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Ed
 Post subject: Assassin 453
PostPosted: Fri Mar 01, 2024 6:53 pm 
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Posts: 1044
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Assassin 453
A fun one for me. Came out quickly from seeing a couple of nice steps. SudokuSolver gives it 1.60. JSudoku has a really hard time with 23 chains on its default settings.
triple click code:
3x3::k:6656:6656:6656:6657:2562:6403:6403:4356:4356:6656:1285:1285:6657:2562:6403:6406:6406:4356:5127:5127:6657:6657:6657:6403:6403:6406:6406:5127:6664:6664:6664:7689:7689:7689:7689:6406:5127:6664:6922:2827:7689:3852:7689:7689:3085:6922:6664:6922:2827:2827:3852:4366:7439:3085:6922:6922:6922:4880:3857:3852:4366:7439:7439:4370:2579:2579:4880:3857:4116:7439:7439:7439:4370:4370:4370:4880:3857:4116:4116:1813:1813:
solution: 
+-------+-------+-------+
| 8 5 6 | 4 7 1 | 3 9 2 |
| 7 1 4 | 2 3 9 | 5 8 6 |
| 2 3 9 | 6 5 8 | 4 1 7 |
+-------+-------+-------+
| 6 8 7 | 5 9 3 | 1 2 4 |
| 9 2 1 | 8 4 7 | 6 5 3 |
| 3 4 5 | 1 2 6 | 8 7 9 |
+-------+-------+-------+
| 4 6 8 | 7 1 2 | 9 3 5 |
| 1 7 3 | 9 6 5 | 2 4 8 |
| 5 9 2 | 3 8 4 | 7 6 1 |
+-------+-------+-------+

Cheers
Ed
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wellbeback
 Post subject: Re: Assassin 453
PostPosted: Thu Mar 07, 2024 1:11 am 
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Thanks again Ed! Another cool puzzle with interesting deductions available. Here's how I did it...
Assassin 453 WT:
1. 17(2)c7 = {89}
-> r9c7 is Max 7.
-> (IOD n8) [r7c6,r9c7] from [16] or [27]
-> (IOD n9) r6c78 from +14(2) or +15(2) (No 1234)
Also r56c6 = +14(2) or +13(2) (No 123)

2. Outies n23 = r3c3 + r4c9 = +13(2)
-> r4c9 is Min 4
-> (12) in n6 in r45c78 (In the 30(7))

3. Outies c6789 = r45c5 = +13(2)
Since 30(7) cannot contain both (67) -> r45c5 from {58} or {49}
-> If r7c6 = 1 this puts 15(3)c6 = [{68}1]

4. Since r7c6 from (12) -> (Remaining IOD n5) r4c46 = +7(2) or +8(2)
-> Exactly one of (123) in r4c46
-> Two of (123) in 11(3)n5
-> 11(3)n5 from {128}, {137}, or {236}

5. Innies n5689 = r4c49 = +9(2)
IOD c123 -> r3c3 = r4c4 + 4
I.e., r4c4 from (12345), r4c9 from (87654), r3c3 from (56789)

6. Remaining Innies c5 = r36c5 = +7(2)
Since one of (456) in there and one of (45) in r45c6 -> 10(2)n2 not {46}
-> If 6 is in r3c3 that puts 6 in n2 in r12c6

7. (12) in n5 either both in 11(3)n5 (= {128}) or one of (12) in r4c4
Trying 2 in r4r4 puts 11(3)n5 = {137}
But it also puts 6 in r3c3 and (previous step) 6 in r12c6 which leaves no place for 6 in n5
-> 2 not in r4c4

8. -> 2 in 11(3)n5
-> 11(3)n5 = {128} or {236}
-> No solution for 15(3)c6 with r7c6 = 1 (Step 3 Line 3)
-> r7c6 = 2 and r9c7 = 7

9. r3c3 cannot be 5 since that puts 5 in n2 in r12c6 which leaves no solution for remaining outies n2 = r13c7 = +11(2)
-> r4c4 not 1
-> 1 in 11(3)n5
-> 11(3)n5 = {128}
-> r45c5 = {49}
-> 15(3)c6 = [{67}2]
-> r4c46 = {35}

10. Since 9 in r45c5 -> 30(7) = {1234569}
-> 6 in 30(7) in n6 in r45c78
-> (Innies n5689) r4c49 = [54], r4c6 = 3, and r45c78 = {1256}
-> 12(2)n6 = {39}
-> 17(2)c7 = [89]
-> r6c8 = 7
-> r56c6 = [76]
Also 11(3)n5 = [8{12}]
Also r45c5 = [94]

11. IOD n4 -> r45c1 = +15(2) (No 5)
-> Outies n7 = r6c1 + r56c3 = +9(3) must have a 5
-> r5c3 = 1 and r6c13 = {35}
-> 12(2)n6 = [39]
Also r7c123 = {468}
Also remaining Innies n4 = r45c1 = +15(2) = [69] (Since (78) in n4 both in r4)
-> r4c23 = {78}
-> r56c2 = [24]
Also r3c12 = +5(2)
-> 26(4)n1 = {5678}
Also r23c2 = {13}
-> 10(2)n7 = [73]
etc.
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Andrew
 Post subject: Re: Assassin 453
PostPosted: Thu Mar 07, 2024 4:55 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for another excellent Assassin. Once I'd found my two interesting steps it came out quickly.

Here's how I solved Assassin 453:
Prelims

a) R12C5 = {19/28/37/46}, no 5
b) R2C23 = {14/23}
c) R56C9 = {39/48/57}, no 1,2,6
d) R67C7 = {89}
e) R8C23 = {19/28/37/46}, no 5
f) R9C89 = {16/25/34}, no 7,8,9
g) 11(3) cage at R5C4 = {128/137/146/236/245}, no 9
h) 19(3) cage at R7C4 = {289/379/469/478/568}, no 1
i) 26(4) cage at R1C1 = {2789/3689/4589/4679/5678}, no 1
j) 30(7) cage at R4C5 = {1234569/1234578}

1a. Naked pair {89} in R67C7, locked for C7
1b. 45 rule on C123 1 innie R3C3 = 1 outie R4C4 + 4 -> R3C3 = {56789}, R4C4 = {12345}
1c. 45 rule on C1234 2 outies R36C5 = 7 = {16/25/34}, no 7,8,9
1d. 45 rule on C6789 2 outies R45C5 = 13 = {49/58} (cannot be {67} because 30(7) cage at R4C5 can only contain one of 6,7)
1e. 45 rule on C6789 5 innies R4C678 + R5C78 = 17 = {12347/12356}, no 8,9
1f. R4C678 + R5C78 = {12347/12356}, CPE no 1,2,3 in R4C9
1g. 11(3) cage at R5C4 = {128/137/146/236} (cannot be {245} which clashes with R45C5), no 5, clean-up: no 2 in R3C5
1h. 45 rule on N7 3 outies R5C3 + R6C13 = 9 = {126/135/234}, no 7,8,9
1i. 45 rule on N7 3 innies R7C123 = 18 = {279/378/459/468/567} (cannot be {189} which clashes with R7C7, cannot be {369} which clashes with R5C3 + R6C13), no 1
1j. 45 rule on N8 3 innies R789C6 = 11 = {128/137/146/236/245}, no 9
1k. 45 rule on N8 1 outie R9C7 = 1 innie R7C6 + 5 -> R7C6 = {12}, R9C7 = {67}
1l. Max R7C6 = 2 -> min R56C6 = 13, no 1,2,3 in R56C6
1m. R45C5 contains one of 4,5, R56C6 contains one of 4,5,6 -> 11(3) cage = {128/137/236} (cannot be {146} killer ALS block), no 4, clean-up: no 3 in R3C5
1n. 45 rule on N5689 2 innies R4C49 = 9, no 9 in R4C9
1o. 45 rule on N47 3(2+1) outies R3C12 + R4C4 = 10 -> max R3C12 = 9, no 9 in R3C12
1p. 45 rule on N47 2 innies R45C1 = 1 outie R4C4 + 10, min R45C1 = 11, no 1 in R45C1
1q. 45 rule on N89 2 outies R6C78 = 1 innie R7C6 + 13
1r. R7C6 = {12} -> R6C78 = 14,15 = [86/87/95/96]
1s. 1,2 in N6 only in R45C78, locked for 30(7) cage, no 1,2 in R4C6
1t. 15(3) cage at R7C5 = {168/249/258/267/357} (cannot be {159/348/456} which clash with R45C5)
1u. 16(3) cage at R8C6 = {178/268/367/457} (cannot be {358} because R9C7 only contains 6,7)
1v. R789C6 = {128/137/245} (cannot be {146} because 16(3) cage doesn’t contain both of 4,6, cannot be {236} which clashes with 15(3) cage), no 6
1w. 15(3) cage = {168/249/258/357} (cannot be {267} which clashes with R789C6)
1x. 19(3) cage at R7C4 = {379/469/568} (cannot be {478} which clashes with R789C6, cannot be {289} which clashes with 15(3) cage combined with R789C6), no 2
1y. Hidden killer triple 7,8,9 in R12C5, R45C5 and 15(3) cage for C5, R45C5 and 15(3) cage both contain one of 7,8,9 -> R12C5 must contain one of 7,8,9 = {19/28/37}, no 4,6
[Alternatively R12C5 cannot be {46} which clashes with R36C5 and R45C5, killer ALS block]
1z. 7 in C5 only in R12C5 = {37} or 15(3) cage = {357}, 3 locked for C5 (locking cages), clean-up: no 4 in R3C5

[I was slow finding step 2d, realised that it didn’t work for R4C4 = 2, then quickly found step 2b, after which it came out quickly.]
2a. 11(3) cage at R5C4 (step 1m) = {128/137/236}, R3C3 = R4C4 + 4 (step 1b)
2b. Consider permutations for R36C5 = 7 (step 1c) = [16/52/61]
R36C5 = [16] => 11(3) cage = {236}
or R36C5 = [52] => 11(3) cage = {128/236}
or R36C5 = [61], no 6 in R3C3 => no 2 in R4C4 => 2 in N5 in R45C4 => 11(3) cage = {128}
-> 11(3) cage = {128/236}, no 7, 2 locked for N5, clean-up: no 6 in R3C3, no 7 in R4C9 (step 1n)
2c. 15(3) cage at R5C6 = {49}2/{58}2/{67}2/{68}1 (cannot be {59}1 which clashes with R45C5)
2d. Consider placements for R4C4 = {1345}
R4C1 = 1 => 11(3) cage = {236}, 6 locked for N5 => 15(3) cage = {49}2/{58}2
or R4C1 = {345}, 1,2 in N5 only in 11(3) cage = {128}, 8 locked for N5 => 15(3) cage = {49}2/{67}2
-> R7C6 = 2, R56C6 = {49/58/67}, R9C7 = 7 (step 1k), R89C6 = 9 = {18/45}, no 3, R56C6 = {49/67} (cannot be {58} which clashes with R89C6, no 5,8
[Cracked. The rest is fairly straightforward.]
2e. R7C6 = 2 -> R6C78 = 15 (step 1r) = [87/96]
2f. 19(3) cage at R7C4 (step 1x) = {379/469} (cannot be {568} which clashes with R89C6), no 5,8, 9 locked for C4 and N8
2g. 15(3) cage at R7C5 (step 1w) = {168/357}, no 4
2h. 4 in C5 only in R45C5 = 13 = {49}, locked for N5, 9 locked for C5, 4 locked for 30(7) cage at R4C5, clean-up: no 1 in R12C5, no 5 in R4C9 (step 1n)
2i. Naked pair {67} in R56C6, locked for C6 and N6, clean-up: no 8 in R3C3 (step 1b), no 1 in R3C5
2j. 11(3) cage = {128} (only remaining combination), 1 locked for N5, 8 locked for C4, clean-up: no 8 in R4C9 (step 1n)
2k. R45C5 = {49} -> 30(7) cage = {1234569}, 6 locked for N6 -> R4C9 = 4, R6C8 = 7, R56C9 = {39}, locked for C9 and N6 -> R4C6 = 3, R4C4 = 5, R3C3 = 9 (step 1b), R45C5 = [94], R56C6 = [76], R67C7 = [89], clean-up: no 1 in R8C2, no 3,4 in R9C8
2l. Naked pair 1,2 in R6C45, locked for R6 and N5 -> R5C4 = 8
2m. Naked quad {1256} in R45C78, 5 locked for R5
2n. R5C3 + R6C13 (step 1h) = {135/234} (cannot be {126} because 1,2,6 only in R5C3) -> R5C3 = {12}, R6C13 = {34/35}, 3 locked for R6 and N4 -> R56C9 = [39], R6C2 = 4, R6C13 = {35}, 3,5 locked for 27(6) cage, R5C3 = 1, clean-up: no 9 in R8C2, no 6 in R8C3
2o. R5C3 + R6C13 = 1{35} = 9 -> R7C123 = 18 = {468} (only remaining combination), locked for R7 and N7, clean-up: no 2 in R8C23
2p. Naked pair {37} in R8C23, locked for R8 and N7
2q. 45 rule on N47 2 remaining innies R45C1 = 15 = [69] (cannot be {78} because 7,8 only in R4C1), R5C2 = 2, clean-up: no 3 in R2C3
2r. R45C1 = 15 -> R3C12 = 5 = [23/41]
2s. Naked quad {1234} in R2C23 + R3C12, 1,3 locked for C2, 2,3,4 locked for N1 -> R8C23 = [73], R4C23 = [87]
2t. 19(3) cage at R7C4 = {379} (only remaining combination, cannot be {469} because R7C4 only contains 3,7) = [793]
2u. 15(3) cage = {168} (only remaining combination) -> R7C5 = 1, R89C5 = {68}, locked for C5, 8 locked for N8, R36C5 = [52], R6C4 = 1, R7C89 = [35], clean-up: no 2 in R9C89
2v. Naked pair {16} in R9C89, locked for R9 and N9
2w. Naked pair {25} in R9C13, locked for N7, 5 locked for R9 -> R9C6 = 4

3a. Naked triple {189} in R123C6, 1 locked for 25(5) cage at R1C4
3b. R123C6 = 18 -> R13C7 = 7 = {34}/[52]
3c. Killer pair 2,4 in R13C7 and R8C7, locked for C7 -> R4C78 = [12]
3d. R17C2 = [56], naked pair {78} in R12C1, 8 locked for C1 and N1, R1C3 = 6, clean-up: no 2 in R3C7
3e. Naked pair {34} in R13C7, locked for N3, 4 locked for C7
3f. R3C9 = 7 (hidden single in R3) -> 17(3) cage at R1C8 = {269} (only remaining combination) = [926]

and the rest is naked singles.
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Ed
 Post subject: Re: Assassin 453
PostPosted: Sun Mar 10, 2024 8:18 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
We all enjoyed this one! Excellent!! And we all worked in the same key area to make progress but I inverted them compared to the other two WTs (see my step 6).
a453:
Preliminaries by SudokuSolver
Cage 17(2) n69 - cells ={89}
Cage 5(2) n1 - cells only uses 1234
Cage 7(2) n9 - cells do not use 789
Cage 12(2) n6 - cells do not use 126
Cage 10(2) n7 - cells do not use 5
Cage 10(2) n2 - cells do not use 5
Cage 11(3) n5 - cells do not use 9
Cage 19(3) n8 - cells do not use 1
Cage 26(4) n1 - cells do not use 1

No clean-up done unless stated
1. 17(2)r6c7 = {89}: both locked for c7

2. 30(7)r4c5 is missing 15(2) = {69/78}
2a. "45" on c6789: 2 outies r45c5 = 13 and are both in the 30(7)
2b. -> can't be {67}
2c. = {49/58} = 5 or 9, 4 or 8, 4 or 5
2d. -> split 17(5) = {12347/12356}(no 8,9)

3. "45" on n8: 1 innie r7c6 + 5 = 1 outie r9c7
3a. = [16/27]

4. 15(3)r5c6 must have 1,2 for r7c6
4a. but {59}[1] blocked by h13(2)n5
4b. = {168/249/258/267}(no 3) = 2 or 5 or 8
4c. can't have both 1,2 -> no 1,2 r56c6
4d. note: if it has 1, must also have 8

5. 15(3)n8: {159/348/456} all blocked by h13(2)n5
5a. = {168/249/258/267/357} = 2 or 5 or 8

6. h13(2)n5: {58} blocked since it forces two 2s into n8 (steps 4d and 5a)
[Alternatively: the two 15(3) cages at r5c6 and r7c5 = 2 or 5 or 8. They can't both have 2, so they must have at least one of 5 and/or 8 -> {58} blocked from the common peers in r45c5]
6a. = {49} only: both locked for n5, c5 and 4 for 30(7)
6b. sp 17(5) = {12356}(no 7)
6c. -> no 1,2,3,5,6 in r4c9 since it sees all them (Common Peer Elimination CPE)

7. "45" n9: 2 outies r6c78 - 8 = 1 innie r9c7
7a. -> r6c78 = 14 or 15
7b. -> r6c8 = (567)

8. 4 in n6 only in r4c9 or 12(2) = {48}
8b. -> no 8 in r4c9 (Locking out cages)
8c. 4 locked for c9

9. "45" on n5689: 2 innies r4c49 = 9 = [54/27]

10. 11(3)n5 = {128/137/236}(no 5)
10a. note: if it has 6 must also have 2

11. "45" on c1234: 2 outies r36c5 = 7 = {16}/[52]

12. "45" on c123: 1 innie r3c3 - 4 = 1 outie r4c4
12a. = [62/95]
12b. but [62] leaves no permutation for the h7(2)r36c5 because of step 10a
12c. = [95] only
12d. -> r4c9 = 4 (h9(2))
12e. -> no 8 in 12(2)n6
12f. -> r6c7 = 8 (hsingle n6)
12g. r7c7 = 9
12h. r45c5 = [94]

13. 9 in n6 only in 12(2) = {39}: both locked for c9, 3 for n6
13a. -> sp17(5) which must have 3 (step 6b) only in r4c6 -> = 3

14. 11(3)n5 = {128} -> r5c4 = 8
14a. 1,2 locked for r6

15. r56c6 = {67}: both locked for c6
15a. and r7c6 = 2 (cage sum)
15a. -> r9c7 = 7 (iodn9=+5)

16. r6c8 = 7 (hsingle n6)
16a. r56c6 = [76]

17. "45" on n1: 2 outies r45c1 = 15 = [69] only permutation
17a. r56c9 = [39]

18. "45" on r6789: 1 remaining outie r5c3 + 3 = 1 remaining innie r6c2 = [14] only

19. r6c13 = {35}: both locked for 27(6)
19a. -> r7c123 = 18 (cage sum) = {468} only: all locked for r7 and n7

20. 10(2)n7 = {37} only: both locked for r8 and n7

21. r9c2 = 9 (hsingle n7)
21a. r5c2 = 2

22. 19(3)n8 = [793] only

23. 15(3)n8 = [1]{68}, 6,8 both locked for c5, 8 for n8
23a. r89c6 = {45}: both locked for c6

24. r3c12 = 5 (cage sum) = [41/23]
24a. naked pair {13} r23c2: 3 locked for c2, n1
24b. naked pair {24} r2c3 + r3c1: both locked n1

25. r8c23 = [73]
25a. r147c2 = [586]
25b. r3c5 = 5

26. naked triple {189} in r123c6: 1 locked for 25(5) and n2

27. "45" on n3: 2 innies r13c7 = 7 = {34} only: both locked for n3, 4 for c7

28. 7(2)n9: {25} blocked by r9c3 = (25)
28a. = {16} only: both locked for r9 and n9

etc
Cheers
Ed
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