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 Post subject: Assassin 384
PostPosted: Sun Sep 15, 2019 8:03 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
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JSudoku found this one very easy so tried it. Hadn't made any of these for a good while and when was completely stuck I wondered if it was really worth so much effort! Then found some really interesting interactions and was hooked (again!). So, a few early placements possible then have to think carefully but nothing stenuous. Actually quite refreshing after the last bunch! SudokuSolver gives it 1.95 but doesn't use any big routines, must be just a very long solution.
triple click code:
3x3::k:4864:4864:3073:3073:2562:2562:2307:6148:6148:2053:4864:4864:5126:5126:5126:2307:6148:6148:2053:2823:0000:2825:5126:5126:8458:8458:8458:2053:2823:0000:2825:4619:4619:4619:8458:2316:4365:0000:0000:7694:7694:2831:8458:8458:2316:4365:3344:7694:7694:7694:2831:2831:4625:4625:4365:3344:0000:7694:5395:5395:2324:4625:4625:2581:2581:0000:5395:3350:3350:2324:2583:2583:2840:2840:2840:5395:5395:3858:3858:2056:2056:
solution:
Code:
+-------+-------+-------+
| 7 3 4 | 8 9 1 | 2 6 5 |
| 5 8 1 | 6 2 3 | 7 9 4 |
| 2 9 6 | 7 4 5 | 3 8 1 |
+-------+-------+-------+
| 1 2 9 | 4 3 7 | 8 5 6 |
| 8 4 5 | 1 6 2 | 9 7 3 |
| 3 6 7 | 9 5 8 | 1 4 2 |
+-------+-------+-------+
| 6 7 8 | 2 1 4 | 5 3 9 |
| 9 1 3 | 5 7 6 | 4 2 8 |
| 4 5 2 | 3 8 9 | 6 1 7 |
+-------+-------+-------+

Cheers
Ed


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 Post subject: Re: Assassin 384
PostPosted: Sun Sep 22, 2019 1:06 am 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Thanks Ed! Happy to find a couple of moves early on which cracked it for me. Not too difficult this one and quite a short solution path.
Assassin 384 WT:
1. Outies n9 -> r6c8 + r6c9 + r9c6 = +15(3)
Since r9c6 from (6789) -> r6c89 between +6 and +9 -> 9 not in r6c89
Innies n36 = r46c7 + r6c89 = +15(4)
Since r6c89 between +6 and +9 -> r46c7 between +6 and +9 -> 9 not in r46c7
-> 9 in 33(6) in n6
-> Outies n3 = r4c8 + r5c78 = +21(3) = {489} or {579}

2! Outies c89 = r35c7 = +12(2)
(Regardless of whether outies n3 = {489} or {579}) -> r35c7 = [39]
-> Remaining cells in 33(6) (r3c89 and r45c8) are [{18}{57}] or [{27}{48}]

3. Innies n2 = r13c4 = +15(2)
-> 12(2)r1 and 11(2)c4 from [57][83] or [48][74] or [39][65]

4! Outies r12 = r3c156 + r4c1 = +12(4)
Since 3 and one of (12) already in r3 and since r3c1 is max 5 -> Only solutions are:

For r3c789 = [3{18}]
(A) r3c156,r4c1 = [{245}1]

For r3c789 = [3{27}]
(B) r3c156,r4c1 = [{145}2]
(C) r3c156,r4c1 = [4{16}1]

But (C) is impossible since that puts r13c4 = [78] which leaves no solution for 10(2)n2.

5. (Edited to make clearer hopefully)
Step 4(A) has 8 already in r3 so puts r3c4 from (67) -> r1c4 from (98) -> r1c3 from (34)
-> 8(3)c1 = [{25}1]
Step 4(B) -> 8(3)c1 = [{15}2]

-> In both cases 8(3)c1 = {125}

6! Cracked
Innies c1 = r189c1 = +20(3) doesn't have a 5 -> Must have a 9
9 in r3 only in r3c23
-> HS 9 in c1 -> r8c1 = 9

7. Basically all singles from here
-> 10(2)n7 = [91]
Since Innies r9 = r9c45 = +11(2) -> (HS 1 in r9) 8(2)r9 = {17}
-> 15(2)r9 = [96]
-> r9c45 = {38}
-> 11(3)n7 = [4{25}]

Also 10(2)n9 = {28}
-> 9(2)n9 = {45}
-> r7c89 = {39}

Also 13(2)n8 = {67}
Also Innies n8 -> r7c4 = 2
-> 21(5)n8 = [{145}{38}] with 1 in r7c56

Also NS r8c3 = 3
Also Innies c1 -> r1c1 = 7
-> 12(2)r1 can only be [48]
-> 11(2)c4 = [74]
-> r3c789 = [3{18}]
-> r45c8 = {57}
etc.


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 Post subject: Re: Assassin 384
PostPosted: Wed Sep 25, 2019 5:02 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin. I found it a very challenging puzzle and it took me a long time to solve it. It took me a long time to reach the 'early' placements, partly because I missed the key part of wellbeback's step 2 and Ed's step 4. :oops:

Here is my walkthrough for Assassin 384:
Prelims

a) R1C34 = {39/48/57}, no 1,2,6
b) R1C56 = {19/28/37/46}, no 5
c) R12C7 = {18/27/36/45}, no 9
d) R34C2 = {29/38/47/56}, no 1
e) R45C9 = {18/27/36/45}, no 9
f) R67C2 = {49/58/67}, no 1,2,3
g) R78C7 = {18/27/36/45}, no 9
h) R8C12 = {19/28/37/46}, no 5
i) R8C56 = {49/58/67}, no 1,2,3
j) R8C89 = {19/28/37/46}, no 5
k) R9C67 = {69/78}
l) R9C89 = {17/26/35}, no 4,8,9
m) 8(3) cage at R2C1 = {125/134}
n) 11(3) cage at R5C6 = {128/137/146/236/245}, no 9
o) 11(3) cage at R9C1 = {128/137/146/236/245}, no 9

1a. 8(3) cage at R2C1 = {125/134}, 1 locked for C1, clean-up: no 9 in R8C2
1b. 45 rule on C1 3 innies R189C1 = 20 = {389/479/569/578}, no 2, clean-up: no 8 in R8C2

2. 45 rule on N2 2 innies R13C4 = 15 = [78/87/96] -> R1C3 = {345}, R4C4 = {345}

3a. 45 rule on N3 3 outies R4C8 + R5C78 = 21 = {489/579/678}, no 1,2,3
3b. 45 rule on C89 2 outies R35C7 = 12 = [39]/{48/57}, no 1,2,6, no 9 in R3C7

4. 45 rule on N8 2 innies R7C4 + R9C6 = 11 = [29/38/47/56]

5. 45 rule on C456789 2 outies R16C3 = 11 = [38/47/56]

6a. 45 rule on R9 2 innies R9C45 = 11 = {29/38/47/56}, no 1
6b. 45 rule on R9 3 outies R7C56 + R8C4 must contain 1 for N8 = 10 = {127/136/145}, no 8,9
6c. 9 in R9 only in R9C45 = {29} or R9C67 = {69} -> R9C45 = {29/38/47} (cannot be {56}, locking-out cages), no 5,6
6d. Hidden killer pair 1,5 in 11(3) cage at R9C1 and R9C89 for R9, neither can contain both of 1,5 -> 11(3) cage at R9C1 = {128/137/146/245}, R9C89 = {17/35}, no 2,6
[Alternatively R9C89 = {26} clashes with R9C45 = {29} or R9C67 = {69}.]
6e. R8C89 = {19/28/46} (cannot be {37} which clashes with R9C89), no 3,7
6f. 11(3) cage at R9C1 = {128/146/245} (cannot be {137} which clashes with R9C89), no 3,7
6g. 8 of {128} must be in R9C1 -> no 8 in R9C23

7a. 45 rule on C789 3 innies R469C7 = 15
7b. Min R69C7 = 7 -> max R4C7 = 8
7c. 45 rule on N9 2 outies R6C89 = 1 innie R9C7
7d. Max R6C89 = 9, no 9 in R6C89
7e. 9 in N6 only in R4C8 + R5C78, locked for 33(6) cage at R3C7
7f. R4C8 + R5C78 (step 3a) contains 9 = {489/579}, no 6
[Oops! At this stage I missed R35C7 cannot be {48/57} which clash with R4C8 + R5C78 = {489/579}. To express this another way, the 12+9 in R4C8 + R5C78 cannot be the same 12 that are in R35C7 because of the overlap at R5C7.
If I’d eliminated the other 9s from N6 earlier, as wellbeback and Ed did, I might have then spotted it when I found step 3b. It would have simplified things, including the time I spent trying to find a nice way to do step 11.]
7g. R45C9 = {18/27/36} (cannot be {45} which clash with R4C8 + R5C78), no 4,5
7h. 45 rule on N3 3 innies R3C789 = 12 = {138/156/237/246} (cannot be {147/345} which clash with R4C8 + R5C78)
7i. R12C7 = {18/27/45} (cannot be {36} which clashes with R3C789), no 3,6

8. 45 rule on R12 2 outies R3C56 = 1 innie R2C1 + 4
8a. Max R2C1 = 5 -> max R3C56 = 9, no 9 in R3C56
8b. 9 in R3 only in R3C23, locked for N1
8c. R189C1 (step 1b) = {389/479/569/578}
8d. 9 of {389/479/569} must be in R8C1 -> no 3,4,6 in R8C1, clean-up: no 4,6,7 in R8C2
8e. 4 of {479} must be in R9C1 -> no 4 in R1C1

9. 11(3) cage at R9C1 (step 6f) = {128/146/245}
9a. Consider combinations for R189C1 (step 1b) = {389/479/569/578}
R189C1 = {389/479/569} => R8C1 = 9, R8C2 = 1 => 11(3) cage = {245}
or R189C1 = {578} => R9C1 = {58} => 11(3) cage = {128/245}
-> 11(3) cage = {128/245}, no 6, 2 locked for R9 and N7, clean-up: no 8 in R8C1
9b. 6 in R9 only in R9C67 = {69}, 9 locked for R9, clean-up: no 3,4 in R7C4 (step 4)

10. R469C7 = 15 (step 7a) = {159/168/249/267/456} (cannot be {258/348/357} because R9C7 only contains 6,9), no 3
10a. 6 of {168/267/456} must be in R9C7 -> no 6 in R46C7
10b. 6 in C7 only in R789C7, locked for N9, clean-up: no 4 in R8C89
10c. Killer triple 7,8,9 in R8C1, R8C56 and R8C89, locked for R8, clean-up: no 1,2 in R7C7

[The best way I could find for this step, even though it’s not a pure forcing chain.]
11. R7C4 + R9C6 (step 4) = [29/56]
11a. Consider combinations for R8C56 = {49/58/67}
R8C56 = {49}, 9 locked for N8 => R9C56 = [69], 6 in C7 only in R78C7 = {36}, 3 locked for N9, R9C89 = {17} => R7C89 = {45} (hidden pair in N9), 5 locked for R7 => R7C4 = 2
or R8C56 = {58/67} => R7C4 + R9C6 = [29] (cannot be [56] which clashes with R8C56)
-> R7C4 + R9C6 = [29] -> R9C7 = 6, clean-up: no 1 in R1C5, no 4 in R8C56, no 3 in R78C7
11b. R35C7 = [39] (hidden pair in C7), clean-up: no 8 in R4C2
11c. R3C7 = 3 -> R3C789 (step 7h) = {138/237}, no 4,5,6
11d. 33(6) cage at R3C7 = {138}{579}/{237}{489}, CPE no 7,8 in R12C8
11e. 45 rule on N9 2 remaining innies R7C89 = 12 = {39/48} (cannot be {57} which clashes with R9C89), no 1,5,7
11f. 45 rule on N9 2 remaining outies R6C89 = 6 = {15/24}
11g. Killer pair 4,5 in R45C8 and R6C89, locked for N6
11h. 4 in N6 only in R45C8 + R6C89, CPE no 4 in R7C8, clean-up: no 8 in R7C9
[With hindsight, step 14 would follow from here.]
11i. R45C9 = {36} (hidden pair in N6), locked for C9, clean-up: no 9 in R7C8, no 5 in R9C8
11j. R7C56 + R8C4 (step 6b) = {136/145}, no 7
11k. 9 in R8 only in R8C12 = [91] or R8C89 = {19}, 1 locked for R8 (locking cages), clean-up: no 8 in R7C7
11l. 1 in N8 only in R7C56, locked for R7

12. R189C1 (step 1b) = {389/479/569/578}
12a. Consider combinations for 11(3) cage at R9C1 (step 9a) = {128/245}
11(3) cage = {128} = 8{12}, 1 locked for N7 => R8C12 = [73] => R189C1 = [578]
or 11(3) cage = {245}, R9C1 = {45} => R189C1 = {479/569/578} -> R189C1 = {479/569/578}, no 3
12b. Killer pair 4,5 in R189C1 and 8(3) cage at R2C1, locked for C1

13. R469C7 = 15 (step 7a), R9C7 = 6 -> R46C7 = 9 = {18/27}
13a. Consider combinations for R3C89 (step 11c) = {18/27}
R3C89 = {18}
or R3C89 = {27}, 7 locked for 33(6) cage at R3C7 => 7 in N6 only in R46C7 = {27} => R12C7 = {18} (hidden pair in C7)
-> 1,8 in R12C7 + R3C89, locked for N3

14. R4C8 + R5C78 (step 3a) = {489/579} -> R45C8 = {48/57}, R6C89 (step 11f) = {15/24}, R7C89 (step 11e) = [39/84]
14a. 18(4) cage at R6C8 = {15}[39]/{24}[39] (cannot be {15}[84] which clashes with R45C8) -> R7C89 = [39], clean-up: no 4 in R6C2, no 1 in R8C89, no 5 in R9C9
[Cracked, at last. The rest is straightforward.]
14b. Naked pair {28} in R8C89, locked for R8, clean-up: no 5 in R8C56
14c. Naked pair {17} in R9C89, locked for R9, 7 locked for N9
14d. 11(3) cage at R9C1 = {245} (only remaining combination), 4,5 locked for N7, 4 locked for R9, clean-up: no 8,9 in R6C2
14e. Naked pair {67} in R8C56, locked for R8, 6 locked for N8 -> R8C123 = [913], clean-up: no 9 in R1C4
14f. R13C4 (step 2) = 15 = {78}, locked for C4 and N2 -> R9C45 = [38], clean-up: no 2,3 in R1C56
14g. R34C4 = 11 = [74], R1C4 = 8 -> R1C3 = 4, R8C4 = 5, R78C7 = [54], clean-up: no 6 in R1C56, no 2 in R3C89 (step 11f), no 7 in R4C2
14h. R1C56 = [91], R7C56 = [14], R256C4 = [619]
14i. Naked pair {18} in R3C89, locked for R3 and N3, 8 locked for 33(6) cage at R3C7, clean-up: no 3 in R4C2
14j. Naked pair {27} in R12C7, locked for C7 and N3
14k. Naked pair {25} in R3C16, locked for R3 -> R3C5 = 4, clean-up: no 6,9 in R4C2
14l. R45C8 = 12 = {57}, locked for C8, 5 locked for N6
14m. 8(3) cage at R2C1 = {125} (only remaining combination), 2,5 locked for C1
14n. 17(3) cage at R5C1 = {368} (only remaining combination), 6 locked for C1, 3 locked for N4
14o. R1C1 = 7, R1C2 = 3 (hidden single in R1) -> R2C23 = 9 = [81], clean-up: no 5 in R6C2
14p. R4C1 = 1 (hidden single in C1) -> R46C7 = [81]
14q. R4C7 = 8 -> R4C56 = 10 = {37}, locked for R4 and N5
14r. Naked pair {56} in R56C5, locked for C5 and N5
14s. R1C3 = 4 -> R6C3 = 7 (step 5), R6C2 = 6, R3C2 = 9 -> R4C2 = 2

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A384 at Hard 1.5.


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 Post subject: Re: Assassin 384
PostPosted: Sat Sep 28, 2019 2:12 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
3 very different experiences with this puzzle! Huge shortcut by wellbeback. I would only look for that sort of step when really stuck. Didn't need it for this one. My steps 4 (same as wellbeback's step 2) & 6 got me hooked on this puzzle. Step 18 is my final cracker.
a384 WT:
Preliminaries
Cage 15(2) n89 - cells only uses 6789
Cage 8(2) n9 - cells do not use 489
Cage 12(2) n12 - cells do not use 126
Cage 13(2) n47 - cells do not use 123
Cage 13(2) n8 - cells do not use 123
Cage 9(2) n9 - cells do not use 9
Cage 9(2) n3 - cells do not use 9
Cage 9(2) n6 - cells do not use 9
Cage 10(2) n9 - cells do not use 5
Cage 10(2) n7 - cells do not use 5
Cage 10(2) n2 - cells do not use 5
Cage 11(2) n14 - cells do not use 1
Cage 11(2) n25 - cells do not use 1
Cage 8(3) n14 - cells do not use 6789
Cage 11(3) n7 - cells do not use 9
Cage 11(3) n56 - cells do not use 9


1. "45" on n9: 2 outies r6c89 = 1 innie r9c7
1a. -> no 9 in r6c89

2. "45" on c789: 3 innies r469c7 = 15
2a. min. r69c7 = 7 -> max r4c7 = 8

3. "45" on n3: 3 outies r45c8 + r5c7 = 21 and must have 9 for n6
3a. = {489/579}(no 1,2,3,6)
3b. 9 locked for 33(6) cage

4. "45" on c89: 2 outies r35c7 = 12
4a. but {48/57} both blocked by clash with {48/57} in h21(3)n6 (step 3a)(combo crossover clash CCC)
4b. = [39] only permutation
4c. no 6 in the two 9(2) cages in c7

5. r3c7 = 3 -> from "45" on n3: r3c89 = 9
5a. but cannot be {45} because r45c8 = 4 or 5
(same cage)
5b. = {18/27}(no 4,5,6)

6. 9(2)n6 sees one cell of the h9(2)r3c89 -> they must have different combinations
6a. -> {18/27} blocked from 9(2)n6 since r45c8 needs one of 7 or 8 (same cage as h9(2))
6b. {45} also blocked by r45c8 = 4 or 5
6c. 9(3)n6 = {36} only: both locked for n6 and c9

7. r9c7 = 6 (hsingle c7), r9c6 = 9
7a. one remaining innie n8 -> r7c4 = 2

8. "45" on n2: 2 innies r13c4 = 15 = [96/87/78]
8a. r1c3 = (345)

9. "45" on r12: 1 innie r2c1 + 4 = 2 outies r3c56
9a. max. r2c1 = 5 -> max. r3c56 = 9 (no 9)

10. 9 in r3 only in n1: locked for n1

11. hidden killer triple 678 in n1: r3c23 can have at most one of 6,7,8 (since 9 must be there) -> 19(4)n1 must have at least 2 of 6,7,8
11a. = {1378/1468/1567/2368/2467}
11b. can't have more than two of 6,7,8 -> r3c23 must have one off -> r3c23 from {6789}
11c. -> killer triple 6,7,8 in r3 with r3c489: locked for r3

12. hidden killer triple 3,4,5 in n1: 19(4) must have exactly one of 3,4,5 (step 11a), r1c3 has one -> r23c1 must have exactly one of 3,4,5
12a. 8(3)n1 = {125/134} ->r23c1 = {15/25/14}/[31] = 1 or 5 (other permutations don't have one of 3,4,5)
12b. 1 must be in 8(3): locked for c1

13. 19(4)n1: {1567} blocked by r23c1 = 1 or 5
13a. = {1378/1468/2368/2467}(no 5)

14. 8(2)n9 = {17}[35](no 2) = 1 or 3
14a. 11(3)n7: must have 2 for r9
14b. = {128/245}(no 3,7)
14c. 2 locked for n7

15. "45" on r9: 2 innies r9c45 = 11 = {38/47}(no 1,5)
15a. r9c45 = 11 -> r7c56 + r8c4 = 10 = {136/145}(no 7,8)

16. 10(2)n7 = [91]{37/46}(no 8, no 9 in r8c2)

17. "45" on c1: 3 innies r189c1 = 20 = {389/479/569/578}(no 2)

Final cracker step
18. 7 in n8 in r89 -> 10(2)n7 and 8(2)n9 cannot be {37}+{17}
18a. -> r89c1 <> [75]
18b. -> h20(3)c1: {578} as [875] only permutation is blocked
18c. h20(3)c1 = {389/479/569}
18d. must have 9 -> r8c1 = 9, r8c2 = 1

19. 11(3)n7 = {245} only: 4 & 5 locked for n7 and r9
19a. -> h20(3)c1 must have 4 or 5 = {479/569}(no 3)
19b. r1c1 = (67)

20. killer pair 4,5 in c1 between 8(3) and r9c1: both locked for c1

21. 8(2)n9 = {17} only: both locked for n9, 7 for r9

22. 10(2)n9 = {28} only: 8 locked for n9 and r8

23. 9(2)n9 = {45}: both locked for c7 and n9
23a. r7c89 = [39]
23b. r7c89 = 12 -> r6c89 = 6 = {15/24}(no 7,8)

24. naked triple {678} in r7c123: 6,7 locked for n7, 6 for r7
24a. r8c3 = 3
24b. no 9 in r1c4

25. 13(2)n8 = {67}: 6 locked for n8

26. "45" on n2: 2 innies r13c4 = 15 = {78} only: both locked for c4 and n2
26a. r9c45 = [38]

27. r34c4 = [74] only permutation
27a. r1c34 = [48]
27b. r8c4 = 5, r78c7 = [54]

28. 10(2)n2 = [91] only permutation
28a. r256c4 = [619]
28b. r7c56 = [14]

29. r12c8 = [69] (both hsingles n3)
29a. r19c1 = [74](h20(3)c1)
29b. r12c7 = [27], r12c9 = [54] (cage sum)

30. naked pair {18} in r3c89: both locked for r3 and 8 for 33(6) cage
30a. -> r45c8 = {57} only: both locked for c8
30b. r6c89 = [42] only permutation h6(2)

31. 18(3)r4c5 must have 1 or 8 for r4c7 = {378} only = {37}[8]: 3 and 7 locked for r4 and n5
31a. r4c8 = 5

32. hidden single 2 in n5 -> r5c6 = 2

33. 11(2)r3c2 = [92] only permutation

34. "45" on c456789: 1 remaining outie r6c3 = 7

easy now
Cheers
Ed


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