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 Post subject: Assassin 21V2 Revisit
PostPosted: Sun Nov 15, 2020 5:32 am 
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Grand Master
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Location: Sydney, Australia
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Assassin 21V2 Revisit

The next puzzle from the archive to get a rating above E1.5 and score of 1.50+. The idea is to find an interesting solution using the newer techniques we've developed in recent years. I'm really enjoying these even though I haven't solved one yet!

JSudoku uses 2 complex intersections, SudokuSolver gives it 1.60.

triple-click code:
3x3::k:3584:3584:4097:5122:5122:5122:5635:5635:5635:3584:4097:4097:5122:4100:4100:4100:3333:5635:3584:6662:6662:6662:4103:4103:776:3333:3333:3849:6662:4618:4618:6923:4103:776:1548:1548:3849:6662:4618:6923:6923:6923:4621:5134:3343:2576:2576:1297:3858:6923:4621:4621:5134:3343:2323:2323:1297:3858:3858:2580:2580:5134:4629:7702:2323:5143:5143:5143:5143:4120:4120:4629:7702:7702:7702:2329:2329:5143:4120:4629:4629:
solution:
+-------+-------+-------+
| 2 8 5 | 1 7 9 | 4 6 3 |
| 1 4 7 | 3 2 6 | 8 5 9 |
| 3 9 6 | 4 5 8 | 2 7 1 |
+-------+-------+-------+
| 7 5 9 | 8 6 3 | 1 4 2 |
| 8 2 1 | 7 9 4 | 6 3 5 |
| 4 6 3 | 2 1 5 | 7 9 8 |
+-------+-------+-------+
| 5 1 2 | 9 4 7 | 3 8 6 |
| 6 3 4 | 5 8 1 | 9 2 7 |
| 9 7 8 | 6 3 2 | 5 1 4 |
+-------+-------+-------+
Cheers


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PostPosted: Sun Nov 15, 2020 10:50 pm 
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Grand Master
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Location: Lethbridge, Alberta, Canada
Thanks Ed. These puzzles are at a good level to be worth revisiting. Probably best to avoid anything 2.0 or higher.

Good luck with this one!


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PostPosted: Sat Nov 21, 2020 9:55 pm 
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Grand Master
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Andrew wrote:
Probably best to avoid anything 2.0 or higher
Noted. The next one in the archive is indeed over 2.00

Solved one of these Revisits! This one was pretty easy this time with a different (though boring) way to start compared to the archive WTs. However, I did notice one feature of the puzzle I enjoyed but couldn't make use of. Decided to also post the boring start I actually used.
Interesting feature:
1. "45" on n7: 2 innies r78c3 = 6 (no 3,6..9)

2. "45" on n78: 4 innies r7c3456 = 22

3. this h22(4) and 20(5)r8c3 makes 9 cells that total 42. If there are no repeats -> only missing 3, -> 3 in n8 in 9(2) = {36}. But this means a 6 is also missing from those two cages
3a. -> those two cages must have at least one repeat
A21v2 start: 12 steps:
Used (nearly) the same start to my archive WT.
Preliminaries from SudokuSolver
Cage 3(2) n36 - cells ={12}
Cage 5(2) n47 - cells only uses 1234
Cage 6(2) n6 - cells only uses 1245
Cage 15(2) n4 - cells only uses 6789
Cage 13(2) n6 - cells do not use 123
Cage 9(2) n8 - cells do not use 9
Cage 10(2) n4 - cells do not use 5
Cage 10(2) n89 - cells do not use 5
Cage 9(3) n7 - cells do not use 789
Cage 20(3) n69 - cells do not use 12
Cage 30(4) n7 - cells ={6789}
Cage 14(4) n1 - cells do not use 9

1. 3(2)n3 = {12}: both locked for c7
1a. no 8,9 in r7c6

2. "45" on n9: 2 innies r7c78 = 11
2a. no 9 in r7c78; no 6 in r7c8
2b. no 1 in r7c6

3. naked quad {6789} in n7: Locked for n7

4. "45" on r89: 1 outie r7c8 - 3 = 1 innie r8c2
4a. -> r7c9 = 4..8

5. 9 in r7 only in 15(3)n5: 9 locked for n8 and 15(3)
5a. 15(3) = 9{15/24}(no 3,6,7,8)

6. hidden killer triple 6,7,8 in r7 in r7c6789
6a. r7c8 = (78), r7c9 = (678)
6b. -> r7c7 = (34)(h11(2)), r7c6 = (67)
6c. 8 locked for n9

7. "45" on n9: 1 outie r7c6 + 1 = 1 innie r7c8
7a. = [67/78]: 7 locked for r7

8. 16(3)n9: {349} blocked by r7c7 = (34)
8a. {367} blocked by h11(2)r7c78
8b. = {169/259/457}(no 3)
8c. 1 in {169} must be in r8c8 -> no 6 in r8c8

9. "45" on n3: 2 innies r23c7 = 10 = [91/82]

10. "45" on c89: 1 outie r1c7 - 2 = 1 innie r8c8
10a. -> no 5,8 in r1c7, no 9 in r8c8

11. "45" on c89: 3 outies r189c7 = 18
11a. = {369/459/567}
11b. no 7 in r1c7 since r89c7 cannot be {56} in overlapping the 16(3)n9 {can't be {56}[5]}
11c. -> no 5 in r8c8 (iodc89=-2)
11d. note: r1c7 + r8c8 = [97/64/42/31]

key step
12. "45" on c789: 4 innies r2678c7 = 24 and must have 8 for c7 = {3489/3678/4578}
12a. but {389}[4] is blocked by iodc89 (step 11d)
12b. and [8]{57}[4] blocked by 18(3)n6 can't be {57}[5]
12c. -> no 4 in r7c7
12d. -> r7c7 = 3

On from there. Much easier now.

Cheers
Ed


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PostPosted: Sun Nov 22, 2020 11:27 pm 
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Grand Master
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I enjoyed this latest Revisit. Ed and I worked in similar areas but it took me rather more interesting/difficult steps to solve it.

Unlike Ed, I haven't been looking at how these Revisit puzzles were originally solved. I'm happy to treat them as new Assassin-level puzzles and just see how others solved them this time.

Here is my walkthrough for Assassin 21V2 Revisit:
Prelims

a) R34C7 = {12}
b) R45C1 = {69/78}
c) R4C89 = {15/24}
d) R56C9 = {49/58/67}, no 1,2,3
e) R6C12 = {19/28/37/46}, no 5
f) R67C3 = {14/23}
g) R7C67 = {19/28/37/46}, no 5
h) R9C45 = {18/27/36/45}, no 9
i) 20(3) cage at R5C7 = {389/479/569/578}, no 1,2
j) 9(3) cage at R7C1 = {126/135/234}, no 7,8,9
k) 30(4) cage at R8C1 = {6789}

1a. Naked pair {12} in R34C7, locked for C7, clean-up: no 8,9 in R7C6
1b. Killer pair 1,2 in R4C7 and R4C89, locked for R4
1c. Naked quad {6789} in 30(4) cage at R8C1, locked for N7
1d. Naked quad {6789} in R4589C1, locked for C1, clean-up: no 1,2,3,4 in R6C2
1e. 9(3) cage at R7C1 = {135/234}, 3 locked for N7, clean-up: no 2 in R6C3
1f. 45 rule on N7 2 innies R78C3 = 6 = [15]/{24}, no 1 in R8C3
1g. 45 rule on N1 2 innies R3C23 = 15 = {69/78}
1h. R3C23 = 15 -> R3C4 + R45C2 = 11 = {128/137/146/236/245}, no 9
1i. 8 on {128} must be in R4C2 -> no 8 in R3C4 + R5C2
1j. 45 rule on N3 2 innies R23C7 = 10 = [82/91]
1k. 16(3) cage at R2C5 = {169/178/259/268/349/358} (cannot be {367/457} because R3C7 only contains 8,9)
1l. R2C7 = {89} -> no 8,9 in R2C56
1m. 45 rule on N9 2 innies R7C89 = 11 = {38/47}/[65], no 9, no 6 in R7C8, clean-up: no 1 in R7C6
1n. 45 rule on N6 2(1+1) outies R6C4 + R7C8 = 1 innie R4C7 + 12
1o. Min R6C4 + R7C8 = 13, no 1,2,3 in R6C4 + R7C8, clean-up: no 8 in R7C7, no 2 in R7C6

[If I’d spotted that importance of Ed’s step 4, my step 5a, at this stage, my solving path would have been somewhat simpler.]

2. R67C3 = {14}/[32], R78C3 (step 1f) = [15]/{24} -> combined cage R678C3 = [142/324/415], 4 locked for C3

3a. 45 rule on N78 1 innie R7C6 = 2 outies R6C34 + 2
3b. Min R6C34 = 3 -> no 3,4 in R7C6, clean-up: no 6,7 in R7C7, no 4,5 in R7C8 (step 1m)
3c. R7C6 = {67} -> R6C34 = 4,5 = {13/14}/[32]
3d. Max R6C4 = 4 -> min R7C45 = 11, no 1 in R7C45
3e. R7C67 = [64/73], R7C78 (step 1m) = [38/47] -> combined cage R7C678 = [647/738], 7 locked for R7
3f. 20(3) cage at R5C8 = {389/479/578} (cannot be {569} because only 7,8 in R7C8), no 6
3g. R6C4 + R7C8 = R4C7 + 12 (step 1n)
3h. R4C7 = {12} -> R6C4 + R7C8 = 13,14 = [58/68/77] (cannot be [67] which clashes with R7C6)
3i. Combining R6C4 + R7C8 with R7C678, R6C4 + R7C678 = [5738/6738/7647], 7 in R67C6, locked for C6

4a. Consider permutations for R6C4 + R7C678 (step 3i) = [5738/6738/7647]
R6C4 + R7C678 = [5738/6738] => R7C8 = 8, 3 in N6 only in R56C8 = 12 = {39}
or R6C4 + R7C678 = [7647], R6C4 = 7 => R56C7 = 11 = {38/56}, R7C8 = 7 => R56C8 = 13 = {49} (cannot be {58} which clashes with R56C7)
-> R56C8 = {39/49}, no 5,7,8, 9 locked for C8 and N6, clean-up: no 4 in R56C9
4b. 18(3) cage at R5C7 = {378/468/567}
4c. 5 of {567} must be in R6C6 (R56C7 cannot be {56/57} which clash with R56C9), no 5 in R56C7
4d. Consider combinations for 18(3) cage
18(3) cage = {378/468}, 8 locked for N6 => R56C9 = {67}
or 18(3) cage = {567} => R6C6 = 5
-> no 5 in R6C9, clean-up: no 8 in R5C9
4e. 5 in R6 only in R6C56, locked for N5
[Looking at the 18(3) cage a different way.]
4f. Consider combinations for 18(3) cage
18(3) cage = {378/468} => R56C7 = {38/48}, killer pair 3,4 in R56C7 + R7C7, locked for C7
or 18(3) cage = {567} => R6C6 = 5, R7C6 = 7 (hidden single in C6) => R7C7 = 3
-> 3 in R567C7, locked for C7
Also R56C7 = {38/48}, locked for C7 => R2C7 = 9 or R56C7 = {67}, locked for C7 -> R89C7 cannot contain both of 6,9
4g. 16(3) cage at R8C8 = {259/358/457} (cannot be {169} because R89C7 cannot contain both of 6,9, cannot be {178} which clashes with R7C8, cannot be {349} which clashes with R7C7, cannot be {268} which clashes with R56C7, cannot be {367} which clashes with R7C78), no 1,6, 5 locked for N9
4h. Min R89C7 = 9 -> max R8C8 = 7

5a. 45 rule on R89 1 outie R7C9 = 1 innie R8C2 + 3 -> min R7C9 = 4
5b. 1 in R7 only in R7C123, locked for N7
5c. R7C9 + R8C2 = [63/85]
5d. Naked triple {678} in R7C689, 6,8 locked for R7
5e. 9 in R7 only in R7C45, locked for N8
5f. 15(3) cage at R6C4 contains 9 = {159/249}, no 3
5g. 8 in R7 only in R7C89, locked for N9, clean-up: no 3 in 16(3) cage at R8C8 (step 4g)
5h. Killer pair 6,8 in R56C9 and R7C9, locked for C9

6a. R6C34 (step 3c) = {14}/[31/32], R78C3 (step 1f) = [15]/{24}, 15(3) cage at R6C6 (step 5f) = 1{59}/{249}
6b. Consider placements for 4 in N8
4 in R7C45 => 15(3) cage = {249}
or 4 in R8C456 + R9C6, locked for 20(5) cage at R8C3, no 4 in R8C3 => no 2 in R7C3 => no 3 in R6C3
or 5 in R9C45 = {45}, 5 locked for N8 => 15(3) cage = {249}
-> no 3 in R6C3 or no 1 in R6C4
6c. R6C34 = {14}/[32] (cannot be [31]) = 5 -> R7C6 = 7 (step 3a), R7C7 = 3, R7C89 = [86], clean-up: no 7 in R56C9, no 2 in R9C45
6d. R56C9 = [58], clean-up: no 1 in R4C89, no 2 in R6C1
6e. Naked pair {24} in R4C89, locked for N6, 4 locked for R4 -> R34C7 = [21], R2C7 = 8 (step 1j)
6f. Naked pair {67} in R56C7, locked for C7, R6C6 = 5 (cage sum)
6g. 2 in R6 only in R6C45, locked for N5
6h. Naked pair {39} in R56C8, 3 locked for C8
6i. 16(3) cage at R8C8 (step 4g) = {259/457}
6j. 2,7 only in R8C8 -> R8C8 = {27}
6k. 5 in C8 only in R123C8, locked for N3
6l. 13(3) cage at R2C8 = {157/346} (cannot be {139} because 3,9 only in R3C9), no 9
6m. 3 of {346} must be in R3C9 -> no 4 in R3C9
6n. Hidden killer pair 5,6 in R1C8 and R23C8 for C8, R23C8 contains one of 5,6 -> R1C8 = {56}

7a. 45 rule on N2 1 innie R3C4 = 1 remaining outie R4C6 + 1 -> R3C4 = {47}, R4C6 = {36}
7b. R3C4 + R45C2 (step 1h) = {137/146/245} (cannot be {128/236} because R3C4 only contains 4,7), no 8
7c. R3C4 = {47} -> R45C2 = [31/52/61]
7d. 45 rule on N5 3 remaining innies R4C46 + R6C6 = 13 = [931/832] (cannot be {36}4 which clashes with R3C4 + R45C2 = [731]) -> R4C4 = {89}, R6C4 = {12}, R4C6 = 3 -> R3C4 = 4, clean-up: no 5 in R9C5
7e. R2C7 = 8 -> R2C56 = 8 = {26}/[71]
7e. R4C6 = 3 -> R3C56 = 13 = [58] (cannot be [76] which clashes with R2C56), clean-up: no 7 in R3C23 (step 1g)
7f. Naked pair {69} in R3C23, locked for N1, 6 locked for R3 and 26(5) cage at R3C2 -> R4C2 = 5, R5C2 = 2 (cage sum)
7g. R8C2 = 3 -> R7C12 = 6 = [24/51]
[I’d forgotten that I could have got R8C2 = 3 after R7C9 = 6, step 6c, because I continued looking at other things.]
7h. 15(3) cage at R6C4 (step 5f) = [159/294]
7i. Killer pair 4,5 in R7C12 and R7C45, locked for R7, clean-up: no 1 in R6C3, no 2 in R8C3 (step 1f)
7j. R6C34 (step 6c) = [32/41]
7k. Consider placement for 1 in N4
R5C3 = 1 => R7C3 = 2, R6C3 = 3 => R6C4 = 2
or R6C1 = 1 => R6C4 = 2
-> R6C4 = 2, R7C45 = [94], R7C23 = [12], R7C1 = 5, R68C3 = [34], R56C8 = [39], clean-up: no 5 in R9C4
7l. R6C15 = [41] (hidden pair in R6) -> R6C2 = 6, R56C7 = [67], R3C23 = [96], clean-up: no 9 in R45C1, no 8 in R9C4
7m. Naked pair {78} in R45C1, locked for C1 and N4
7n. R123C1 = {123} -> R1C2 = 8 (cage sum)
7o. 13(3) cage at R2C8 (step 6l) = {157} (cannot be {346} because 4,6 only in R2C8) -> R2C8 = 5, R3C89 = {17}, locked for N3, 1 locked for R3
7p. R45C3 = [91], R9C23 = [78], clean-up: no 1 in R9C4
7q. Naked pair {36} in R9C45, 6 locked for R9 and N8
7r. Naked pair {12} in R89C6, locked for C6 and N8, R2C6 = 6 -> R2C5 = 2 (cage sum)
7s. R1C67 = [94], R89C7 = {59} -> R8C8 = 2 (cage sum)

and the rest is naked singles.


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