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 Post subject: Assassin 288
PostPosted: Fri Mar 21, 2014 12:35 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Assassin 288

Again the is a serendipity one SS gives it 1.5 - quite interesting

Serendipity: when I run JSudoku it creates a puzzle if it has a high number of guesses in its solution and I like the pattern then I check the score in SS. I then swap numbers and merge cages to get to assassin level (and reverse this to get a messy and easy).


Image

JS Code:
3x3:d:k:4353:4353:3330:3330:1795:1795:2564:3845:3845:4353:4102:4102:1799:1799:7688:2564:3845:3593:1802:4102:4102:7179:7688:7688:7688:3593:3593:1802:2316:7179:7179:7179:7688:6157:6157:6157:2062:2316:8207:7179:3856:3856:7441:4370:6157:2062:8207:8207:8207:3856:3856:7441:4370:4370:1811:1811:8207:4884:7441:7441:7441:4370:7445:4886:4886:4119:4884:4376:4376:4376:7445:7445:4886:4119:4119:4884:4884:4376:7445:7445:7445:

Solution
978561342
162348795
435729681
314295867
287614953
659837214
523186479
841972536
796453128


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 Post subject: Re: Assassin 288
PostPosted: Mon Mar 24, 2014 7:37 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
Thanks HATMAN for another challenging Assassin!

The first two placements are easy and the next one was fairly easy; then I had to work hard before I managed to get any more placements, so the SS score seems reasonable. I'll be interested to see how Afmob, Ed and/or wellbeback solve this puzzle.

Here is my walkthrough for Assassin 288:
Thanks Ed for your comment about step 7, which I've re-phrased for clarity, and to Afmob for correcting a couple of typos and pointing out the easy step which I missed (see note after step 12b); if I'd spotted it the rest of my solving path would have been a lot easier.

Prelims

a) R1C34 = {49/58/67}, no 1,2,3
b) R1C56 = {16/25/34}, no 7,8,9
c) R12C7 = {19/28/37/46}, no 5
d) R2C45 = {16/25/34}, no 7,8,9
e) R34C1 = {16/25/34}, no 7,8,9
f) R45C2 = {18/27/36/45}, no 9
g) R56C1 = {17/26/35}, no 4,8,9
h) R7C12 = {16/25/34}, no 7,8,9
i) 19(3) cage at R8C1 = {289/379/469/478/568}, no 1
j) 32(5) cage at R6C3 = {26789/35789/45689}, no 1

1. 45 rule on N3 1 innie R3C7 = 6, placed for D/, clean-up: no 4 in R12C7, no 1 in R4C1
1a. 30(5) cage at R2C6 contains 6 = {25689/34689/35679/45678}, no 1

2. 45 rule on N7 1 innie R7C3 = 3, placed for D/, clean-up: no 4 in R7C12
2a. 32(5) cage at R6C3 contains 3 = {35789} (only remaining combination), no 2,4,6

3. 19(3) cage at R8C1 = {289/469/478} (cannot be {568} which clashes with R7C12), no 5

4. Killer quint 5,6,7,8,9 in R45C2, R56C1 and 32(5) cage at R6C3, locked for N4, clean-up: no 1,2 in R3C1
4a. 9 in N4 only in R5C3 + R6C23, locked for 32(5) cage, no 9 in R6C4

5. 45 rule on N1 2 innies R1C3 + R3C1 = 12 = [75/84/93] -> R1C4 = {456}

6. Killer triple 4,5,6 in R1C4 + R1C56 + R2C45, locked for N2

7. 30(5) cage at R2C6 (step 1a) = {25689/34689/35679} (cannot be {45678} because 4,5 only in R4C6) -> R4C6 = {45} (only possible place for 4 or 5), 9 locked for N2
7a. Killer triple 1,2,3 in R1C56, R2C45 and 30(5) cage, locked for N2
[Alternatively hidden killer pair 7,8 in R3C4 and 30(5) cage for N2, 30(5) cage contains one of 7,8 -> R3C4 = {78}.]

8. 45 rule on C89 2 outies R49C7 = 9 = {18/27/45}, no 3,9

[At this stage I saw locking-out cages in N4 using places for 6, but after the next few steps it’s not needed although the placements for 6 in N4 was useful later as part of my key breakthrough.]

9. 45 rule on C123 2 outies R16C4 = 1 innie R4C3 + 9
9a. R16C4 cannot total 10 -> no 1 in R4C3

10. 45 rule on N47 1 outie R6C4 = 2 innies R4C13 + 1
10a. Min R4C13 = 5 -> no 5 in R6C4
10b. R6C4 = {78} -> R4C13 = 6,7 = {24}/[34], 4 locked for R4 and N4 -> R4C6 = 5, placed for D/, clean-up: no 2 in R1C5, no 5 in R5C2, no 4,5 in R9C7 (step 8)

11. Naked pair {78} in R36C4, locked for C4
11a. Naked pair {78} in R36C4, CPE no 7,8 in R4C5

12. 45 rule on N2 2 remaining innies R13C4 = 12 = [48/57], no 6, clean-up: no 7 in R1C3, no 5 in R3C1 (step 5) -> no 2 in R4C1
12a. Naked pair {34} in R34C1, locked for C1, clean-up: no 5 in R56C1
12b. R45C2 = {18/36} (cannot be {27} which clashes with R56C1), no 2,7 in R45C2
[Afmob pointed out that after this I missed 7 in R4 only in R4C789, locked for N6 -> 24(4) cage at R4C7 must contain 7 so cannot contain 1.]

13. R12C7 = {19/37} (cannot be {28} which clashes with R49C7), no 2,8 in R12C7
13a. Killer pair 1,7 in R12C7 and R49C7, locked for C7

14. 28(5) cage at R3C4 = {14689/23689/24679} (cannot be {13789} because R4C3 only contains 2,4, cannot be {34678} because 7,8 only in R3C4), 6,9 locked for N5

15. 15(4) cage at R5C5 = {1248/1347}, 1,4 locked for N5

16. 45 rule on N2 1 remaining outie R1C3 = 1 innie R3C4 + 1 -> R1C3 + R3C4 = [87/98], CPE no 8 in R3C23

17. 45 rule on N1 1 outie R1C4 = 1 innie R3C1 + 1 -> R1C4 + R3C1 = [43/54], CPE no 4 in R1C2

18. 45 rule on N8 2 innies R7C56 = 1 outie R8C7 + 9
18a. Max R7C56 = 17 -> max R8C7 = 8

19. 45 rule on N89 4 innies R7C5678 = 25 = {1789/4579/4678} (cannot be {2689} which clashes with R7C12), no 2, 7 locked for R7
19a. 5 must be in R7C12 + R7C5678, locked for R7

20. 17(3) cage at R1C1 = {179/269/278/359} (cannot be {368} which clashes with R1C3 + R3C1)
20a. 3 of {359} must be in R1C2 -> no 5 in R1C2
20b. Killer pair 8,9 in 17(3) cage and R1C3, locked for N1

[I’m struggling to make progress, so I’ll try a short forcing chain.]
21. Consider combinations for 19(3) cage at R8C1 (step 3) = {289/469/478}
19(3) cage = {289} => R7C12 = {16}, killer pair 1,6 in R56C1 and R7C1, locked for C1
or 19(3) cage = {469/478} => killer pair 6,7 in R56C1 and 19(3) cage, locked for C1
-> no 6 in R12C1
21a. 17(3) cage at R1C1 (step 20) = {179/278/359} (cannot be {269} which clashes with R45C2 + R56C1 which must contain 6 in C2 or {26} in C1), no 6
[I first saw this as 17(3) cage at R1C1 (step 20) = {179/278/359} (cannot be {269} which clashes with 19(3) cage = {289/469} and with 19(3) cage = {478} + R56C1), no 6]

22. 6 in R1 only in R2C23 = {16}, locked for R1 and N2, clean-up: no 9 in R2C7

23. 15(3) cage at R1C8 = {249/258/348/357} (cannot be {159} which clashes with R1C34), no 1

24. R5C5 = 1 (hidden single on D/), placed for D\, R1C56 = [61], clean-up: no 8 in R4C2, no 7 in R6C1
24a. 6 in N5 only in R45C4, locked for C4

25. 1 in N8 only in 19(4) cage at R7C4 = {1279/1459} (cannot be {1378} because 7,8 only in R9C5), no 3,8, 9 locked for N8
25a. 7 of {1279} must be in R9C5 -> no 2 in R9C5
25b. R7C56 = R8C7 + 9 (step 18)
25c. Max R7C56 = 15 -> no 8 in R8C7

26. 3 in N8 only in R8C56 + R9C6, locked for 17(4) cage at R8C5, no 3 in R8C7
26a. 17(4) cage = {2348/2357}, no 6
26b. 17(4) cage = {2348/2357}, CPE no 2 in R8C4

27. R7C6 = 6 (hidden single in N8), clean-up: no 1 in R7C12
27a. Naked pair {25} in R7C12, locked for R7 and N7
27b. R7C5678 (step 19) contains 6 = {4678} (only remaining combination), locked for R7

28. 19(3) cage at R8C1 (step 3) = {469/478} -> R8C2 = 4, placed for D/

29. 2 on D/ only in 15(3) cage at R1C8 (step 23) = {249/258}, no 3,7, 2 locked for N3
29a. 4,5 only in R1C8 -> R1C8 = {45}
29b. Naked pair {45} in R1C48, locked for R1

30. 4 in C7 only in R567C7, locked for 29(5) cage at R5C7, no 4 in R7C5
30a. 29(5) cage contains 4,6 = {24689} (only remaining combination, cannot be {34679} which clashes with R12C7) -> R7C5 = 8, R7C7 = 4, placed for D\, R56C7 = {29}, locked for C7 and N6, clean-up: no 1 in R2C7, no 7 in R49C7 (step 8)
30b. Naked pair {37} in R12C7, locked for N3

31. R8C7 = 5 -> 17(4) cage at R8C5 = {2357}, 2,7 locked for N8
31a. Naked pair {19} in R78C4, locked for C4 and N8
31b. Naked pair {45} in R19C4, locked for C4, clean-up: no 2,3 in R2C5
31c. R4C5 = 9 (hidden single in N5)

32. R7C8 = 7 -> 17(4) cage at R5C8 = {1367/1457}, no 8, 1 locked for R6 and N6 -> R49C7 = [81], R7C9 = 9, R78C4 = [19], clean-up: no 7 in R5C1

33. Naked pair {26} in R56C1, locked for C1 and N4 -> R4C3 = 4, R34C1 = [43]

34. R2C1 = 1 (hidden single in C1), R1C1= 9 (hidden single on D\), R1C2 = 7 (cage sum), R1C3 = 8 -> R1C4 = 5, R1C89 = [42], R2C2 = 9 (cage sum), R2C5 = 4 -> R2C4 = 3

35. R6C6 = 7 (hidden single on D\), R6C4 = 8, placed for D/, R89C1 = [87]

36. R4C789 = [867], R5C9 = 3 (cage sum)

37. R8C8 = 3 (hidden single on D\)

and the rest is naked singles, without using the diagonals.

Rating Comment:
I'll rate my walkthrough for A288 at 1.5. I used a short forcing chain, with killer pairs in each of the paths.

HATMAN wrote:
I then swap numbers and merge cages to get to assassin level (and reverse this to get a messy and easy).
I must have a look at the messy and easy for A287; I haven't had time to try them and, of course, Assassins take priority. ;)


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 Post subject: Re: Assassin 288
PostPosted: Tue Mar 25, 2014 7:34 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
I echo Andrew and thank HATMAN for the puzzle. As well as Ed and Pinata for their puzzles. I've been lurking for a while now, but still do all the puzzles and look forward to all new ones.

Here is how I did (or at least started) this one.
Error fixed thanks to Andrew spotting it!
Hidden Text:
1. Innies n7 -> r7c3 = 3
-> 32/5@r5c3 = {5789}[3]

2. Innies n1 -> r1c3+r3c1 = +12
-> Since r3c1 in a 7/2 -> r3c1 from (345)
-> r1c3 from (987)
-> r1c4 from (456)

3. Innies n3 -> r3c7 = 6
Where are (789) in n2?
30/5@r2c6 can only contain at most two of (789).
-> r3c4 from (789) and two of (789) in r2c6,r3c56
-> r4c6 is max 5.

4. Also 1 cannot be in 30/5@r2c6
-> One of the 7/2s in n2 is {16}
-> r1c4 from (45)
-> r1c3 from (98)
-> r3c1 from (34)
-> r4c1 from (43). I.e., 7/2@r3c1 = {34}

5. Innies - Outies n12 (given r3c7 = 6) -> r4c1 + r4c6 = r3c4 + 1
Since r4c1 is max 4 and r4c6 is max 5 and r3c4 is min 7
-> (r3c4,r4c1,r4c6) from [735] or [845]
-> r4c6 = 5
-> 5 in n4 in (r5c3,r6c23) and r6c4 from (789)

6. Given r3c4 from (78) and r4c6 = 5
-> 15/4@r5c5 from {1347} or {1248}
-> 6 in n5 locked in r4c45 or r5c4.

7. Innies - Outies n5
Since r4c6 = 5 -> r3c4 + r4c3 = r6c4 + 3
Since r3c4 from (78) and r6c4 from (789) -> r4c3 from (24)

8. 8/2@r5c1 from {26} or {17}
-> 9/2@r4c2 cannot be {27}
-> 9/2@r4c2 from {18} or {36}
But putting 9/2@r4c2 = {36} puts 1 in r4 in r4c789 and 6 in r6 in r6c789
which leaves no solution for 24/4@r4c7
-> 9/2@r4c2 = {18}

9. -> 8/2@r5c1 = {26}
Also r6c4 = 8
-> r3c4 = 7
-> 30/5@r2c6 = {289}[65]
Also -> 15/4@r5c5 = {1347}
-> 28/5@r3c4 = [74]{269} (4 in r4c3)
-> 7/2@r3c1 = [43]
-> 13/2@r1c3 = [85]

10. 4 in c2 only in r89c2.
But since at least one of (57) already in c3 in r56c3 -> 4 cannot go in r9c2
-> r8c2 = 4
-> 19/3@r8c1 = [847] (D/)
-> r5c5 = 1 (D/)
-> (r1c9,r2c8) = {29} (D/)
-> r1c8 = 4
-> 7/2@r2c4 = {34}
-> 7/2@r1c5 = [61]
Also 10/2@r1c7 = [37]

etc....


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 Post subject:
PostPosted: Wed Mar 26, 2014 7:39 am 
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Grand Master
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for the new Assassin, HATMAN! This was surprisingly easy despite SudokuSolver's score. I looked at how it solved this Killer and in my opinion, the rating is too high for the techniques it uses.
A288 Walkthrough:
1. N1237 !
a) Innie N3 = R3C7 = 6
b) Innie N7 = R7C3 = 3
c) Innies N1 = 12(2) <> 1,2; R1C3 = (789)
d) 13(2): R1C4 = (456)
e) 7(2) @ C1: R4C1 = (234)
f) ! Killer triple (456) locked in R1C4 + both 7(2) for N2
g) 30(5) = 69{258/348/357} <> 1 since 4,5 only possible @ R4C6 -> R4C6 = (45), 9 locked for N2
h) Innies+Outies N12: 1 = R4C16 - R3C4: R3C4 = (78) since R4C16 >= 6
i) ! Innies+Outies N12: 1 = R4C16 - R3C4: R4C16 = [3/4]5 since R3C4 >= 7 -> R4C6 = 5

2. N1234
a) 32(5) = {35789} -> 5 locked for N4
b) 9(2) <> {27} since it's a Killer pair of 8(2)
c) Killer pair (16) locked in 8(2) + 9(2) for N4
d) Innies+Outies N4: 1 = R6C4 - R4C13: R4C3 = (24) since R4C1 >= 3
e) 9 locked in 32(5) @ N4 for 32(5)
f) 28(5) = 69{148/238/247} since R4C3 = (24) and {34678} blocked by R6C4 = (78) -> 6,9 locked for N5; R4C45+R5C4 <> 7,8 since R3C4 = (78)

3. R456
a) 15(4) = 14{28/37} -> 1,4 locked for N5
b) 7 locked in 24(4) @ R4 <> 1 for N6+24(4)
c) Hidden Single: R4C2 = 1 @ R4 -> R5C2 = 8
d) 32(5) = {35789} -> R6C4 = 8; 7 locked for N4
e) 28(5) = {24679} -> R4C3 = 4, R3C4 = 7; 2 locked for N5
f) R4C1 = 3 -> R3C1 = 4
g) 8 locked in 24(4) @ R4 = {3678} since 4,5 only possible @ R5C9 -> R5C9 = 3; 6 locked for R4+N6

4. C123
a) Innie N1 = R1C3 = 8
b) Cage sum: R1C4 = 5
c) 8(2) = {26} locked for C1
d) 19(3) = 8{29/47} -> R8C1 = 8, R8C2 = (24)

5. D/ + C789
a) 15(3) = {249} locked for N3
b) Naked triple (249) locked in R1C9+R2C8+R8C2 for D/
c) R9C1 = 7 -> R8C2 = 4, R5C5 = 1, R1C1 = 9, R4C4 = 2, R3C3 = 5
d) 10(2) = {37} locked for C7+N3
e) Outies C89 = 9(2) = [81] -> R4C7 = 8, R9C7 = 1

6. Rest is singles without considering diagonals.

Rating:
Easy 1.25. I used a Killer triple.


Last edited by Afmob on Wed Apr 02, 2014 4:53 pm, edited 1 time in total.

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 Post subject: Re: Assassin 288
PostPosted: Tue Apr 01, 2014 8:46 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Great solution Afmob!. Enjoyed the variety from Andrew and wellbeback. This was a fun puzzle even though I didn't get the third placement that the first three walkthroughs found. Went on a very different path (from step 11), and much longer but it just kept flowing. Avoided looking much at combo's in the larger cages. It felt easier than recent Assassins. Great to have a puzzle which allows four completely different ways. [Many thanks to Afmob and Andrew for telling me about typos]

A288
31 steps:
Preliminaries
Cage 7(2) n2 - cells do not use 789
Cage 7(2) n7 - cells do not use 789
Cage 7(2) n14 - cells do not use 789
Cage 7(2) n2 - cells do not use 789
Cage 8(2) n4 - cells do not use 489
Cage 13(2) n12 - cells do not use 123
Cage 9(2) n4 - cells do not use 9
Cage 10(2) n3 - cells do not use 5
Cage 19(3) n7 - cells do not use 1
Cage 32(5) n457 - cells do not use 1

1. "45" on n3: 1 innie r3c7 = 6, placed for D/
1a. 30(5)r2c6 must have 6 = {25689/34689/35679/45678} (no 1)
1b. no 4 in 10(2)n3
1c. no 1 in r4c1

2. "45" on n1: 2 innies r1c3+r3c1 = 12 = [93/84/75]
2a. r4c1 = (234)
2b. r1c4 = (456)

3. "45" on n23: 1 outie r4c6 + 7 = 2 innies r13c4
3a. -> min. r13c4 = 9 -> min. r3c4 = 3

4. 1 in n2 only in one of 7(2) cages -> 6 locked for n2 (Locking cages)
4a. no 7 in r1c3
4b. no 5 in r3c1 (h12(2)r1c3+r3c1)
4c. -> 7(2)r3c1 = {34} only: both locked for c1
4d. ->8(2)n4 = {17/26}(no 5) = [2/7..]
4c. no 3,4 in r7c2

5. "45" on n7: 1 innie r7c3 = 3, Placed for D/
5a. 32(5)r5c3 must have 3 = {35789}(no 2,4,6)

6. "45" on c123: 2 outies r16c4 - 9 = 1 innie r4c3
6a. -> min. r16c4 = 10 (no 5 in r6c4)
6b. min. r16c4 = 11 -> min. r4c3 = 2
6c. max. r16c4 = 14 -> max. r4c3 = 5

7. 5 must be in 32(5)r5c3 and is only in n4: 5 locked for n4
7a. no 4 in 9(2)n4

8. 9(2)n4: {27} blocked by 8(2) = [2/7](step 4b)
8a. 9(2) = {18/36}(no 2,7) = [1/3,3/8..]

9. 9 in n4 only in 32(5)r5c3: locked for that cage -> no 9 in r6c4

10. 19(3)n7: {568} blocked by 7(2)n7 = [5/6..]
10a. = {289/469/478}(no 5)

11. "45" on c1: 2 outies r18c2 - 6 = 1 innie r7c1
11a. since r7c1 & r8c2 are in the same nonet -> the innie/outie difference of 6 cannot be in r1c2 -> no 6 in r1c2 (IOU)

12. "45" on c1: 3 outies r178c2 = 13
12a. but {139/238} blocked by 9(2)n4 = [1/3,3/8..](step 8a)
12b. = {148/157/247/256/346}(no 9)
12c. 2 in {247} must be in r8c2 and 2 in {256} must be in r8c2 -> no 2 in r1c2

12d. "45" on n1: 1 outie r1c4 - 1 = 1 innie r3c1 = [43/54]: must have 4 -> no 4 in common peers in r1c2 nor r3c456

13. 17(3)n1: {269} blocked by no 2,6,9 in r1c2
13a. {368} blocked by h12(2)r1c3+r3c1 = [3/8..]
13b. 17(3) = {179/278/359}(no 6)

14. 6 in r1 only in 7(2)r1c5 = {16} only: both locked for n2 and 1 for r1
14a. no 9 in r2c7

15. "45" on r1: 2 outies r2c18 - 7 = 1 innie r1c7
15a. Since r1c7 and r2c8 are in the same nonet -> r2c1 cannot have the innie/outie difference of 7 -> no 7 in r2c1 (IOU)

16. "45" on r1: 3 outies r2c178 = 17
16a. but {359/458} blocked by 7(2)r2c45 = [3/5,4/5..]
16b. h17(3) = {179/278}(no 3,4,5)
16c. must have 7 which is only in n3 -> 7 locked for r2 and n3

17. 7 in r1 only in 17(3)n1 = {179/278}(no 3,5)
17a. 7 locked for n1

18. Hidden single 5 in c1 in r7c1 -> r7c12 = [52]

19. h13(3)r178c2 = [724] only permutation: 4 placed for D/

20. {59}[1] blocked from 15(3)n3 by 13(2)r1c3 = [5/9..]
20a. -> no 1 in 15(3)n3
20b. -> hidden single 1 in D/ -> r5c5 = 1, Placed for D\
20c. r1c56 = [61]

21. Killer pair 4,5 in r1c4 + 7(2)n2: both locked for n2

22. 4 in n4 only in r4: locked for r4

23. 30(5)r2c6 = {25689/35679}
23a. must have 5 -> r4c6 = 5, Placed for D/

24. 2 in D/ only in n3 -> 2 locked for n3 and 15(3)
24a. no 2 in r1c8
24b. 15(3)n3 must have 2 = {249/258}(no 3,7)

25. Hidden single 3 in r1 -> r1c7 = 3
25a. r2c7 = 7

25. "45" on n23: 2 innies r13c4 = 12 = [48/57]

26. Naked pair {78} in r36c4: both locked for c4 and no 7,8 in common peer r4c5

27. "45" on c89: 2 outies r49c7 = 9 = {18} only: both locked for c7

28. 4 in c7 only in 29(5)r5c7 = {24689}(no 5,7):
28a. must have 2, 2 locked for c7 & n6 and
28b. 4 locked for 29(5)->no 4 in r7c56
28c. naked triple {249} in r567c7: 9 locked for c7 and no 9 in r7c56
28d. r7c5 = 8, r7c6 = 6
28e. r8c7 = 5
28f. r8c7 = 5 -> r8c56+r9c6 = 12 = {237} only: all locked for n8

29. "45" on c1234: 3 outies r249c5 = 18 = {459} only
29a. -> r4c5 = 9

30. 2 in r4 only in r4c34-> no 2 in r5c4 nor r3c3 through D\

31. 2 in r3 only in n2: 2 locked for n2
31a. -> 7(2)r2c4 = [34] only permutation
on from there.
Cheers


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