 = 8 (hidden single in N2)
7n. 6 in C7 only in R123C7, locked for N3

8a. 23(5) cage at R4C9 = {12479/12569/14567/23459/23567} (cannot be {12389/13469/13478/13568} which clash with R2C9, cannot be {12578/23468} which clash with R1C9, cannot be {14567} which clashes with R9C9), no 8
8b. R1C9 = 8 (hidden single in C9) -> R1C8 = 2, clean-up: no 5 in R9C7
8c. 13(3) cage at R5C8 = {148/157/346}
8d. Killer pair 1,3 in 13(3) cage and R2C8, locked for C8, clean-up: no 4 in R9C7
8e. 8 in C8 only in R78C8
8f. Consider placements for R9C8 = {456}
R9C8 = 4 => 13(3) cage = {157}
or R9C8 = 5, no 8 in R8C8 => 13(3) cage = {148}
or R9C8 = 6
-> 13(3) cage = {148/157}, no 3,6, 1 locked for C8 and N6
8g. R2C89 = [31], R4C29 = [12]
8h. 23(5) cage at R4C9 = {23459/23567}, 5 locked for C9, clean-up: no 8 in R8C8
8i. R7C8 = 8 (hidden single in C8) -> R56C8 = [41], clean-up: no 3 in R9C7
8j. 4 in C7 only in R23C7, locked for N3
8k. R8C5 = 8 (hidden single in N8)

9a. R9C78 = [25] (cannot be [16] which clashes with R9C49, ALS block)
[Cracked at last; clean-ups omitted from here]
9b. Naked pair {79} in R3C89, locked for R3, N3 and 39(6) cage at R2C7 -> R4C8 = 6
9c. R1C7 = 6 (hidden single in N3) -> R123C6 = 15 = {345}, 5 locked for C6 and N2
9d. R8C7 = 1 (hidden single in N9) -> R78C6 = {26}, locked for N8, 6 locked for C6 -> R56C6 = [18]
9e. R7C5 = 5, R9C4 = 1 (hidden pair in N8) -> R9C5 = 7 (cage sum), R12C5 = [96]
9f. R2C123 = {789} (hidden triple in R2), R2C13 = {89} -> R2C2 = 7, R3C2 = 2
9g. R5C4 = 6 -> 23(4) disjoint cage at R5C1 = {278}6 (step 4t) -> R5C13 = {78}, 7 locked for R5 and N4, R6C3 = 2
9h. R4C2 = 1, R5C2 + R6C12 = {356} -> R7C1 = 2 (cage sum)
9i. R7C3 = 1 (hidden single in R7) -> R7C24 = 13 = [94]
9j. R1C1 = 1 (hidden single in C1) -> 22(4) cage at R1C1 = {1489} (only remaining combination) = [1849], R4C3 = 4, R5C1 = 7
9k. R8C123 = [547] (hidden triple in N7)

and the rest is naked singles.
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