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 Post subject: Assassin 400
PostPosted: Thu Oct 01, 2020 8:52 am 
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Location: Sydney, Australia
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a400.JPG
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Note: disjoint 12(2)r9c47

Assassin 400
Made it to 400!! A little while ago Andrew said, "Hope we manage to reach the next anniversary of A400 and that I'll still be an active solver"..... then finish?? I have at least a couple more in me so will see....

I found this one really hard, hence a milestone puzzle. Resists a long way in. But my solution fails the 'must be interesting' test. Hoping that the big cages allow a better solution than mine. Jury's out on it being a decent puzzle. SS gives it 1.70. JSudoku uses 2 'complex intersections'.
triple click code:
3x3::k:4864:4864:4865:4865:3586:3586:7683:7683:1796:6162:4864:4865:3586:3586:1798:7683:7683:1796:6162:6162:4865:6663:6663:8200:1798:1798:5897:6162:4618:4618:6663:6663:8200:5897:5897:5897:6162:4618:5387:6663:8200:8200:8460:8460:5897:7955:6162:5387:8200:8200:8460:8460:8460:8460:7955:7955:5387:5387:4110:6671:6671:2320:4881:4877:7955:7955:7955:4110:6671:6671:2320:4881:4877:4877:4877:3077:6671:6671:3077:4881:4881:
solution:
+-------+-------+-------+
| 3 7 2 | 8 1 5 | 6 9 4 |
| 1 9 5 | 6 2 4 | 7 8 3 |
| 6 8 4 | 9 3 7 | 1 2 5 |
+-------+-------+-------+
| 4 6 7 | 2 5 9 | 3 1 8 |
| 2 5 1 | 7 8 3 | 9 4 6 |
| 8 3 9 | 1 4 6 | 2 5 7 |
+-------+-------+-------+
| 7 4 8 | 3 9 2 | 5 6 1 |
| 9 1 6 | 5 7 8 | 4 3 2 |
| 5 2 3 | 4 6 1 | 8 7 9 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 400
PostPosted: Thu Oct 01, 2020 5:33 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks Ed for posting this landmark Assassin! :D

A little while ago Andrew said, "Hope we manage to reach the next anniversary of A400 and that I'll still be an active solver"..... then finish?? I have at least a couple more in me so will see....

I hope that Assassins will continue, even though Ed probably needs a break. That recent Revisit of an early variant was a good one.

Still plenty of life in me, including solving Assassins and whichever puzzles in Other Variants interest me and, as Ed knows, I'm still active working for the monthly magazine of a British railway enthusiasts society. When our second grandson was born our elder daughter instructed me to still be around when he and his elder brother graduate from high school; they'll be 7 and 5 this month so still a long time to go!


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 Post subject: Re: Assassin 400
PostPosted: Fri Oct 02, 2020 5:26 am 
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Location: Lethbridge, Alberta, Canada
Just like wellbeback did for Assassin 399, I've finished this one quickly. It started fairly easily, then got harder. Possibly a few interesting steps. I've now made a few detail changes and clarifications.

Thanks Ed for pointing out what I missed in step 6c, which would have simplified my later steps.

Here's my walkthrough for Assassin 400:
Prelims

a) R12C9 = {16/25/34}, no 7,8,9
b) R78C5 = {79}
c) R78C8 = {18/27/36/45}, no 9
d) Disjoint cage R9C47 = {39/48/57}, no 1,2,6
e) 19(3) cage at R1C1 = {289/379/469/478/568}, no 1
f) 7(3) cage at R2C6 = {124}
g) 14(4) cage at R1C5 = {1238/1247/1256/1346/2345}, no 9
h) 30(4) cage at R1C7 = {6789}

Steps resulting from Prelims
1a. Naked pair {79} in R78C5, locked for C5 and N8, clean-up: no 3,5 in R9C7
1b. Naked quad {6789} in 30(4) cage at R1C7, locked for N3, clean-up: no 1 in R12C9
1c. Naked triple {124} in 7(3) cage at R2C6, CPE no 1,2,4 in R2C9 + R3C456, clean-up: no 3,5 in R1C9
1d. R23C9 = {35} (hidden pair in N3), locked for C9
1e. 1 in N3 only in R3C78, locked for R3 and 7(3) cage

2a. 45 rule on N36 R26C6 = 10 = [28/46]
2b. 45 rule on N14789 1 outie R1C4 = 8, clean-up: no 4 in R9C7
[Or, of course, 45 rule on N2356]
2c. 8 in N3 only in R2C78, locked for R2
2d. 19(3) cage at R1C1 = {379/469}, no 2,5, 9 locked for N1
2e. R1C4 = 8 -> R123C3 = 11 = {137/146/245} (cannot be {236} which clashes with 19(3) cage)
2f. 45 rule on N1 3 remaining outies R45C1 + R6C2 = 9 = {126/135/234}, no 7,8,9
2g. 45 rule on N89 2 innies R78C4 = 8 = {26/35}
2h. 8 in N1 only in R3C12
2i. 45 rule on N1 3 remaining innies R2C1 + R3C12 = 15 = {168/348} (cannot be {258} which clashes with R45C1 + R6C2), no 2,5,7
2j. R123C3 = {245} (cannot be {137/146} which clash with R2C1 + R3C12), locked for C3, 4 locked for N1
2k. R2C1 + R3C12 = {168} -> R2C1 = 1, R3C12 = {68}, 6 locked for R3 and N1
2l. R45C1 + R6C2 = {234} (only remaining combination), locked for N4
2m. 3 in C3 only in R789C3, locked for N7
2n. R3C46 = {79} (hidden pair in R3), 7 locked for N2
2o. Naked pair {79} in R3C46, CPE no 7,9 in R6C4
2p. Naked pair {35} in R3C59, 5 locked for R3

3a. 45 rule on N14 3 innies R5C3 + R6C13 = 18 = {189/567}
3b. 5 of {567} must be in R6C1 -> no 6,7 in R6C1
3c. R56C3 = {18/19/67} = 9,10,13 -> R7C34 = 12,11,8 = [75/93/65/83/35] (cannot be 21(4) cage at R5C3 cannot be {19}[92] or {67}[62]), no 1 in R7C3, no 2,6 in R7C4
3d. R78C4 (step 2g) = {35} (only remaining combination), locked for C4 and N8, R9C4 = 4 -> R9C7 = 8, clean-up: no 1 in R78C8
3e. R2C8 = 8 (hidden single in N3)
3f. 8 in N8 only in R78C6, locked for C6, R6C6 = 6 -> R2C6 = 4 (step 2a)
3g. R9C5 = 6 (hidden single in N8)
3h. Naked triple {128} in R789C6, 1,2 locked for C6 and 26(6) cage at R7C6
3i. R2C4 = 6 (hidden single in N2) -> 14(4) cage at R1C5 = {1256} (only remaining combination) -> R1C6 = 5, R12C5 = [12], R3C59 = [35], R2C9 = 3 -> R1C9 = 4
3j. R345C6 = {379} = 19 -> R5C5 + R6C45 = 13 = {148} -> R6C4 = 1, R56C5 = {48} locked for N5 -> R4C5 = 5
3k. 18(3) cage at R4C2 = {189/567}
3l. 5 of {567} must be in R5C2 -> no 6,7 in R5C2
3m. R5C3 + R6C13 = {189/567}
3n. 1,6 only in R5C3 -> R5C3 = {16}

4a. 45 rule on N9 2 remaining innies R78C7 = 9 = {45} (locked for C7 and N9)
4b. 3 in C7 only in R456C7, locked for N6
4c. 5 in R9 only in R9C12, locked for N7

5a. Variable hidden killer pair 3,7 in R9C123 and R9C89 for R9, R9C89 cannot be [37] which clashes with R78C8 -> R9C123 must have at least one of 3,7
5b. 5 in R9 only in R9C12 -> 19(4) cage at R8C1 = {1567/2359/3457} (cannot be {1459/2458} which don’t contain 3 or 7), no 8
5c. 4,6 of {1567/3457} must be in R8C1 -> no 7 in R8C1
5d. 3 of {2359} must be in R9C3 -> no 9 in R9C3

6a. R5C3 + R6C13 (step 3a) = {189/567} = 1{89}/[657], R78C8 = {27/36}
6b. R3C9 = 5, 6 in N6 only in 23(5) cage at R3C9 = {12569/13568/14567/23567}
6c. Consider placement for 8 in C9
8 in R45C9 -> 23(5) cage = {13568}
or R6C9 = 8 => R5C3 + R6C13 = [657] => R7C34 = [35] => R9C8 = 3 (hidden single in R9) => R78C8 = {27} => 2 in C9 only in R45C9 => 23(5) cage = {12569/23567}
[Ed pointed out that after R78C8 = {27} I’d missed => R45C9 = {27} which would have then reduced the 23(5) cage to {13568/23567} and simplified the rest on my walkthrough by omitting the need for steps 7c and 7d.]
-> 23(5) cage = {12569/13568/23567}, no 4
6d. R4C1 = 4 (hidden single in R4)
6e. R56C8 = {45} (hidden pair in N6)
6f. Hidden killer pair 2,3 in R6C2 and R6C79 for R6, R6C2 = {23} -> R6C79 must contain one of 2,3
6g. 33(6) cage at R5C7 contains 4,5,6 = {245679/345678} (cannot be {145689} which doesn’t contain 2 or 3), no 1, 7 locked for N6
6h. 2,3 of {245679/345678} must be in R6C79 (cannot be 2{79}/[378] because R6C79 must contain one of 2,3), no 2,3 in R5C7
6i. Naked pair {79} in R25C7, locked for C7 -> R1C7 = 6

6j. Naked pair {23} in R6C27, 2 locked for R6
6k. Naked quad {2379} in R5C1467, 2,9 locked for R5

7a. 18(3) cage at R4C2 (step 3k) = {189/567} must have 6 or 9 in R4
7b. 23(5) cage at R3C9 (step 6c) = {12569/13568}
7c. {12569} cannot be 5{269}1 which clashes with 18(3) cage
7d. 23(5) cage = {13568} (cannot be 5{129}6 which clashes with R4C234 = {67}{29}) -> R4C7 3, R4C89 + R5C9 = {168}, 8 locked for N6
7e. R6C7 = 2, R5C1 + R6C2 = [23]
7f. Naked pair {79} in R12C2, locked for C2 and N1
7g. R3C78 = [12], clean-up: no 7 in R78C8
7h. Naked pair {36} in R78C8, locked for N9, 6 locked for C8 -> R4C8 = 1
7i. Naked pair {68} in R34C2, locked for C2

8a. 19(4) cage at R8C1 (step 5b) = {1567/2359}
8b. Killer pair 1,2 in R9C23 and R9C6, locked for R9
8c. Naked pair {79} in R9C89, locked for R9 and N9
8d. R9C1 = 5, R9C3 = 3 (hidden single in R9) -> R8C1 + R9C2 = 11 = [92]
8e. R6C1 = 8, R4C2 = 6, R5C23 = [51], R4C3 = 7 (cage sum)

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A400 at a full 1.5. One path of my forcing chain was fairly long.


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 Post subject: Re: Assassin 400
PostPosted: Sat Oct 03, 2020 7:33 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Thanks again Ed! I found it a very nice puzzle and my WT has a few interesting steps I think. Agree with both of you that it got harder in the middle.
Corrections & clarifications thanks to Andrew & Ed.
Assassin 400 WT:
1. 30(4)n3 = {6789}
7(3)r2c6 = {124}
-> (since (35) cannot both go in 7(2)n3) r3c9 from (35)
-> 7(2)n3 and 7(3)r2c6 from [25] and [2{14)], or [43] and [4{12}]
i.e., 1 locked in r3c78

2. Innies n2356 = r1c4 = 8
16(2)n8 = {79}
Since r2c6 from (24) -> 7 in n2 not in 14(4)n2
-> HP r3c46 = {79}

3. 8 in n3 in r2c78
-> 8 in n1 in r3c12
-> 24(6)r2c1 = {123468}
-> 9 in n1 in 19(3)
-> 5 in n1 in r123c3
-> r123c3 = {245}
-> 19(3)n1 = {379}
-> 24(6)r2c1 = [1{68}{234}]

4! (Some rare combination analysis from me)
Remaining Innies n4 = r6c1 + r56c3 = H+18(3)
-> For the two 18(3)s in n4 - One is {567} and the other is {189}
-> r6c1, r56c3 from one of:
(A) 5, {67}
(B) 9, {18}
(C) 8, {19}

Remaining outies c123 = r78c4 = +8(2)
-> r7c34 from:
(A) [35]
(B) [75] or [93]
(C) [83] or [65]

-> In all cases r7c4 from (35)
-> r78c4 = {35}

5. Remaining Innies n25 = r26c6 = +10(2) = [28] or [46]
-> Whichever of (79) is in r3c4 goes in n5 in r45c6
Also whichever of (79) is in r3c6 goes in n5 in r45c4
-> Disjoint cage 12(2)r9 can only be [48]
-> 8 in n8 in r78c6
-> (Innies n25) r26c6 = [46]
-> (HS 6 in n8) r9c5 = 6
-> r789c6 = {128}
-> r78c7 = {45}
Also -> 14(4)n2 = [1562]
-> r3c5 = 3
-> 26(5)r3c4 = {23579} with r34c5 = [35] and 2 in r45c4
Also (NS 1 in c4) r6c4 = 1
Also 3 in n5 in r45c6
-> (NP in n5) r56c4 = {48}

6. 6 in n6 in 23(5)
Along with the 5 in r3c9 -> the remaining values in 23(5)r3c9 from {129}, {138}, {147}, or {237}
But cannot be {237} since that leaves no place for both (23) in r6.

7. 8 in n6 either in r45c9 or r6c9
If the former this puts 23(5) = [5{1368}] which puts 3 in r6 in r6c2 which puts 4 in r45c1
If the latter this puts r56c5 = [84] which again puts 4 in r45c1
Either way -> 4 in n4 in r45c1 and 4 in n7 in r78c2

8! 9(2)n9 from {36} or {27}
But the latter puts r456c9 = {278} and no two of those numbers can both go in the 23(5)
-> 9(2)n9 = {36}

9. Continuing from that
-> Both (35) in n7 in r9 (Option (A) from Step 4 eliminated)
-> (since 3 locked in c3 in n7) 19(4)n7 = [{259}3]
-> 9 in n4 in c3
-> Option (B) in Step 4 eliminated - Only option (C) remains
-> r6c1 = 8 and r56c3 = [19]
-> (HS 8 in n7) r7c34 = [83]
-> r8c4 = 5 and r78c7 = [54]
Also r3c12 = [68]
-> 31(6)r6c1 = [874165]
-> 18(3)n4 = [675]

10. Also r1c7 = 6
Also 8 in n6 not in r6c9 -> 23(5)r3c9 = [53186]
-> r5c6 = 3
-> r6c2 = 3
Also r3c78 = [12]
Also r5c7 = 9
-> 30(4)n3 = [6978]
etc.


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 Post subject: Re: Assassin 400
PostPosted: Mon Oct 12, 2020 1:24 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
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Well done to Andrew and wellbeback for having an easier time than me. A worthy puzzle after all! Thanks guys. And very glad for us that Andrew still has a lot to give.

I didn't use the combo analysis that both WTs above used very early. I eventually got there, but way too late (my step 30/31). Hence, my WT is quite different. [Many thanks to Andrew for checking my WT and for a simplification to step 21]
a400 WT:
Preliminaries courtesy of SudokuSolver
Cage 16(2) n8 - cells ={79}
Cage 7(2) n3 - cells do not use 789
Cage 12(2) n89 - cells do not use 126
Cage 9(2) n9 - cells do not use 9
Cage 7(3) n23 - cells ={124}
Cage 19(3) n1 - cells do not use 1
Cage 30(4) n3 - cells ={6789}
Cage 14(4) n2 - cells do not use 9

1. "45" on n2356: 1 innie r1c4 = 8

2. 30(4)n3 = {6789}: all locked for n3, 8 locked for r2

3. 7(3)r2c6 = {124} -> no 1,2,4 in r2c9, nor r3c456 (Common Peer Elimination CPE)
3a. r12c9 = [43/25]

4. naked triple 1,2,4 in n3: locked for n3
4a. 1 only in r3: locked for r3 and 7(3) cage

5. r23c9 = naked pair {35}: both locked for c9

6. 8 in r3 only in 24(6)r2c1 = {123468}(no 5,7,9)
6a. 8 also locked for 24(6) that's in n4

7. "45" on n1: 3 innies r2c1 + r3c12 = 15
7a. must have 8 = {168/348}(no 2)

8. r123c3 = 11 (cage sum)
8a. but {137/146/236} all blocked by step 7a.
8b. = {245} only: all locked for n1 and c3
8c. -> h15(3)n1 = {168} only: r2c1 = 1, r3c12 = {68}: 6 locked for n1, r3 & 24(6) cage

9. naked triple {234} in n4: locked for n4

10. 16(2)n8 = {79}: both locked for c5 and n8

11. naked pair {35} in r3c59: both locked for r3

12. naked pair {79} in r3c46: 7 locked for n2, no 7,9 in r6c4 since it sees both (CPE)

13. "45" on n89: 2 innies r78c4 = 8 = {26/35}(no 1,4)

14. 1 and 8 in n8 only in 26(6)r7c6 = {123578/124568}(no 9)
14a. 1 & 8 both locked for that cage
14b. note: must also have 2 & 5

15. h8(2)r78c4 has one of 2/5 (step 13)
15a. -> 26(6) can only have one of 2,5 in n8
15b. and must also have at least one of 2,5 in r78c7 (from step 14b)

16. 12(2)r9c47 = [39/48/57], r9c7 = (789)
16a. "45" on n9: 3 innies r789c7 = 17 and must have 2/5 (step 15b)
16b. = {26}[9]/{27}[8]/{35}[9]/{45}[8]
16c. no 7 in r9c7, no 5 r9c4
16d. 26(6)r7c6 = {123578/124568}(step 14)
16e. {123578} must have 7 in r78c7 so can't have both 3 & 5 in r78c7
16f. -> {35}[9] blocked from r789c7
16g. = {26}[9]/{27}[8]/{45}[8](no 3)

17. 3 in n9 only in c8: locked for c8

This step took a very long time to find
18. 3 in r9c8 -> r9c47 = [48] -> {1378/2368} blocked from 19(4)n9
18a. {2359/3457} blocked from 19(4) by 3 & 5 only in r9c8
18b. -> only combination with 3 possible in 19(4) = {1369}: note: must have 6
18c. since 3 in n9 only in 9(2) or 19(4) -> 6 locked for n9 (Locking cages)
18d. -> r789c7 = {27}[8]/{45}[8](no 9)
18e. r9c7 = 8, r9c4 = 4

19. r2c8 = 8 (hsingle n3)
19a. 8 in n8 only in c6: locked for c6

20. "45" on n6: 2 outies r3c9 + r6c6 = 11 = [56] only
20a. r12c9 = [43]
20b. r3c5 = 3

21. 32(6)r3c6 = {125789/134789}
21a. must have 1, locked for n5
21b. r6c4 = 1 (hsingle c4)
[Andrew noticed that at this spot, 3 in n5 is only in that 32(6) which would have gotten it down to 1 combination and also simplified step 22)

22. 26(5)r3c4 = {23489/23579}
22a. must have 2, locked for n5
22b. -> 32(6)r3c6 = {134789} (no 5)
22c. r56c5 = {48}:both locked for n5, 4 for c5
22d. r345c6 = {379}: 3 locked for c6

23. 3 in n8 only in h8(2)r78c4 = {35}: 5 locked for n8, c4 and both not in r7c12 (CPE)
23a. r9c5 = 6 (hsingle n8)
23b. r4c5 = 5 (hsingle n5)
23c. r2c456 = [624], r1c56 = [15], r123c3 = [254]

24. 2 in n8 only in 26(6) cage: -> no 2 in r78c7
24a. -> r78c7 = {45} only (step 16g): both locked for n9 and c7

25. "45" on n789: 3 outies r5c3 + r6c13 = 18 = {189/567}
25a. = [1]{89}/[657]
25b. r5c3 = (16), r6c1 = (589)
25c. note: has 5 or 8 in r6

Another step that took a lot of finding
26. 33(6)r5c7 must have 5 for n6 = [6]{14589/23589/24579/34578}
26a. but {48} in r6c89 blocked by r6c5 = (48)
26b. and {58} in r6c89 blocked by r6c13 (step 25c)
26c. -> [6]{14589/34578} blocked from 33(6) since 8 can only be in r6c9
26d. = [6]{23589/24579}(no 1)
26e. 2 & 9 both locked for n6

27. "45" on c9: 3 outies r4c78 + r9c8 - 4 = 1 innie r6c9
27a. outies can only sum to 6 as [141] which leaves no 1 for c9, or [312] which is blocked by r3c8 = (12)
27b. -> no 2 in r6c9

28. 2 in c9 only in n9 in 19(4) = {1279} only, 1,2 7 all locked for n9
28a. 9(2)n9 = {36}: 6 locked for c8
28b. r1c7 = 6 (hsingle n3)

29. 3 & 5 in r9 only in n7: both locked for n7
29a. r9c3 = 3 (hsingle c3)
29b. 19(4)n7 = {2359/3457}(no 1,6,8)

30. r5c3 + r6c13 = 18 = [1]{89}/[657] (step 25a)
30a. -> 21(4)r5c3 must have {18/19/67}
30b. = {1389/1569/1578/3567}
30c. but [67] in r56c3 blocked by no 3,5 in r7c3
30d. -> r5c3 + r6c13 = 18 = [1]{89} only
30e. 8 & 9 locked for n4, r6 and no 8,9 in r8c3 (CPE)

31. r56c5 = [84], r56c9 = [67]
31a. r4c789 = 12 (cage sum) = [318]

etc
Cheers
Ed


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