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 Post subject: Assassin 404
PostPosted: Thu Oct 14, 2021 8:24 pm 
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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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Note: there is a broken 22(4)cage in n47

Assassin 404
Felt like a messy cage structure after all the beautiful symmetry we've been having with the Revisits. And a nice fun one! It gets 1.30 and two 'complex intersections'. If its not hard enough for you guys I can try to toughen it up.
triple-click code:
3x3::k:3840:3840:6913:5890:5890:5890:5890:7171:1796:1541:1541:6913:6913:6913:5890:7171:7171:1796:5638:5638:5638:2311:2311:2311:7171:7176:7171:8201:5642:5638:6923:6923:6923:7176:7176:6668:8201:8201:5638:6923:6923:6923:6668:7176:6668:8201:8201:7949:7949:3086:3086:7695:6668:6668:1040:8201:7949:7949:7695:7695:7695:3345:6668:1040:5642:7949:4882:2579:1300:7695:3345:3345:5642:5642:4882:4882:2579:1300:7695:2325:2325:
solution:
+-------+-------+-------+
| 7 8 3 | 1 6 9 | 2 5 4 |
| 2 4 9 | 7 8 5 | 6 1 3 |
| 6 5 1 | 3 4 2 | 7 8 9 |
+-------+-------+-------+
| 9 3 2 | 4 1 8 | 5 6 7 |
| 4 6 8 | 2 5 7 | 3 9 1 |
| 5 1 7 | 6 9 3 | 4 2 8 |
+-------+-------+-------+
| 1 7 4 | 9 2 6 | 8 3 5 |
| 3 2 5 | 8 7 1 | 9 4 6 |
| 8 9 6 | 5 3 4 | 1 7 2 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 404
PostPosted: Sun Oct 17, 2021 10:31 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 Ed for your new Assassin!

An easy start, then I just used one short forcing chain to crack it.

Ed wrote:
If its not hard enough for you guys I can try to toughen it up.
I would usually say "yes please" but I'm busy so happy to wait for whatever you post at the beginning of November.

Here's my walkthrough for Assassin 404:
Prelims

a) R1C12 = {69/78}
b) R12C9 = {16/25/34}, no 7,8,9
c) R2C12 = {15/24}
d) R6C56 = {39/48/57}, no 1,2,6
e) R78C1 = {13}
f) R89C5 = {19/28/37/46}, no 5
g) R89C6 = {15/24}
h) R9C89 = {18/27/36/45}, no 9
i) 9(3) cage at R3C4 = {126/135/234}, no 7,8,9
j) 19(3) cage at R8C4 = {289/379/469/478/568}, no 1
k) 27(4) cage at R1C3 = {3789/4689/5679}, no 1,2
l) 28(4) cage at R3C8 = {4789/5689}, no 1,2,3

1a. Naked pair {13} in R78C1, locked for C1 and N7, clean-up: no 5 in R2C2
1b. 45 rule on N5 1 innie R6C4 = 6
1c. 31(5) cage at R6C3 contains 6 = {16789/35689/45679}, no 2
1d. 45 rule on R12 2 outies R3C79 = 16 = {79}, locked for R3 and N3
1e. 28(4) cage at R3C8 = {4789/5689}, 9 locked for N6, CPE no 8 in R6C8
1f. 45 rule on N3 2 innies R1C7 + R3C8 = 10 = [28/46/64]
1g. 45 rule on C12 2 innies R3C12 = 11 = [56/65/83]
1h. Killer pair 6,8 in R1C12 and R3C12, locked for N1
1i. 45 rule on C12 3 outies R345C3 = 11 = {128/137/146/245} (cannot be {236} which clashes with R3C12), no 9
1j. 9(3) cage at R3C4 = {126/234} (cannot be {135} which clashes with R3C12), no 5, 2 locked for R3 and N2
1k. Killer pair 3,6 in R3C12 and 9(3) cage, locked for R3, clean-up: no 4 in R1C7
1l. 45 rule on N1 using R3C12 = 11, 3 remaining innies R123C3 = 13 = {139/157} -> R3C3 = 1, R12C3 = {39/57}
1m. R2C12 = {24} (hidden pair in N1), locked for R2, clean-up: no 3,5 in R1C9
1n. 9(3) cage at R3C4 = {234} (only remaining combination), 3,4 locked for R3 and N2 -> R3C8 = 8, R1C7 = 2, clean-up: no 5 in R2C9, no 1 in R9C9
1o. Naked pair {56} in R3C12, locked for N1 and 22(5) cage at R3C1 -> R12C3 = {39}, locked for C3, 9 locked for N1 and 27(4) cage at R1C3
1p. R45C3 = 10 = {28}, locked for C3 and N4
1q. Naked pair {78} in R1C12, locked for R1
1r. R12C3 = 12 -> R2C45 = 15 = {78}, locked for R2
1s. R9C3 = 6 (hidden single in C3), clean-up: no 4 in R8C5, no 3 in R9C89
1t. R678C3 = {457}, R6C4 = 6 -> R7C4 = 9 (cage sum), clean-up: no 1 in R89C5
1u. R9C3 = 6 -> R89C4 = 13 = {58}, locked for C4 and N8 -> R1C4 = 1, R2C45 = [78], clean-up: no 6 in R2C9, no 4 in R6C6, no 2 in R89C5
1v. Killer pair 3,4 in R89C5 and R89C6, locked for N8
1w. 9 in N7 only in R8C2 + R9C12, locked for 22(4) disjoint cage at R2C4, no 9 in R2C4

2a. 2 in R6 only in R6C89, locked for 26(6) cage at R4C9, no 2 in R7C9
2b. 45 rule on N6 1 remaining outie R7C9 = 1 innie R6C7 + 1 -> R6C7 = {3457}, R7C9 = {4568}
2c. 26(6) cage at R4C9 = {123578/124568}
2d. 8 in N6 only in R4C9 + R5C79 + R6C89, locked for 26(6) cage, no 8 in R7C9 -> no 7 in R6C7
2e. Hidden killer pair 6,7 in 28(4) cage at R3C8 and 26(6) cage for N6, 28(4) cage contains one of 6,7 -> 26(6) cage must contain one of 6,7 in N6, no 6 in R7C9 -> no 5 in R6C7
2f. R9C89 = [18/27/72] (cannot be {45} which clashes with R7C9)
2g. 45 rule on C789 2 outies R7C56 = 8 = {17/26}
2h. R7C56 = 8 -> R6789C7 = 22 = {1489/3469/3568} (cannot be {1579/1678} because R6C7 only contains 3,4, cannot be {3478} which clashes with R9C89, cannot be {4567} which clashes with R7C56), no 7
2i. Consider permutations for R12C9 = [43/61]
R12C9 = [43] => R6C7 + R7C9 = [45]
or R12C9 = [61] => R2C7 = {35} => R6789C7 cannot be {3568}
-> R6789C7 = {1489/3469}, no 5, 4,9 locked for C7, 9 locked for N9
2j. R3C79 = [79]
2k. R4C7 = {56} -> 28(4) cage at R3C8 = {5689}, 5,6 locked for N6
2l. 26(6) cage = {123578}, 3 locked for N6 -> R6C7 = 4, R7C9 = 5, clean-up: no 8 in R6C6
2m. R6C56 = {39} (cannot be {57} which clashes with R6C3), locked for R6 and N5
2n. Naked pair {57} in R6C13, locked for N4, 7 locked for R6 -> R6C2 = 1, R6C89 = [28]
2o. 7 in N6 only in R45C9, locked for C9 -> R9C9 = 2, R8C9 = 7, clean-up: no 3 in R8C56
2p. 13(3) cage at R7C8 = {346} (only possible combination), 3,6 locked for N9
2q. Naked triple {189} in R789C7, 1 locked for C7 and 30(6) cage at R6C6 -> R5C7 = 3, clean-up: no 7 in R7C56
2r. Naked pair {17} in R45C9, 1 locked for C9 -> R12C9 = [43], R8C9 = 6, R8C5 = 7 -> R9C5 = 3, R6C56 = [93], clean-up: no 2 in R8C6

3a. 4 in C3 only in R78C3, locked for N7
3b. R4C2 = 3 (hidden single in N4) -> R8C2 + R9C12 = 19 = {289} (only possible combination) -> R8C2 = 2, R9C12 = {89}, locked for R9, 8 locked for N7

and the rest is naked singles.


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 Post subject: Re: Assassin 404
PostPosted: Mon Oct 25, 2021 6:58 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Really nice forcing chain by Andrew. I got around that spot a different way but otherwise, used the same path. Glad I didn't have a whole WT already written since Andrew's is so beautifully optimised already. [edit: Thanks to Andrew for checking my steps.]

alternate way to crack this puzzle - paste candidates into A404 in SudokuSolver:
Code:
.-------------------------------.-------------------------------.-------------------------------.
| 78        78        39        | 1         569       569       | 2         3456      46        |
| 24        24        39        | 7         8         569       | 1356      1356      13        |
| 56        56        1         | 234       234       234       | 79        8         79        |
:-------------------------------+-------------------------------+-------------------------------:
| 45679     134567    28        | 234       1234579   12345789  | 45679     45679     1345678   |
| 45679     1345679   28        | 234       1234579   12345789  | 1345678   45679     1345678   |
| 4579      134579    457       | 6         34579     35789     | 34        123457    1234578   |
:-------------------------------+-------------------------------+-------------------------------:
| 13        24578     457       | 9         1267      1267      | 1345678   1234567   45        |
| 13        245789    457       | 58        367       1234      | 13456789  12345679  123456789 |
| 245789    245789    6         | 58        347       1234      | 1345789   12457     24578     |
'-------------------------------.-------------------------------.-------------------------------'
Andrew's end of step 2e above.

3. From step 2b, the iodn6 = -1 = [34/45]
3a. ie, must have 4 in r6c7 or r7c9
3b. -> no 4 in r5c7, r6c8, r456c9, r789c7 (Common Peer Elimination CPE)

4. 28(4)r3c8 = [8]{479/569}
4a. "45" on c89: 4 outies r2345c7 = 21
4b. but {1389} blocked by 1,3,8 only in r25c7
4c. {1479} must be [1947] only, blocked by 7 also in 28(4)r3c8 (Combo Crossover Clash CCC)
4d. {3459} blocked by r6c7 = (34)
4e. {3468} blocked by no 7,9 for r3c7
4f. = {1569/1578/3567}(no 4)

5. r6c7 = 4 (hsingle c7)
5a. -> r7c9 = 5
5b. and r4c78 + r5c8 = {569} only: 6 locked for n6

6. 12(2)n5: {57} blocked by r6c3 = (57)
6a. = {39}: both locked for r6 and n5

7. r6c123 = (57)[1](57): 5,7 locked for n4, 7 for r6
7a. r6c89 = [28]

8.. naked triple {137} in r245c9: all locked for c9, 7 for n6
8a. r3c79 = [79]

then back to Andrew's 2o.
Cheers
Ed


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