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 Post subject: Assassin 368
PostPosted: Sun Jan 20, 2019 5:32 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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Disjoint 9(2)r3c46. Also, X-killer: 1-9 cannot repeat on either diagonal

Assassin 368
Really enjoyable puzzle. Easy start then keep making steady progress with just one vaguely advanced step. Some others are a little hidden but perhaps practice from previous versions of this puzzle might have made them easier to see. If you go heavy you've missed something! SudokuSolver gives it 1.55 JSudoku has a very interesting solver log including two chains.
code:
3x3:d:k:4352:8193:8193:3842:3842:3587:3587:3587:2308:4352:3333:8193:8193:3842:3842:2310:2310:2308:3333:3333:8193:2311:7176:2311:0000:0000:5130:11531:11531:8193:7176:7176:7176:0000:5130:5130:11531:11531:11531:7176:2572:2572:0000:7693:5130:11531:11531:11531:4366:2572:5647:5647:7693:3088:2065:11531:4366:4366:0000:5647:5647:7693:3088:2065:3859:3859:0000:0000:0000:0000:7693:3088:3090:3090:3859:1033:1033:0000:000:7693:7693:
solution:
Code:
+-------+-------+-------+
| 8 3 6 | 5 7 4 | 1 9 2 |
| 9 5 4 | 8 2 1 | 3 6 7 |
| 7 1 2 | 6 9 3 | 5 4 8 |
+-------+-------+-------+
| 3 2 9 | 4 6 8 | 7 5 1 |
| 5 4 7 | 1 3 2 | 9 8 6 |
| 1 6 8 | 9 5 7 | 4 2 3 |
+-------+-------+-------+
| 2 9 1 | 7 8 5 | 6 3 4 |
| 6 7 3 | 2 4 9 | 8 1 5 |
| 4 8 5 | 3 1 6 | 2 7 9 |
+-------+-------+-------+


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 Post subject: Re: Assassin 368
PostPosted: Tue Jan 22, 2019 6:17 am 
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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 Ed. As you said an easy start, then I had to start thinking and found some of my later steps enjoyable.

I like:
killer-Xs which use the diagonals as an active part of the solving path.
Of course I've nothing against killer-Xs which just use the diagonals to provide a unique solution; other aspects of these puzzles are usually good.
Here's my walkthrough for Assassin 368:
Prelims

a) R12C1 = {89}
b) R12C9 = {18/27/36/45}, no 9
c) R2C78 = {18/27/36/45}, no 9
d) R3C46 = {18/27/36/45}, no 9
e) R78C1 = {17/26/35}, no 4,8,9
f) R9C12 = {39/48/57}, no 1,2,6
g) R9C45 = {13}
h) 10(3) cage at R5C5 = {127/136/145/235}, no 8,9

Steps Resulting From Prelims
1a. Naked pair {89} in R12C1, locked for C1 and N1, clean-up: no 3,4 in R9C2
1b. Naked pair {13} in R9C45, locked for R9 and N8, clean-up: no 9 in R9C2

2. 45 rule on N1 2 outies R2C4 + R4C3 = 17 = {89}
2a. Naked pair {89} in R2C14, locked for R2, clean-up: no 1 in R1C9, no 1 in R2C78
2b. 45 rule on N4 1 outie R7C2 = 1 innie R4C3 -> R7C2 = {89}
2c. 45 rule on N7 2 innies R7C23 = 10 = [82/91]
2d. 45 rule on C123 3 outies R267C4 = 24 = {789}, locked for C4, clean-up: no 1,2 in R3C6

3. 45 rule on N2 3 innies R1C6 + R2C4 + R3C5 = 21 = {489/579/678}, no 1,2,3

4. 45 rule on C89 3 innies R123C8 = 19 = {289/379/469/478/568}, no 1
4a. 2 of {289} must be in R2C8 -> no 2 in R13C8
4b. Min R1C6 + R1C8 = 7 -> max R1C7 = 7

5. R78C1 = {17/26/35}, R7C23 = [82/91] -> combined cage R7C23 + R78C1 = [82]{35}/[91]{26}/[91]{35} (cannot be [82]{17} which clashes with R9C12) -> R78C1 = {26/35}, no 1,7
5a. Hidden killer pair 4,7 in 15(3) cage at R8C2 or R9C12 for N7, R9C12 contains one of 4,7 -> 15(3) cage must contain one of 4,7 = {249/267/348/357} (cannot be {159/168/258} which don’t contain 4 or 7, cannot be {456} which clashes with R78C1), no 1
5b. R7C3 = 1 (hidden single in N7), placed for D/, R7C2 = 9, R4C3 = 9 (hidden single in N4) -> R2C14 = [98], R1C1 = 8, placed for D\, R7C4 = 7, R6C4 = 9, placed for D/, clean-up: no 1 in R2C9, no 1 in R3C4
5c. 9 on D\ only in R8C8 + R9C9, locked for N9 and 30(6) cage at R5C8
5d. R5C7 = 9 (hidden single in C7)
5e. R2C4 = 8 -> R1C6 + R3C5 (step 3) = {49/67}, no 5
5f. R1C6 + R3C5 = {49/67}, R3C46 = [27]/{36/45} -> combined cage R1C6 + R3C345 = {49}[27]/{49}{36}/{67}{45}, 4 locked for N2
5g. 45 rule on N5 1 outie R3C5 = 1 innie R6C6 + 2, R3C5 = {4679} -> R6C6 = {2457}
5h. 8 in N5 only in R4C56, locked for R4
5i. 45 rule on C9 1 innie R9C9 = 1 outie R4C8 + 4 -> R9C9 = {5679}, R4C8 = {1235}

6. 45 rule on R12 1 innie R2C2 = 1 remaining outie R3C3 + 3 -> R2C2 = {567}, R3C3 = {234}
6a. 1 on D\ only in R4C4 + R8C8, CPE no 1 in R4C8, clean-up: no 5 in R9C9
6b. 13(3) cage at R2C2 = {157/256} (cannot be {247/346} = 7{24}/6{34} which clash with R3C3 + R3C46, ALS block), no 3,4, 5 locked for N1
[Alternatively variable hidden killer triple 2,3,4 in R3C12, R3C3 and R3C46 for R3, R3C4 = {234}, R3C46 contains one of 2,3,4 -> R3C12 cannot contain more than one of 2,3,4 …]
6c. 13(3) cage at R2C2 = {157} (only remaining combination, cannot be {256} because 5{26} clashes with R2C2 + R3C3 = [52] while R2C2 + R3C123 = 6{25}3 clashes with R3C46), locked for N1, 1 also locked for R3, clean-up: no 3 in R3C3
6d. R1C7 = 1 (hidden single in N3) -> R1C68 = 13 = {49/67}, no 3,5 in R1C7

7. R2C2 = R3C3 + 3 (step 6), R3C5 = R6C6 + 2 (step 5g)
7a. Consider placements for R2C2 = {57}
R2C2 = 5
or R2C2 = 7, R3C3 = 4, no 4 in R3C5 => no 2 in R6C6 => R6C6 = {457} => naked triple [745] in R2C2 + R3C3 + R6C6
-> 5 in R2C2 + R6C6, locked for D\
5 on D\ in R2C2 + R6C6, CPE no 5 in R2C6 + R6C2

8. R1C6 + R3C5 (step 5f) = {49/67}, R3C46 = [27]/{36/45}
8a. Consider permutations for 13(3) cage at R2C2 = {157}
R2C2 = 5 => R3C12 = {17}, locked for R3
or R2C2 = 7, R3C12 = {15} => R3C46 = [27]/{36} => R1C6 + R3C5 = {49) (cannot be {67} which clashes with R3C46)
-> no 7 in R3C5, clean-up: no 6 in R1C6, no 7 in R1C8 (step 6d), no 5 in R6C6 (step 5g)
[Spotted later, an alternative which I prefer because it is more balanced and starts at a distance from both remaining 5s on D\
Consider permutations for R1C6 + R3C5
R1C6 + R3C5 = {49} => R6C6 = {27} (step 5g)
or R1C6 + R3C5 = {67}, locked for N2 => R3C46 = {45}, locked for R3 => R3C12 = {17}, locked for N1 => R2C2 = 5, placed for D\
-> no 5 in R6C6
Then 7 is eliminated from R3C5 by step 9, with the associated clean-ups.]


9. R2C2 = 5 (hidden single on D\), R3C3 = 2 (step 6), placed for D\, naked pair {17} in R3C12, locked for R3, clean-up: no 4 in R1C9, no 4 in R2C78, no 4 in R3C5 (step 5g), no 9 in R1C6 (step 5f), no 4 in R1C8 (step 6d), no 7 in R9C1
9a. R1C23 + R2C3 must be {34}6/{36}4 (cannot be {46}3 which clashes with R1C68), 3 locked for R1 and N1, clean-up: no 6 in R2C9
9b. Killer pair 4,6 in R1C23 and R1C68, locked for R1, clean-up: no 3 in R2C9

10. 8 in N5 only in 28(5) cage at R3C5 = {14689/23689/24589} (cannot be {13789} which clashes with 10(3) cage at R5C5, cannot be {34678} which clashes with R6C6, cannot be {25678} because R3C5 + R4C4 don’t contain 2,5,7,8) -> R3C5 = 9, R1C6 = 4 (step 5g), R1C8 = 9 (cage sum), R6C6 = 7, placed for D\, clean-up: no 5 in R3C46
[Cracked.]
10a. Naked pair {36} in R3C46, locked for R3 and N2
10b. 5 in N2 only in R1C45, locked for R1, clean-up: no 4 in R2C9
10c. Naked pair {27} in R12C9, locked for C9 and N3
10d. R9C9 = 9 (hidden single in C9) -> R4C8 = 5 (step 5i)
10e. R3C7 = 5 (hidden single in N3), placed for D/, R9C1 = 4, placed for D/, R9C2 = 8
10f. Naked pair {36} in R2C8 + R5C5, locked for D/, CPE no 3,6 in R5C8 + R8C8 (using D\)
10g. R4C6 = 8 (hidden single on D/)

11. R123C8 = 19 (step 4), R1C8 = 9 -> R23C8 = 10 = [64], 6 placed for D/ -> R5C5 = 3, placed for D\, R8C8 = 1, placed for D\, R2C7 = 3, R9C45 = [31], R3C46 = [63], R4C4 = 4, placed for D\
11a. R5C4 = 1 (hidden single in C4), R3C5 + R4C46 = [948] -> R4C5 = 6 (cage sum)
11b. R6C6 = 7, R7C7 = 6 -> R6C7 + R7C6 = 9 = [45]
11c. R8C4 = 2, R8C2 = 7, placed for D/, R89C3 = 8 = [35]
11d. R3C9 = 8, R4C8 = 5, R5C9 = 6 -> R4C9 = 1 (cage sum)

and the rest is naked singles, without using diagonals.

Rating Comment:
I'll rate my walkthrough for A368 at Easy 1.5. I used a couple of forcing chains.


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 Post subject: Re: Assassin 368
PostPosted: Sat Jan 26, 2019 8:25 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
You and I like the same thing Andrew! See steps 10 & 12 below. I worked in the same areas as Andrew, except for the final cracking spot, but generally saw things quite differently. My step 9 was my key.

a368 WT:
Preliminaries courtesy of SudokuSolver
Cage 4(2) n8 - cells ={13}
Cage 17(2) n1 - cells ={89}
Cage 8(2) n7 - cells do not use 489
Cage 12(2) n7 - cells do not use 126
Cage 9(2) n3 - cells do not use 9
Cage 9(2) n3 - cells do not use 9
Cage 9(2) n2 - cells do not use 9
Cage 10(3) n5 - cells do not use 89

1. 4(2)n8 = {13}: both locked for r9 and n8
1a. no 9 in 12(2)n7

2. "45" on n1: 2 outies r2c4 + r4c3 = 17 = {89} only

3. "45" on n4: 1 outie r7c2 = 1 innie r4c3 = {89} only

4. "45" on n7: 2 innies r7c23 = 10 = [82/91]
4a. but [82] blocked by 12(2)n7 & 8(2)n7 = {57}{26} only (ie two 2's n7)
4b. r7c23 = [91] only: 1 placed for d/
4c. -> r4c3 = 9 (innie/outie difference (iodn4)=0)
4d. -> r2c4 = 8 (outiesn1=17)
4e. r12c9 = [89]; 8 placed for d\
4f. no 1 in 9(2)n2
4g. no 1 in r2c7, no 1 in r2c9

5. r7c3 = 1 -> r67c4 = 16 = [97] only; 9 placed for d/
5a. no 2 in r3c6

6. "45" on r12: 1 innie r2c2 - 3 = 1 remaining outie r3c3 = [52/63/74], r2c2 = (567), r3c3 = (234)

7. "45" on r12: 3 remaining outies r3c123 = 10
7a. but {136} as {16}[3] only, blocked by iodr12=+3
7b. but {235} blocked by 9(2)n2 = {27/36/45} = 2/3/5
7c. h10(2)r3c123 = {127/145}(no 3,6)
7d. must have 1: 1 locked for r3 and n1 and 13(3)
7e. no 6 in r2c2 (iodr12=+3)
7f. 13(3)n1 = {157} only: 5,7 locked for n1

8. "45" on n2: 2 remaining innies r1c6 + r3c5 = 13 = {49/67}(no 1,2,3,5)

Critical step
9. h10(3)r3c123 = {127/145} = 4/7
9a. when h13(2)r1c6+r3c5 = {67} -> 9(2)n2 = {45}
9b. but {45}[7] clashes with r3c123 -> no 7 in r3c5
9c. no 6 in r1c6

Enjoyed this one
10. "45" on n5: 1 outie r3c5 - 2 = 1 remaining innie r6c6
10a. but [42] blocked by r3c3 = (24) (through d\)
10b. = [64/97] only
10c. no 9 in r1c6 (h13(2))

11. naked pair {47} in r16c6: both locked for c6
11a. no 2,5 in r3c4

12. "45" on r12: 1 innie r2c2 - 3 = 1 remaining outie r3c3: but [74] blocked by r6c6 = (47) (through D\)
12a. = [52] only: both placed for d\
12b. naked pair {17} in r3c12: 7 locked for r3
12c. no 4 in r2c78, no 4 in r1c9

13. "45" on c89: 3 innies r123c8 = 19 (no 1)
13a. hidden single 1 in n3 -> r1c7 = 1
13b. -> r1c68 = 13 = [49/76]

14. "45" on c89: 3 innies r123c8 = 19: must have 6,9 for r1c8: but {568} blocked by 5,8 only in r3c8
14a. = {289/379/469}(no 5)
14b. [6]{49} blocked by 4,9 only in r3c8
14c. -> r1c8 = 9
14d. r1c6 = 4 (cage sum), r6c6 = 7 (Placed for D\)
14e. r3c5 = 9 (h13(2)r1c6+r3c5)

15. hidden single 9 in d\ -> r9c9 = 9, r5c7 and r8c6 = 9 (both hsingles)

16. "45" on c9: 1 outie r4c8 = 5

17. 9(2)n2 = {36} only: both locked for r3 and n2

18. hsingle 5 in r3 -> r3c7 = 5, placed for d/

19. 12(2)n7 = [48] only permutation, 4 placed for d/

20. r4c6 = 8 (hsingle d/)

21. 22(4)r6c6: [7]{258} blocked by no 2,5,8 in r7c7
21a. [7]{348} blocked by no 3,4,8 in r7c6
21b. = [7]{456} only
21c. -> r7c6 = 5, r67c7 = {46}: both locked for c7

22. r8c9 = 5 (hsingle n9)

23. 8(2)n7 = {26} only combination: both locked for c1 and n7

24. 20(4)r3c9: must have 4 or 8 for r3c9
24a. = [5]{168/348}(no 2,7)

25. 7 in c9 only in 9(2)r1c9 = {27}: both locked for n3, 2 for c9
25a. r2c78 = [36]: 6 placed for d/

26. 30(6)r5c8 = {12378}[9] only (no 4)
26a. r3c8 = 4 (hsingle c8)

easier now.
Cheers
Ed


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 Post subject: Re: Assassin 368
PostPosted: Sat Jan 26, 2019 10:26 pm 
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Grand Master
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Thanks Ed again! My solution is much more similar to yours than to Andrew's. And, like both of you pointed out for your WTs, the diagonals played a large part in my WT. Even more than in yours I think!
I missed a very easy conclusion in the WT. See Step 11.
Assassin 368 WT:
1. 17(2)n1 = {89}
Outies n1 -> r2c4,r4c3 = {89}
IOD n4 -> r4c3 = r7c2 = 8 or 9

2. -> Innies n7 -> r7c23 = [91] or [82]
4(2)n8 = {13}
-> 12(2)n7 = [48] or {57}
If the latter -> 8(2)n7 = {26}
Either way r7c23 cannot be [82]
-> r7c23 = [91]
-> r4c3 = 9
-> r2c4 = 8
-> 17(2)n1 = [89]
Also r67c4 = [97]
Also 8 in r3 in n3 in r3c789

3. Remaining Innies n23 = r3c5789 = +26(4) (No 1)
-> 1 in r3 only in r3c12
-> 13(3)n1 = [5{17}] or [7{15}]
Also remaining innies r3 -> r3c123 = +10(3)
-> r3c123 = [{17}2] or [{15}4}
Also 8 in r3c789 -> 1 in n3 in r1c78
-> 1 in n2 in r2c56

4. Innies n2 = r1c6,r3c5 = +13(2) = {49} or {67}
IOD n5 -> r3c5 = r6c6 + 2
-> If r3c5 from (467) that value in n5 can only be in r5c6

5! [r1c6,r3c5] cannot be [94] since that puts 2 in r3c3 and in r6c6 - both on D\.
[r1c6,r3c5] cannot be [76] since that puts 6 in r5c6 which leaves no solution for 10(3)n5 since r9c5 from (13).
[r1c6,r3c5] cannot be [67] since that puts 9(2)n3 = {45} which contradicts one of (57) in r3c12.
-> [r1c6,r3c5] = [49]

6. -> IOD n5 -> r6c6 = 7
-> 13(3)n1 = [5{17}]
-> r3c3 = 2
-> r2c3 = 4
-> r1c23 = {36}
Also 9(2)n2 = {36}
-> r3c789 = {458}
-> Since (36) both in r2 in n3 -> 9(2)r2c7 = {36}
-> 9(2)r1c9 = {27}

7. Innies c89 = r123c8 = +19(3)
-> r123c8 = [964]
-> r12c7 = [13]
Also HS 9 in D\ -> r9c9 = 9
-> Outie c9 = r4c8 = 5
-> r3c789 = [548]
Also HS r5c7 = 9
Also HS r8c6 = 9

8. 5 in c2 and in D/ -> 12(2)n7 = [48]
-> HS 8 in D/ -> r4c6 = 8

9. Previous placements mean 22(4)r6c6 cannot contain any of (139) and r7c7 only from (46)
Only solutions are for r67c6 = [75] and r67c7 = {46}
-> HS r8c9 = 5
-> r9c3 = 5
-> 8(2)n7 = {26}
-> 15(3)n7 = [{37}5]
-> 3 in n9 in r7c89
-> NS in D\ r8c8 = 1

10. 8 in n6 only in r67c8
-> HS r8c7 = 8
-> HS r7c5 = 8

Ed pointed out that r5c5 is a naked single 3 already at this point. (Actually by the end of Step 8). So this is not an exclamation point worthy step!

11! (145) already on D/ -> 10(3)n5 cannot be {145}
It also cannot be {127} since 7 in r6c6
-> 10(3)n5 must contain a 3
Also 3 on D\ only in n5
-> r5c5 = 3
-> 4(3)n8 = [31]
-> 9(2)n2 = [63]
-> HS 6 on D\ -> r7c7 = 6
-> NS on D\ -> r4r4 = 4
Also r6c7 = 4
-> r7c9 = 4
-> r7c8 = 3
-> r6c9 = 3

12. Also r8c23 = [73]
-> r12c9 = [27]
Also r3c12 = [71]
-> r5c3 = 7
-> r4c7 = 7
Also r45c9 = {16}
Also r6c3 = 8
-> r56c8 = [82]
-> r9c78 = [27]
etc.


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