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frank Regular
Joined: 07 Oct 2006 Posts: 10 Location: Victoria, B.C., Canada

Posted: Fri Feb 15, 2008 1:27 am Post subject: Assassin 90 


My procedure for attacking Assassins.
1. Open JSudoku.
2. File>Fetch>SudoCue>Weekly Assassin Killer.
3. Hit <ctrl> D 100 times.
4. If the grid turns every colour of the rainbow and the log
file says "No enabled solver can progress !" head off to the pub.
5. If not, get pencil and paper and start work.
6. I am off to the pub! 

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mhparker Grandmaster
Joined: 20 Jan 2007 Posts: 345 Location: Germany

Posted: Fri Feb 15, 2008 10:46 am Post subject: 


Afmob (on Bored89 thread) wrote:  We cannot expect that Ruud's makes all V2 for us so it's good that other users do this. But right now, I would love to have some easier assassins which aren't of rating 1.251.5 since they are the most fun to solve. 
frank wrote:  6. I am off to the pub! 
Hope you at least had a good time at the pub, Frank!
Ruud certainly seems to have turned up the heat with his recent Assassins! In bygone times, we used to create V2's based on the same cage pattern. Now, if anything, the only practical option left is to create a "Lite" version!
Like Afmob, I think it's nice to have easier V1 Assassins interspersed with the more difficult ones, because it's fun to do an Assassin without using eliminationbased solving from time to time. The fact that someone then quickly posts a message on the forum saying that the puzzle was easy doesn't necessarily mean that they didn't enjoy solving it, or that the puzzle was substandard.
BTW, hope to be able to join you guys solving these things as soon as work eases off a bit. (Is that a bit of light I can see at the end of the tunnel, or am I starting to hallucinate... ) _________________ Cheers,
Mike 

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Nasenbaer Master
Joined: 20 Jul 2006 Posts: 167 Location: Fellbach (Deutschland)

Posted: Fri Feb 15, 2008 9:20 pm Post subject: 


This assassin drives me crazy. I've already used several chains (and two sheets of paper) in 45 steps but still only 3 placements.
And all of it on the left side. I don't see a way to move on. I think I'm missing something significant...
Cheers,
Nasenbaer 

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goooders Regular
Joined: 18 Feb 2007 Posts: 16 Location: london

Posted: Sat Feb 16, 2008 9:39 am Post subject: 


When was the last time, errors excepted, that an assassin hasnt been completed on day 1 ? 

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HATMAN Regular
Joined: 06 Jan 2008 Posts: 16 Location: Britain, Turkey

Posted: Sat Feb 16, 2008 9:58 am Post subject: 


Frank
I use control shift D  easier on the fingers, and I can't use pencil and paper for hard puzzles my writing is just too messy  otherwise I agree with you, Guinness being my preference.
And this one is a complete swine. _________________ Save a GRUE: eat a brass lantern 

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Afmob Expert
Joined: 22 Sep 2007 Posts: 103 Location: MV, Germany

Posted: Sat Feb 16, 2008 5:08 pm Post subject: 


Seems my plea didn't get heard .
I used some forcing chains and one (or two) contradiction chain(s) to crack this monster. As always I tried to eliminate candidates by using Killer pairs/triples and this assassin offered some chances to do this.
A90 Walkthrough:
1. C456
a) 23(3) = {689} locked for C6
b) Innies C6 = 14(3) = 7{25/34}
c) 22(3) = 9{58/67} > 9 locked for C4
d) Innies C4 = 9(3) <> 7,8
e) 14(3) @ N2 <> 5{27/36} since they are blocked by Killer pairs (56,57) of 22(3)
2. C123
a) 6(3) @ N1 = {123} locked for N1
b) 6(3) @ N7 = {123} locked between R9+N7 > R9C12 <> 1,2,3
c) Outies C12 = 9(2): R3C3 <> 9; R7C3 <> 6,7,8,9
d) Innies C1 = 12(3) <> 8,9 because (123) only possible @ R1C1
e) 13(2): R5C2 <> 4,5
f) 16(3): R4C1 <> 8,9 because R23C1 >= 9
g) 15(3) @ N1: R4C2 <> 7,8,9 because R3C23 >= 9
h) 15(3) @ N7: R8C2 <> 7,8,9 because R9C12 >= 9
i) 17(3) @ R6C2: R67C2 <> 1,2 because R7C3 <= 5
j) Outies N7 = 10(2+1) <> 9; R6C1 <> 7,8 because R6C2+R9C4 >= 4
k) 17(3) @ C1 <> 4 since 4{58/67} blocked by Killer pair (45,46) of Innies C1
l) Hidden Killer pair (89) in 16(3) for C1 since 17(3) can't have both
> 16(3) <> 7{36/45}
3. C789
a) Outies C89 = 10(2) <> 5; R7C7 <> 2,3
b) Outies N9 = 19(2+1): R6C89 <> 1,2 because R9C6 <= 7
c) Outies N3 = 16(2+1): R4C9 <> 1,2 because R1C9+R4C8 <= 13
4. R789
a) Innies+Outies R9: 6 = R8C2378  R9C5 > R9C5 <> 2,3
b) Consider placement of (123) in 15(3) @ N7 > R78C1 <> 1,2,3:
 i) 15(3) has one of (123) > 15(3) with R89C3 builds naked triple (123) in N7 > R78C1 <> 1,2,3
 ii) 15(3) = {456} > R7C3+R89C3 = {123} > R78C1 <> 1,2,3
c) 17(3) @ C1 must have one of 1,2,3 and it's only possible @ R6C1 > R6C1 <> 5,6
d) Outies N7 = 10(2+1): R6C2 <> 3 because R6C1+R9C4 <= 6
e) 17(3) @ R6C2: R7C2 <> 3 because R6C2+R7C3 <= 13
5. C123 !
a) Hidden triple (123) in R146C1 for C1 > R4C1 = (123)
b) Outies N1 = 11(2+1): R4C2 <> 1 because R1C4+R4C1 <= 9
c) 19(3) <> 2 because {289} blocked by Killer pair (89) of 16(3)
d) Outies C123 = 9(3): R5C4 <> 6 because R1C4 <> 1,2
e) Killer pair (89) locked in 16(3) + 19(3) for N1
f) Outies C12 = 9(2): R7C3 <> 1
g) Hidden killer pair (89) in 19(3) + 20(4) for C3
> 20(4) <> {1289/2567/3467}
h) Consider placement of (23) in Innies C12 = 23(4) > 15(3) @ N7 <> 8, R9C1 <> 7
 i) Innies have none of (23) > R3467C2 = {4568} > R9C2 = (79) > R9C1 @ 15(3) @ N7 <> 7
 ii) Innies have one of (23) > Innies+R12C2 build Naked triple for C2 > 15(3) @ N7 = {456} <> 7,8
i) Innies C12 = 23(4) = {2579/2678/3578/4568} because:
 <> {2489} since 17(3) @ C2 can't have 8 and 9
 <> {3569} since it clashes with 15(3) @ N7 = {456} (step 5h)
 <> {3479} because R4C2 = 3 forces 15(3) @ N1 = [753] > Innies = [7349]
> 17(3) @ C2 can't have 4 and 9
j) ! Outies C1 = 22(5) = 19{237/246/345} because {13468} can only be {13}8{46}
which forces 13(2) = [58] and 15(3) = {456} with R9C1 = 5 > Two 5s in C1
> 9 locked for C2
6. C123 !
a) 13(2) <> 5
b) 8 locked in 17(3) @ C2 = 8{27/36/45}
c) 20(4) = {1568/2378/2459/3458} since other combos blocked by Killer pairs (46,47,69,79) of 13(2)
d) ! Consider placement of (123) in 15(3) @ N7 > R7C2 <> 6,7
 i) 15(3) has one of (123) > 15(3) + R89C3 builds Naked triple for N7 > 17(3) @ C2 = {458}
 ii) 15(3) = {456} > 17(3) @ C1 = 7{19/28} with 7 locked for N7 > R7C2 = 8
e) ! 15(3) @ N7 <> 9 since 17(3) @ C1 can't have 6 and 7
7. C123
a) Hidden Single: R5C2 = 9 @ C2 > R5C1 = 4
b) 15(3) @ N7 = {267/357/456} <> 1
c) 1 locked in R12C2 for N1
d) 1 locked in 6(3) @ N7 for C3; R9C4 <> 1
e) Outies C123 = 9(3): R5C4 <> 5 because R19C4 >= 5
f) Outies C123 = 9(3) must have 4,5 xor 6 and it's only possible @ R1C4 > R1C4 <> 3
g) 20(4) = 8{156/237} > 8 locked for C3+N4
h) 19(3) = {469} > 9 locked for N1
i) Hidden Single: R7C2 = 8 @ C2
j) 17(3) @ C2 = 8{27/36/45} > R7C3 <> 5
k) Outies C123 = 9(3) = 2{16/34} because R1C4 = (46) > 2 locked for C4
l) Outies C12 = 9(2): R3C3 <> 4
8. C6789
a) 1 locked in 8(3) for N8 > R6C6 <> 1
b) 9(2) <> 5
c) Outies C89 = 10(2) <> 2
d) 15(4) <> 9 because (123) is a Killer triple of 9(2)
e) 15(4) <> {1347} since (137) is a Killer triple of 9(2)
9. C123
a) Hidden Killer pair (57) in 20(4) + R3C3 for C3 > R3C3 <> 6
b) Outies C12 = 9(2): R7C3 <> 3
c) 17(3) @ C2: R6C2 <> 6
d) Killer pair (57) locked in 20(4) + R6C2 for N4
10. C456 !
a) Innies+Outies N2: 4 = R4C46  R1C46
> R4C4 <> 4 because R1C4 = R4C6 (HS @ C4) would be 6 > equation impossible (R1C6 = 0)
b) 4 locked in R123C4 for N2
c) 14(3) @ C4: R4C4 <> 6 because {17}6 blocked by Killer pair (17) of 12(3)
d) ! 14(3) @ C4: R4C4 <> 8 because 14(3) would be {15}8 > 12(3) = {237} > no candidate for R1C6
e) 23(3): R4C6 <> 9 because R1C4 + R23C6 = {468} is blocked by Killer triple (468) of 14(3) @ N2
f) 9 locked in 23(3) for N2
g) Innies+Outies N2: 4 = R4C46  R1C46 > R1C6 <> 2 because sum of R4C46 is always odd
h) 2 locked in 12(3) = {237} locked for C5+N2
i) R1C6 = 5
11. C456
a) 19(3) = 6{49/58} > 6 locked for C5+N8
b) 14(3) @ C5 = 1{49/58} > 1 locked for N5
c) Innies C4 = {234} > R1C4 = 4
d) 8(3) = {134} locked for C6
e) 20(4) = {2378} > 7 locked for C3+N4
f) 17(3) @ N2 = 5[39/84/93]
12. C123
a) 17(3) @ C2 = {458} > R6C2 = 5, R7C3 = 4
b) 15(3) @ N7 = 7{26/35} > R9C2 = 7
c) Hidden pair (78) in R23C1 for N1
d) 16(3) = {178} > R4C1 = 1
13. C789
a) R9C6 = 2
b) 17(3) @ N8 = 2{69/78}; R8C7 <> 8
c) 15(4) = {1257} > R6C5 = 7, {125} locked for C7+N8
d) 9(3) = 2{16/34} because (15) only possible @ R3C8 > R3C8 = 2
e) 9(2) = {36} locked for R5+N6
f) 9(3) = {234} > R3C7 = 3, R4C8 = 4
g) 17(3) @ R1C6 = {458} > R1C7 = 8, R2C7 = 4
h) 17(3) @ R2C9 = {179} locked C9; 1 locked for N3
i) 17(3) @ N7 = {269} > {69} locked for N9
14. N7
a) R9C4 = 3, R9C3 = 1, R8C3 = 2
b) 15(3) @ N7 = {357} > R8C2 = 3, R9C1 = 5
15. Rest is singles.
Rating: Hard 1.75. I tried to avoid contradiction chains by using forcing chains but I couldn't resist using very short ones (step 5j and maybe 10d).
By the way, if your software can't solve it than see it as a chance to show you can do better .
Last edited by Afmob on Fri Feb 22, 2008 7:40 am; edited 2 times in total 

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HATMAN Regular
Joined: 06 Jan 2008 Posts: 16 Location: Britain, Turkey

Posted: Sat Feb 16, 2008 8:08 pm Post subject: 


Afmob
You sound as bad as Udosuk.
There is also the balance of: sudoku solving time; drinking time; and sudoku creation time. In my world the latter two dominate.
Check out the KNight AntiConsecutives I've been putting together with Evert on sudoku.com.
Maurice _________________ Save a GRUE: eat a brass lantern 

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Nasenbaer Master
Joined: 20 Jul 2006 Posts: 167 Location: Fellbach (Deutschland)

Posted: Sat Feb 16, 2008 10:28 pm Post subject: 


This assassin was a real beast. I used a lot of chains, almost gave up.
SudokuSolver rates it as 1.61 which is much too low in my opinion. The rating of hard 1.75 from Afmob seems ok with me.
Cheers,
Nasenbaer 

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goooders Regular
Joined: 18 Feb 2007 Posts: 16 Location: london

Posted: Sun Feb 17, 2008 9:43 am Post subject: 


This was horrible.Took me nearly 10 hours.And near on 2 bottles of sauvignon blanc/chardonnay.If anything I would go north of 1.75. 

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gary w Addict
Joined: 07 Sep 2007 Posts: 84 Location: south wales

Posted: Tue Feb 19, 2008 12:28 am Post subject: 


Like Afmob I was only able to solve this one using a contradiction "move".
IO combos on N1 together with constraints from the 6(3) cage N1 and r159c4=9 > r4c1=4
The 14(3) cage c4 thus contains a 1 and the IO N2 then >r4c6=5
So r4c4=5/7,r4c6=6/8.
Also r59c6=[27] and only by a contradiction move could I easily resolve this combo(r5c69=72).
With this move assassin took only about 2.5 hours.Without it?????
Regards
Gary 

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Andrew Grandmaster
Joined: 11 Aug 2006 Posts: 300 Location: Lethbridge, Alberta

Posted: Thu Feb 21, 2008 11:24 pm Post subject: 


Like everyone else I found A90 a really tough Assassin.
Nasenbaer wrote:  This assassin was a real beast. I used a lot of chains, almost gave up.
SudokuSolver rates it as 1.61 which is much too low in my opinion. The rating of hard 1.75 from Afmob seems ok with me. 
Afmob also used chains. My solution used fairly heavy combination and permutation analysis. I only finished A74 Brick Wall fairly recently (I'll post a message and possibly a walkthrough once I've looked at Afmob's and Para's walkthroughs for it) so it seemed natural to use the same sort of techniques although not to anywhere near the same extent. For that reason I agree with Afmob's rating of Hard 1.75.
Maybe the reason that SudokuSolver gives a lower rating is that it's Richard's solver and he's very good at combination and permutation analysis.
Here is my walkthrough for A90
Prelims
a) R5C12 = {49/58/67}, no 1,2,3
b) R5C89 = {18/27/36/45}, no 9
c) 6(3) cage in N1 = {123}, locked for N1
d) 19(3) cage at R1C3 = {289/379/469/478/568}, no 1
e) R234C6 = {689}, locked for C6
f) 9(3) cage at R3C7 = {126/135/234},no 7,8,9
g) R678C4 = {589/679}, 9 locked for C4
h) R678C6 = {125/134}, 1 locked for C6
i) 19(3) cage at R6C8 = {289/379/469/478/568}, no 1
j) R789C5 = {289/379/469/478/568}, no 1
k) 6(3) cage at R8C3 = {123}, CPE no 1,2,3 in R9C12
1. Min R23C1 = 9 > max R4C1 = 7
1a. Min R3C23 = 9 > max R4C2 = 6
1b. Min R9C12 = 9 > max R8C2 = 6
2. 45 rule on C1 3 innies R159C1 = 12 = {147/156/246/345} (cannot be {129/138/237} because 1,2,3 only in R1C1), no 8,9, cleanup: no 4,5 in R5C2
3. R234C1 = {169/178/259/268/349/358} (cannot be {367/457} which clash with R159C1)
3a. 1,2,3 must be in R4C1 > R4C1 = {123}
4. R678C1 = {179/269/278/359/368} (cannot be {458/467} which clash with R159C1), no 4
5. 45 rule on C4 3 innies R159C4 = 9 = {126/135/234},no 7,8
6. 45 rule on C12 2 outies R37C3 = 9 = {45}/[63/72/81], no 9, no 6,7,8 in R7C3
7. 45 rule on C89 2 outies R37C7 = 10 = [19/28/37]/{46}, no 5, no 2,3 in R7C7
8. 45 rule on N7 3 outies R6C12 + R9C4 = 10 > max R6C12 = 9, no 9
9. 45 rule on N7 2 innies R7C23 = 2 outies R6C1 + R9C4 + 7
9a. Max R7C23 = 14 > max R6C1 + R9C4 = 7, no 7,8 in R6C1
9b. Min R6C1 + R9C4 = 2 > min R7C23 = 9, max R7C3 = 5 > min R7C2 = 4
10. R678C1 (step 4) = {179/269/278/359/368}
10a. 1 of {179} must be in R6C1 > no 1 in R78C1
11. 17(3) cage at R6C2 = {179/269/278/359/368/458/467}
11a. 1,2 of {179/269/278} must be in R7C3 > no 1,2 in R6C2
12. 45 rule on N9 3 outies R6C89 + R9C6 = 19, max R9C6 = 7 > min R6C89 = 12, no 1,2
13. R789C5 = {289/379/469/478/568}
13a. Hidden killer pair 8,9 in R78C4 and R789C5 > R78C4 cannot have both of 8,9 > no 5 in R6C4
14. 45 rule on N1 3 outies R1C4 + R4C12 = 11, max R1C4 = 6 > min R4C12 = 5, max R4C1 = 3 > no 1 in R4C2
15. 45 rule on N3 2 outies R1C6 + R4C9 = 2 innies R3C78 + 7
15a. Min R3C78 = 3 > min R1C6 + R4C9 = 10, max R1C6 = 7 > min R4C9 = 3
16. 45 rule on C12 4 innies R3467C2 = 23 = {2489/2579/2678/3479/3578/4568} (cannot be {3569} because killer triple 1,2,3 in R12C2 and R46C2 => R8C2 = 4, R9C2 = {78} which leaves no combinations for 15(3) cage at R8C2)
16a. If R3467C2 = {2489/2579/2678/3479/3578} => killer triple 1,2,3 in R12C2 and R46C2, locked for C2 => 15(3) cage can only be {456} => max R7C3 = 3 => min R67C2 = 14
> no 3 in R6C2, cleanup: no 6 in R6C1 (step 8)
16b. For these combinations of R3467C2, R7C12 + R8C1 = {789}, R78C1 cannot be {89} => R7C2 cannot be 4,5,6,7
> no 7 in R7C2
16c. 4 of {2489/3479} must be in R3C2 (cannot make valid combinations for 17(3) with 4 in R6C2; step 16a has already eliminated 4,5 from R7C23 for these combinations)
16d. Cannot be {2489} because no valid combination for 17(3) with R67C2 = [89]
16d. If R3467C2 = {4568} => 15(3) cage = [159/249/267/357]
16e. Combining steps 16a and 16d > no 7 in R9C1, no 8 in R9C2
16f. 8 of {2678} must be in R67C2 (R67C2 cannot be {67} because max R7C3 = 3, step 16a), 8 of {4568} must be in R67C2 (15(3) cage at R3C2 can only be {456} for {4568} in R3467C2) > no 8 in R3C2
16g. R3467C2 = {2579/2678/3479/3578/4568}
16h. If R3467C2 = {2579/2678/3479/3578} => R7C12 + R8C1 = {789} (step 16b), if R3467C2 = {4568} => R8C2 = {123} => killer triple 1,2,3 in R8C2 + R89C3 for N7 > no 2,3 in R78C1
16i. 9 of {2579} cannot be in R3C2 because 17(3) cage at R6C2 cannot be [755], 4 of {3479} must be in R3C2 (step 16c) > no 9 in R3C2
17. Hidden triple {123} in R146C1 > R6C1 = {123}
18. R159C1 (step 2) = {147/156/246/345}
18a. R1C1 = 1 => R12C2 = {23} => R8C2 = 1 => R9C12 = [59] (step 16d)
> no {147} in R159C1
18b. R159C1 = {156/246/345}, no 7, cleanup: no 6 in R5C2
18c. R234C1 (step 3) = {169/178/268/349/358} (cannot be {259} which clashes with R159C1
18d. R678C1 (step 4) = {179/269/278/359} (cannot be {368} which clashes with R159C1)
19. R3467C2 (step 16g) = {2678/3479/3578/4568} (cannot be {2579} which clashes with R678C1)
19a. If R3467C2 = {2678/3479/3578} => no 4,5,6 in R7C2 (step 16b)
19b. {4568} must have {458} in 17(3) cage at R6C2 because 1,2,3 of N7 locked in R8C2 (step 16d) and R89C3)
19c. > no 6 in R7C2
20. R3467C2 (step 16g) = {2678/3479/3578/4568}
20a. If {2678} => R5C12 = [49]
20aa. If [6278] => R3C3 = 7, R456C3 = {568} => R12C3 = {49} > no valid combination for 19(3) cage at R1C3
20ab. If [7268] => R456C3 = {578} > no valid combination for 20(4) cage at R4C3
20b. If {3479} => R5C12 = [58], R3467C2 = [4379], R3C3 = 8, R456C3 = {469}, R12C3 = {57} > no valid combination for 19(3) cage at R1C3
20c. If {3578} => R5C12 = [49]
20ca. If [5378] => R3C3 = 7, R456C3 = {568} => R12C3 = {49} > no valid combination for 19(3) cage at R1C3
20cb. If [7358] => R456C3 = {678} > no valid combination for 20(4) cage at R4C3
20cc. If [7385] => R3C3 = 5, R456C3 = {567} clashes with R3C3
20d. > R3467C2 = {4568}, locked for C2, cleanup: no 5 in R5C1
21. Naked triple {123} in R8C23 + R9C3, locked for N7, cleanup: no 6,7,8 in R3C3 (step 6)
21a. Naked pair {45} in R37C3, locked for C3
22. 15(3) cage at R3C2 = {456}, 6 locked in R34C2, locked for C2
23. 19(3) cage at R1C3 = {289/379/469/478/568}
23a. 2,3,4,5 must be in R1C4 > R1C4 = {2345}
24. R234C1 (step 18c) = {169/178/268/349/358}
24a. If {169} => R12C3 = {78}, R3C23 = {45}, R4C2 = 6 > cannot place 6 in C3 > R234C1 cannot be {169}
24b. If {178} => R12C3 = {69}, R1C4 = 4
24c. If {268} => R12C3 = {79}, R1C4 = 3
24d. If {349} => R3C23 = [65], R12C3 = {78}, R1C4 = 4
24e. If {358} => R3C23 = [64], R12C3 = {79}, R1C4 = 3
24f. > R1C4 = {34}, R234C1 = {178/268/349/358}, R12C3 = {69/78/79}
25. R159C4 (step 5) = {135/234} (cannot be {126} because R1C4 only contains 3,4), no 6, 3 locked for C4
25a. 5 of {135} must be in R5C4 > no 1 in R5C4
26. Hidden killer pairs 6,7 and 8,9 in R12C3 and R456C3 > R456C3 must contain one of 6,7 and one of 8,9
26a. 20(4) cage at R4C3 = {1568/2378/2468} (cannot be {1379} which clashes with R5C2, cannot be {1469/2369} which clash with R5C12, cannot be {1478} because 4 in R5C4 clashes R12C3 = {69} => R1C4 = 4), no 9
27. R5C2 = 9 (hidden single in N4), R5C1 = 4, R9C2 = 7, cleanup: no 5 in R5C89
27a. R8C2 + R9C1 = [26/35] (step 16d), no 1
27b. Max R9C6 = 5 > min R6C89 = 14 (step 12), no 3,4
28. 4 in N1 locked in R3C23, locked for R3, cleanup: no 6 in R7C7 (step 7)
28a. 4 in N7 locked in R7C23, locked for R7, cleanup: no 6 in R3C7 (step 7)
29. 20(4) cage at R4C3 (step 26a) = {1568/2378}, 8 locked in R456C3, locked for C3 and N4 > R6C2 = 5, R7C23 = [84], R4C2 = 6, R3C23 = [45], cleanup: no 2 in R3C7 (step 7)
29a. Min R6C89 = 15 > max R9C6 = 4 (step 12)
30. 20(4) cage at R4C3 (step 29) = {2378}, no 1,5, 7 locked in R456C3, locked for C3
31. Naked pair {69} in R12C3, locked for N1, R1C4 = 4 (step 23), R59C4 = {23} (step 5)
31a. Naked pair {23} in R59C4, locked for C4
32. R23C1 = {78} > R4C1 = 1 (step 18c)
33. 1 in C4 locked in R23C4, locked for N2
33a. 1 in N8 locked in R78C6, locked for C6
33b. 6 in C6 locked in R23C6, locked for N2
34. R234C4 = {158} (only remaining combination), no 7, locked for C4
35. R123C5 = {237} (only remaining combination), locked for C5 and N2 > R1C6 = 5, cleanup: no 2 in R678C6 (Prelim h)
35a. R12C7 = 12 = {39}/[84], no 1,2,6,7, no 8 in R2C7
36. Naked triple {134} in R678C6, locked for C6 > R9C6 = 2, R9C4 = 3, R89C3 = [21], R8C2 = 3, R5C4 = 2, R5C6 = 7
36a. R89C7 = 15 = {69}/[78], no 1,4,5, no 8 in R8C7
36b. 2 in C7 locked in R46C7, locked for N6
36c. R5C6 = 7 > R456C7 = 8 = {125}, locked for C7 and N6 > R3C7 = 3, R4C8 = 4, R3C8 = 2 (cage sum), R3C5 = 7, R23C1 = [78], R234C4 = [815], R456C7 = [251], cleanup: no 8 in R5C89, no 9 in R12C7 (step 35a)
36d. R12C7 = [84], cleanup: no 7 in R8C7 (step 36a)
37. Naked pair {36} in R5C89, locked for R5 and N6 > R5C3 = 8, R5C5 = 1
37a. Naked pair {37} in R46C3, locked for N4 > R6C1 = 2, R1C1 = 3, R12C5 = [23], R12C2 = [12]
38. Naked pair {89} in R4C56, locked for R4 and N5 > R4C9 = 7, R46C3 = [37], R6C456 = [643], R78C6 = [14]
38a. R23C9 = 10 = [19] > R1C9 = 6, R12C8 = [75], R12C3 = [96], R234C6 = [968], R4C5 = 9, R5C89 = [63], R6C89 = [98], R7C78 = [73], R89C8 = [18], R78C9 = [25], R9C9 = 4, R78C4 = [97]
39. R6C1 = 2 > R78C1 = 15 = [69]
and the rest is naked singles 

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