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PostPosted: Tue Jun 15, 2021 6:41 pm 
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Assassin 60 RP-Lite Revisit

A classic. This puzzle set the benchmark in my mind for the upper level of v1 Assassin. Thanks Mike! It gets a score of 2.05 and Jsudoku uses 7 'complex intersections'.
Code: Select, Copy & Paste into solver:
3x3::k:2560:2560:3330:3330:3330:4869:4869:6151:6151:2560:4874:4874:3084:3084:2574:4869:4869:6151:2322:4874:5908:5908:3084:2574:2574:3353:6151:2322:4124:5908:4894:4894:5152:5152:3353:3353:2322:4124:4124:4894:3880:3880:5152:5419:3353:5677:4654:4654:2608:3880:2866:2866:5419:5419:5677:5677:4654:2608:2608:2866:4412:4412:5419:5951:5677:4161:4161:6467:6467:4412:5190:5190:5951:5951:5951:4161:4161:6467:6467:5190:5190:
Solution:
+-------+-------+-------+
| 2 1 3 | 4 6 5 | 7 9 8 |
| 7 6 9 | 1 8 2 | 3 4 5 |
| 5 4 8 | 9 3 7 | 1 6 2 |
+-------+-------+-------+
| 1 7 6 | 8 5 3 | 9 2 4 |
| 3 5 4 | 6 2 9 | 8 7 1 |
| 8 9 2 | 7 4 1 | 6 5 3 |
+-------+-------+-------+
| 9 3 7 | 2 1 4 | 5 8 6 |
| 6 2 1 | 5 9 8 | 4 3 7 |
| 4 8 5 | 3 7 6 | 2 1 9 |
+-------+-------+-------+
Cheers
Ed


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PostPosted: Wed Jun 16, 2021 1:30 am 
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Ruud (on the 'Assassin 60 - the Rejected Pattern' thread) wrote:
Here is a cage pattern that I tried over and over again, but failed to create a suitable Assassin.

To which Mike replied:
Well, being concerned that the "24-carat piece" created by Ruud may prove to be impregnable, I set about continuing the search for an alternative based on the same rejected pattern (RP). After several hours' intensive work, I came up with this. It waits for your approval...


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PostPosted: Thu Jun 24, 2021 6:28 pm 
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Not overly happy with my intermediate steps here, but here is how I did it. (With all the dead ends removed!).
Assassin 60RP-Lite WT:
1. 23(3)r3c3 = {689}
Innies r123 = r3c1348 = +28(4) = {(47|56)89}
Since neither r3c1 nor r3c8 can be from (89) -> 23(3)r3c3 = [{89}6]

2. Remaining Innies n47 = r45c1 + r8c3 = +5(3)
-> Either (A) 9(3)r3c1 = [5{13}] and r8c3 = 1,
or (B) 9(3)r3c1 = [6{12}] and r8c3 = 2.
-> r3c18 = {56}

3. Innies n1 = r1c3, r3c1 (5 or 6), r3c3 (8 or 9) = +16(3)
(A) For the case 9(3)r3c1 = [5{13}] and r8c3 = 1
this puts 10(3)n1 = <217> and r13c3 = [38]

(B) For the case 9(3)r3c1 = [6{12}] and r8c3 = 2
this puts r13c3 = [19] and 10(3)n1 = <325>

4. (A) r6789c1 = {4689} and r8c3 = 1
or (B) r6789c1 = {4789} and r8c3 = 2
IOD n7 -> r6c1 = r7c3 + r8c3
-> r7c3 cannot be the same as any of the numbers in r6789c1 (not 489)
Since r18c3 = [31] or [12] -> r7c3 + r8c3 cannot be +4
-> r6c1 cannot be 4
-> r6c1 is Min 7
-> r7c3 is Min 5 (since r8c3 from (12))
6 already in c3 -> r7c3 from (57)

5. Innies r89 = r8c27 = +6(2)
That cannot be [42] since 4 already in r789c1

6. For case r7c3 = 5, [r6c1,r7c3] can only be [72]
this puts r8c27 = [15], 22(4)r6c1 = [7861] and 17(3)n9 = [{39}5]

For case r7c3 = 7, r6789c1 must be {4689} and r8c3 = 1
this puts r8c27 = [24], 22(4)r6c1 = [8932] and 17(3)n9 = [{58}4]

i.e., r7c12378 = [865{39}] or [937{58}]
-> {3589} locked in r7 in r7c12378
Also remaining cells in r7 = r7c4569 = {124(7|6)}

7. Innies n9 = r7c9 + r9c7 = +8(2) (No 4)
-> 4 in r7 in n8 in r7c456

8! 13(4)r3c8 from [6{124}] or [5{134}]
-> (14) locked in n6
-> 1 in r6 only in n5 in r6c456
IOD r6789 -> r5c8 = r6c5 + 3
Since r5c8 cannot be 4 -> r6c5 cannot be 1
-> 1 in n5/r6 in r6c46
Innies n5 = +11(3) and includes 1
-> Innies n5 do not have a 5
-> 5 not in 10(3)r6c4
-> 10(3)r6c4 from {127} or {136}
-> HS 4 in r7 -> r7c6 = 4

9. For (6789) in n6 - at least two of them must be in c7 (I.e., in r456c7)
Since 1 in r6c46 and innies n5 cannot have a 5 -> r6c67 only from [16] or [25]
But the latter puts r6c4 = 1 and 20(3)r4c6 = [8(39)] (Innies n5) which contradicts first line in this step.
-> r6c67 = [16]
-> 1 in 10(3)r6c4 in r7c45

10! 6 in r6c7 -> (Innies n9) r7c9 cannot be 2
-> 2 in r7 only in r7c45
-> 10(3)r6c4 = [7{12}]
-> (Innies n5) 20(3)r4c6 = [3{89}]
-> 7 in n6 in 21(4)
-> (Remaining outies n6) r3c8 + r7c9 = +12(2) = [66]
-> Step 2 (A) must be the correct option

Straightforward from here


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PostPosted: Sat Jun 26, 2021 8:52 pm 
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Thanks for the history Andrew. I'd forgotten what "RP" meant.

As often happens, wellbeback compresses 5 of my steps into one line! But overall, our solutions are quite different. I found this very resistant to cracking with a very, very long solution. No wonder it set the bar for a high end level of Assassin. Loved it! No way could I have solved it this way back then. Found a couple of really interesting steps (one is very 'wellbebackish' step 15). [edit: Thanks to Andrew for a suggestion how one step could have been simpler]

Am planning to have an Assassin ready for the first. Need some big cages to recover from the last couple of puzzles.
start to A60 RP-Lite:
Preliminaries
Cage 23(3) n124 - cells ={689}
Cage 9(3) n14 - cells do not use 789
Cage 10(3) n1 - cells do not use 89
Cage 10(3) n58 - cells do not use 89
Cage 10(3) n23 - cells do not use 89
Cage 20(3) n56 - cells do not use 12
Cage 11(3) n568 - cells do not use 9
Cage 19(3) n5 - cells do not use 1
Cage 19(3) n1 - cells do not use 1
Cage 13(4) n36 - cells do not use 89

No clean-up done unless stated
1. "45" on r123: 4 innies r3c1348 = 28 = {4789/5689}
1a. 8,9 only in r3c34 = 17 -> r4c3 = 6
1b. and r3c18 = 11 = [47]/{56}(no 1,2,3; no 4 in r3c8)
1c. 8,9 locked for r3

2. "45" on n47: 1 outie r3c1 - 4 = 1 innie r8c3 = [51/62]
2a. -> h11(2)r3c18 = {56} only: both locked for r3

3. 9(3)r3c1 must have 5,6 for r3c1 = {126/135} = 3 or 6, 2 or 5
3a -> r45c1 = {12/13}(no 4,5): 1 locked for c1 and n4

4. "45" on c123: 3 remaining innies r138c3 = 12 = [192/291/381](r1c3 = (123)
4a. -> r13c3 = [19/29/38]
4b. 1 locked for c3

5. "45" on n1: 3 innies r1c3 + r3c13 = 16, must have one of 5,6 for r3c1, one of 8,9 for r3c3
5a. but[268] blocked by r13c3 can't be [28] (step 4a)
5b. = [169/259/358]

6. 19(3)n1: {289/379/568} all blocked by innies n1
6a. = {469/478}(no 2,3,5)
6b. 4 locked for n1
6c. 6 in {469} must be in r2c2 -> no 9 in r2c2
6d. -> 9 in n1 only in c3: locked for c3

7. "45" on c1: 1 outie r1c2 + 26 = 4 innies r6789c1
7a. Max. 4 innies = 30 -> max. r1c3 = 4

8. 10(3)n1: {136} blocked since {36} in c1 clashes with 9(3)r3c1 (step 3.)
8a. {235} must have {35} in r12c1 to avoid clashing with 9(3)
8b. = {27}[1]/{35}[2](no 6) = 2 or 3 in c1
8c. r1c2 = (12)
8d. 2 locked for n1

9. killer pair 2,3 in r1245c1: locked for c1 (or can use the "45" in step 7)

10. 5 in n1 only in c1: locked for c1

Upping things now
11. "45" on n7: 1 outie r6c1 = 2 innies r78c3 (iodn7=0)
11a. min. r78c3 = 4 -> no 2 r7c3 [actually, can't be {13} because r1c3 = (13). Min. 5]
11b. note: also means r6c1 cannot repeat in r78c3, must repeat in n7 in r9c23 (no eliminations yet)

12. 4,8,9 in c1 are in r6789c1, r78c2 see all those directly, r7c3 sees all those indirectly (step 11b)(Common Peer Elimination CPE)
12a. -> no 4,8,9 in r7c23 nor r8c2

13. "45" on r89: 2 innies r8c27 = 6 = {15}/[24]

14. from step 4, r138c3 = 12 = [192/381]
14a. and from step 11, r6c1 = r78c3
14b. -> iodn7=0 as [431] blocked by 3 in r1c3
14c. = [752/871/972](no 4 in r6c1, no 3 in r7c3) [see note at step 11a for a more direct way to do this]
14d. must have 7 in r7c1 or r8c3 -> no 7 in r5c3, r6c23, r7c2, r789c1 (Common Peer Elimination CPE)

Really enjoyed this one
15. from step 11b. r6c1 repeats in r9c23
15a. from step 12, 4,8,9 = 21 are only in r6789c1
15b. "45" on c1: 3 outies r1c2 + r9c23 + 3 = 2 innies r67c1
15c. but one outie in r9c23 = 1 innie r6c1
15d. -> remaining two outies r1c2 + one of r9c23 + 3 = 1 innie r7c1
15e. min. two outies = {12}(since no 1 in r9c3) = 3 -> min. r7c1 = 6
15f. max. two remaining outies = 6 (no 5,6 r9c2)(but of course r9c23 must also have one of 7,8,9)

16. 4 in c1 only in 21(4)n7 = {2489/3479/4568}(no 1)
16a. no 4 r9c23
16a. but {2489} blocked by [511] in r8c237 (h6(2)r8c27)
16b. = {3479/4568}(no 2) = 5 or 7

17. killer pair 5,7 in 23(4)n7 and r7c3: 5 locked for n7

18. naked pairs 1,2 in r8c23: both locked for n7 & r8
18a. and r18c2: 2 locked for c2

19. "45" on n7: r8c23 = 3 -> 3 remaining innies r7c123 = 19 = [937/865] = 6 or 7, 3 or 8, 3 or 5
19a. -> r7c12 = [93/86]
19b. -> 22(4)r6c1 = [8932/7861](no 9 in r6c1)

20. from step 14d. must have 7 in r7c1 or r8c3
20a. but not both
20b. -> 18(3)r6c2: {38}[7] blocked
20c. = {279/459}(no 3,8)
20d. -> r6c2 = 9
20e. -> r67c3 = 9 = [45/27]

21. 17(3)n9 must have 4 or 5 for r8c7
21a. but {67}[4] blocked by r7c123 (step 19.)
21b. = {359/458}(no 1,2,6,7)
21c. -> r7c78 = {39/58/48} = 3 or 8
21d. & 5 locked for n9

22. killer pair 3,8 in r7c1278: both locked for r7

23. deleted

24. 13(4)r3c8 must have 5 or 6 for r3c8 = {1246/1345}(no 7)
24a. can't have both 5,6 -> no 5,6 in n6
24b. must have 1 & 4 in n6: both locked for n6

25. "45" on r6789: 1 outie r5c8 - 3 = 1 innie r6c5 = [52/63/74/85/96](r5c8 = (5..9), r6c5 = (2..6)

26. "45" on n5: 3 innies r4c6 + r6c46 = 11 and must have 1 for r6 = {128/137/146}(no 5,9)
26a. 1 locked for n5

27. 20(3)r4c6: can't be {569} since none of those in r4c6
27a. = {389/479/578}(no 6)

Nice progression the next few steps. Something we didn't look for in the early days.
28. 6 in n6 only in r5c8 or r6c789
28a. and from step 25. r5c8 - 3 = r6c5
28b. -> [96] blocked from iodr6789 (Locking-out cages)
28c. -> no 9 in r5c8, no 6 in r6c5

29. 9 in n6 only in 20(3) = {389/479}(no 5)
29a. 9 locked for c7
29b. 4 in {479} must be in r4c6 -> no 7 in r4c6

30. 5 in r6 only in r6c5 or r6c789
30a. and from step 25. r5c8 - 3 = r6c5
30b. -> [52] blocked from iodr6789 (Locking-out cages)
30c. -> 5 in n6 only in r6: locked for r6
30d. -> r5c8 + r6c5 = [63/74]

31. "45" on c89: 2 innies r27c8 = 12
31a. but [75] blocked by r35c8 = {567}(Almost locked set)
31b. = {39/48}(no 1,2,5,6,7)

32. 5 in n9 only in c7: locked for c7

33. "45" on n9: 2 innies r7c9 + r9c7 = 8 = {17/26}(no 3,4,8,9)

34. 5 in n6 only in 21(4) and must have 6 or 7 for r5c8 = {1569/1578/2568/3567}
34a. 2 in {2568} must be in r7c9 -> no 2 in r6c89

35. h11(3)n5 = {128/137/146} = one of 3,4,8 which must go in r4c6 -> no 3,4,8 in r6c46

36. 11(3)r6c6: {245} blocked by 4&5 only in r7c6
36a. = {128/137/146/236}(no 5)
36a. 8 in {128} must be in r6c7, 3 in {236} must be in r6c7 -> no 2 in r6c7

37. 2 in n6 only in 13(4) = [6]{124}

cracked. Pretty straight forward now.
Cheers
Ed


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PostPosted: Wed Jun 30, 2021 10:53 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
I thought I'd finished a week ago but, on checking my walkthrough, I found that I'd carelessly overlooked a combination which proved stubborn to remove, so I've had to rework some of my later steps.

Thanks Ed for spotting some typos and finding and pointing out that my CPE in step 8b was incomplete. I've also made a detail correction in step 10f.
Here's how I solved Assassin 60 RP-Lite Revisited:
Prelims

a) 10(3) cage at R1C1 = {127/136/145/235}, no 8,9
b) 19(3) cage at R2C2 = {289/379/469/478/568}, no 1
c) 10(3) cage at R2C6 = {127/136/145/235}, no 8,9
d) 9(3) cage at R3C1 = {126/135/234}, no 7,8,9
e) 23(3) cage at R3C3 = {689}
f) 19(3) cage at R4C4 = {289/379/469/478/568}, no 1
g) 20(3) cage at R4C6 = {389/479/569/578}, no 1,2
h) 10(3) cage at R6C4 = {127/136/145/235}, no 8,9
i) 11(3) cage at R6C6 = {128/137/146/236/245}, no 9
j) 13(4) cage at R3C8 = {1237/1246/1345}, no 8,9

1a. 45 rule on R89 2 innies R8C27 = 6 = {15/24}
1b. 45 rule on C89 2 innies R27C8 = 12 = {39/48/57}, no 1,2,6
1c. Max R7C8 + R8C7 = 14 -> min R7C7 = 3
1d. 45 rule on N9 2 innies R7C9 + R9C7 = 8 = {17/26/35}, no 4,8,9
1e. 45 rule on N5 3 innies R4C6 + R6C46 = 11 = {128/137/146/236/245}, no 9
1f. Min R4C6 + R6C4 = 4 -> max R6C6 = 7
1g. 45 rule on R6789 1 outie R5C8 = 1 innie R6C5 + 3 -> R5C8 = {456789}, R6C5 = {123456}

2a. 45 rule on C1 4 innies R6789C1 = 1 outie R1C2 + 26
2b. Max R6789C1 = 30 -> max R1C2 = 4
2c. Min R6789C1 = 27, no 1,2
2d. 8,9 in C1 only in R6789C1 -> no 8,9 in R7C2 (CPE)

3a. 45 rule on N47 2 innies R48C3 = 1 outie R3C1 + 2
3b. Max R3C1 = 6 -> max R48C3 = 8 -> R4C3 = 6
[Ed and wellbeback both used 45 rule on R123 4 innies R3C1348 = 28 = {4789/5689} with 8,9 only in R3C34 -> R4C3 = 6.]
3c. R3C1 = R8C3 + 4 -> R3C1 + R8C3 = [51/62]
3d. Naked pair {89} in R3C45, locked for R3
3e. 19(3) cage at R2C2 = {379/469/478/568} (cannot be {289} which clashes with R3C3), no 2
3f. 45 rule on C123 1 outie R3C4 = 2 innies R18C3 + 5
3g. R3C4 = {89} -> R18C3 = 3,4 = {12/13}, 1 locked for C3
3h. Killer pair 1,2 in R8C27 and R8C3, locked for R8
3i. 9(3) cage at R3C1 = {126/135} (cannot be {234} because R3C1 only contains 5,6), no 4
3j. R3C1 = {56} -> R45C1 = {12/13}, 1 locked for C1 and N4
3k. 10(3) cage at R1C1 = {127/136/145/235}
3l. 1 of {145} must be in R1C2 -> no 4 in R1C2
3m. 19(3) cage = {379/469/478} (cannot be {568} which clashes with R3C1), no 5
3n. 1 in N1 only in R1C23, locked for R1
3o. 5 in N1 only in R123C1, locked for C1
3p. 45 rule on R123 2 remaining innies R3C18 = 11 = {56}, locked for R3
3q. 13(4) cage at R3C8 = {1246/1345} (cannot be {1237} because R3C8 only contains 5,6), no 7, 1,4 locked for N6, clean-up: no 1 in R6C5 (step 1g)
3r. R3C8 = {56} -> no 5,6 in R4C89 + R5C9
3s. 1 in R6 only in R6C46, locked for N5
3t. R4C6 + R6C46 (step 1e) = {128/137/146}, no 5
3u. 4 of {146} must be in R4C6 -> no 4 in R6C46
3v. 20(3) cage at R4C6 = {389/479/578} (cannot be {569} because no 5,6,9 in R4C6), no 6

4a. Consider permutations for R3C1 + R8C3 (step 3c) = [51/62]
R3C1 + R8C3 = [51] => R45C1 = 4 = {13}, 3 locked for C1, R1C2 = 1 (hidden single in N1) => R12C1 = 9 = {27}
or R3C1 + R8C3 = [62] => R1C3 = 1, 10(3) cage at R1C1 = {235}
-> 10(3) cage = {127/235}, no 4,6, 2 locked for N1
4b. 4 in N1 only in 19(3) cage at R2C2 = {469/478}, no 3
4c. 6 of {469} must be in R2C2 -> no 9 in R2C2
4d. 9 in N1 only in R23C3, locked for C3
4e. 4 in C1 only in R6789C1, CPE no 4 in R78C2, clean-up: no 2 in R8C7 (step 1a)
4f. 2 in R8 only in R8C23, locked for N7
4g. 45 rule on N7 1 outie R6C1 = 2 innies R78C3
4h. Min R78C3 = 5 (cannot be [31] which clashes with R1C3) -> no 3,4 in R6C1
4i. R6C1 = {789}, R8C3 = {12} -> R7C3 = {578}
4j. 4 in C1 only in R789C1, locked for N7
4k. R6789C1 = R1C2 + 26 (step 2a) -> R6789C1 = {4689/4789}, no 3, R1C2 = {12}
4l. 18(3) cage at R6C2 = {279/378/459}
4m. 5 of {459} must be in R7C3 -> no 5 in R6C23
4n. 5 in N4 only in 16(3) cage at R4C2
4o. Consider combinations for 10(3) cage (step 4a)
10(3) cage = {127}, 2,7 locked for C1, R45C1 = {13}, 3 locked for N4, R6C1 = {89} => no 5 in R7C3 (step 4i) => 18(3) cage = {279}, 2 locked for N4
or 10(3) cage = {235}, 3 locked for C1, R45C1 = {12}, 2 locked for N4
-> 16(3) cage = {358/457}, no 2,9
4p. 9 in N4 only in R6C12, locked for R6
4q. 18(3) cage = {279/378/459}
4r. {378} = {38}7 (cannot be {37}8 which clashes with 16(3) cage) -> no 7 in R6C23, no 8 in R7C3
4s. 9 of {459} must be in R6C2 -> no 4 in R6C2

5a. 17(3) cage at R7C7 = {179/359/458/467} (cannot be {368} because R8C7 only contains 1,4,5)
5b. Consider placements for R7C3 = {57}
R7C3 = 5, naked pair {12} in R8C23, locked for R8 => 17(3) cage = {359/458/467}
or R7C3 = 7 => 17(3) cage = {359/458}
-> 17(3) cage = {359/458/467}, no 1, clean-up: no 5 in R8C2 (step 1a)
5c. Naked pair {12} in R8C23, 1 locked for N7
5d. Naked pair {12} in R18C2, locked for C2
[Taking that forcing chain a bit further …]
5e. R6C1 = {789} -> R78C3 = [52/71/72] (steps 4e and 4g), R8C27 = [15/24] (step 1a)
5f. R7C3 = 5 => R8C3 = 2, R8C27 = [15]
or R7C3 = 7
-> 17(3) cage = {359/458}, no 6,7, 5 locked for N9, clean-up: no 3 in R7C9 + R9C7 (step 1d)

6a. 45 rule on N3 2 innies R3C78 = 1 outie R1C6 + 2
6b. Min R3C78 = 6 -> min R1C6 = 4
6c. R3C78 cannot total 11 -> no 9 in R1C6
6d. Max R1C6 = 8 -> max R3C78 = 10, no 7 in R3C7

7a. Consider placements for 5 in R3C18
R3C1 = 5 => R45C1 = 4 = {13} => R6C3 = 2 (hidden single in N4)
or R3C8 = 5 => R4C89 + R5C9 = 8 = {134} => 2 in N6 only in R6C789
-> 2 in R6C3 or R6C789, locked for R6, clean-up: no 5 in R5C8 (step 1g)
7b. R4C6 + R6C46 (step 3t) = {137/146}, no 8
7c. 20(3) cage at R4C6 (step 3v) = {389/479/578}
7d. 3 of {389} must be in R4C6 -> no 3 in R45C7

8a. R6C1 = R78C3 (step 4g), R8C3 = {12}
8b. Consider placements for R7C3 = {57}
R7C3 = 5 => R6C1 = 7
or R7C3 = 7
-> 7 in R6C1 or R7C3, CPE no 7 in R5C3 + R789C1 + R7C2
8c. 10(3) cage (step 4a) = {127/235}, 18(3) cage at R6C2 (step 4q) = {279/378/459}
8d. Consider placements for 7 in C1
7 in 10(3) cage = {127}, 2 locked for C1 => R45C1 = {13}, 3 locked for N4
or R6C1 = 7 => R7C3 = 5 => 18(3) cage = {459}
-> 18(3) cage = {279/459} -> R6C2 = 9, R6C3 = {24}

9a. R5C8 = R6C5 + 3 (step 1g)
9b. 20(3) cage at R4C6 (step 3v) = {389/479/578}
9c. Consider placement for 9 in N6
9 in R45C7 => 20(3) cage = {389/479}
or R5C8 = 9 => R6C5 = 6 => 5 in R6 only in R6C789, locked for N6 => 20(3) cage = {389/479}
-> 20(3) cage = {389/479}, no 5, 9 locked for C7 and N6, clean-up: no 6 in R6C5
9d. 20(3) cage = {389/479} -> R4C6 = {34}
9e. 5 in N6 only in R6C789, locked for R6, clean-up: no 8 in R5C8
9f. Naked pair {34} in R4C6 + R6C5, locked for N5
9g. 19(3) cage at R4C4 = {289/568}, no 7, 8 locked for N5
9h. 6 of {568} must be in R5C4 -> no 5 in R5C4

10a. 17(3) cage at R7C7 (step 5f) = {359/458}
10b. 9 of {359} must be in R7C8 -> no 3 in R7C8
10c. R6C1 = R78C3 (step 4g), R8C27 (step 1a) = [15/24]
10d. Consider combinations for R4C6 + R6C46 (step 7b) = {137/146}
R4C6 + R6C46 = {137}, 7 locked for R6, R6C1 = 8 => R78C3 = 8 = [71] => R8C27 = [24] => 17(3) cage = {58}4
or R4C6 + R6C46 = {146} = [461] => R7C45 = 4 = {13}, 3 locked for R7=> 17(3) cage = {458}
or R4C6 + R6C46 = {146} = [416] => R6C7 + R7C6 = 5 = {23} (because no 1,4 in R6C7), CPE no 3 in R7C7 => 17(3) cage = {458}
-> 17(3) cage = {458}, 4,8 locked for N9, 8 locked for R7
10e. R7C1 = 9 (hidden single in R7)
10f. R6C1 + R78C2 = 13 = {238} (only possible combination, cannot be {157} = [751] which clashes with R6C1 + R78C3 = [752], cannot be {256} because R6C1 only contains 7,8) -> R6C1 = 8. R78C2 = [32], R78C3 = [71], R8C7 = 4, R89C1 = [64], R3C1 = 5 -> R45C1 = 4 = {13}, 3 locked for C1 and N4, R6C3 = 2 (cage sum)

11a. R2C2 = 6 (hidden single in N1) -> R2C3 + R3C2 = 13 = [94], R3C34 = [89]
11b. R3C8 = 6 -> R5C8 = 7, R5C2 = 5
11c. R6C5 = 4 (hidden single in R6) -> R5C56 = 11 = {29}, locked for R5 and N5
11d. R4C6 = 3 -> R45C1 = [13], R5C9 = 1 (hidden single in N6)
11e. R7C9 + R9C7 = 8 (step 1d) = {26}, locked for N9
11f. R45C7 = [98] -> R7C78 = [58], R2C8 = 4 (step 1b)
11g. 10(3) cage at R6C4 = {127} (only remaining combination) -> R6C4 = 7, R7C45 = {12}, locked for R7 and N8, R7C9 = 6 -> R9C7 = 2
11h. R7C6 = 4 -> R6C67 = 7 = [16]
11i. R9C7 = 2 -> R8C56 + R9C6 = 23 -> R9C6 = 6, R8C56 = {89}, locked for N8, 9 locked for R8, R8C89 = [37], R8C4 = 5, R9C45 = [37], R4C45 = [85]
11j. R1C3 = 3, R1C7 = 7, R12C1 = [27]
11k. R3C6 = 7 (hidden single in N2) -> R2C6 + R3C7 = 3 = [21]

and the rest is naked singles.


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