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Ed
 Post subject: Assassin 291
PostPosted: Fri May 02, 2014 12:42 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
A nice hard one to celebrate another year. JSudoku found it very easy which is why I tried it. Enjoyed it. SudokuSolver finds it hard going and gives it a 1.75.

Assassin 291

Image
code: paste into solver:
3x3::k:4096:4096:3329:3329:5378:5378:771:771:5124:5381:4096:3590:5378:5378:5124:5124:5124:5124:5381:3591:3590:3590:4104:4104:4104:7433:7433:5381:3591:3591:1546:1546:2315:2315:3596:7433:2829:2829:8974:7183:7183:7183:2315:3596:7433:5136:8974:8974:8974:7183:3345:3345:7186:7433:5136:8974:4371:8974:7183:4116:7186:7186:7186:5136:5136:4371:8974:4885:4116:7186:4374:7186:1303:1303:4371:4885:4885:4885:4885:4374:4374:
solution: 
+-------+-------+-------+
| 6 7 5 | 8 9 4 | 1 2 3 |
| 9 3 8 | 1 7 2 | 4 6 5 |
| 4 2 1 | 5 3 6 | 7 8 9 |
+-------+-------+-------+
| 8 9 3 | 4 2 1 | 6 5 7 |
| 5 6 4 | 7 8 3 | 2 9 1 |
| 2 1 7 | 9 6 5 | 8 3 4 |
+-------+-------+-------+
| 3 5 2 | 6 4 7 | 9 1 8 |
| 7 8 6 | 3 1 9 | 5 4 2 |
| 1 4 9 | 2 5 8 | 3 7 6 |
+-------+-------+-------+
Cheers
Ed
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Afmob
 Post subject:
PostPosted: Fri May 02, 2014 4:13 pm 
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for this interesting Assassin, Ed! This is one of the rare cases where every section of my walkthrough features a "!" move which means it was either a difficult, an interesting or an important move. While optimizing, I noticed that I didn't need to use the 3(2) cage, so omitted the concerning step.
A291 Walkthrough:
1. R123 !
a) Innies R12 = 17(2) = {89} locked for R2+N1
b) 16(3) @ N1 <> 1,2
c) Hidden pair (12) in R3C23 @ N1 locked for R3
d) ! Using R2C13+R3C23 = (1289): Innies N1 = 9(2) = {45} locked for N1
e) 13(2): R1C4 = (89)
f) Innies+Outies N23: -17 = R1C3 - R3C489: R3C489 <> 3 since R1C3 >= 4
g) 14(3) @ R2: R3C4 = (45) since R2C3 = (89)
h) Naked pair (45) locked in R3C14 for R3
i) 16(3) @ R3 = {367} locked for R3

2. R123 !
a) 8,9 locked in R3C89 @ R3 for N3+29(5)
b) Outies R12 = 18(3+1) <> 9 since R3C134 >= 10
c) 21(3) = 9{48/57} since R3C1 = (45) -> R2C1 = 9, R4C1 = (78)
d) Using R3C89 = (89): Innies N23 = 13(2)
e) ! Outies N1 = 33(3+2) = Innies N23 + R4C123 -> R4C123 = 20(3) <> 1,2,6 since R4C1 = (78)

3. N5689 !
a) 9(3): R4C6 <> 6 because 6{12} blocked by R1C7 = (12)
b) 6 locked in R4C789 @ R4 for N6
c) Outies R1234 = 16(4) = 1{249/258/348/357} since R5C8 = (589) -> 1 locked for N6
d) 16(2) = {79} locked for C6+N8
e) Killer pair (89) locked in R3C8 + 14(2) for C8
f) Hidden Killer pair (89) in R6C7 for N6 since 14(2) can only have one of (89) -> R6C7 = (89)
g) 13(2): R6C6 = (45)
h) Killer pair (45) locked in 6(2) + R6C6 for N5
i) ! 29(5) = 789{14/23} since R3C89 = (89) and other combos blocked by Killer triple (456) in 9(3) + 14(2) -> 7 locked for C9+N6
j) Innies+Outies N9: R6C8 = R9C7 = (2345)

4. N5689 !
a) ! Using R4C123 = 20(3): Outies N47 = 18(3) = {369/378/567} <> 1,2,4 since R78C4 <> 7,9 and (45,48,89) are Killer pairs of Innies N23 -> R6C4 = (79)
b) Killer pair (35) locked in Outies N47 + 19(5) = 135{28/46} for N8; 19(5) must have two of (35) -> R9C7 = (35)
c) Innies+Outies N9: R6C8 = R9C7 = (35)
d) ! Outies R1234 = 16(4) = 1{249/258/348} <> 7 since {1357} blocked by R6C8 = (35) -> R5C8 = (89)
e) Hidden Single: R4C9 = 7 @ N6, R4C1 = 8 -> R3C1 = 4, R3C4 = 5, R2C3 = 8 -> R3C3 = 1, R1C3 = 5 -> R1C4 = 8
f) Outies N47 = 18(3) = {369} -> R6C4 = 9; 3,6 locked for C4+N8
g) R6C7 = 8 -> R6C6 = 5, R5C8 = 9 -> R4C8 = 5, R6C8 = 3
h) 29(5) = {14789} -> 1,4 locked for C9+N6
i) 35(7) = {1345679} since R78C4 = (36) -> R7C2 = 5, R6C2 = 1

5. Rest is singles.

Rating:
1.25 - Hard 1.25. I used a Killer triple and some hidden cages.
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Andrew
 Post subject: Re: Assassin 291
PostPosted: Sat May 03, 2014 11:04 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for another nice Assassin. I wasn't sure whether my breakthrough was appropriate for another anniversary of this site but maybe it was, since I used SudokuSolver-type steps. Maybe I "jumped in" too quickly in that key area; Afmob managed to make more eliminations elsewhere, so his work in that key area was simpler.

Here is my walkthrough for Assassin 291:
Prelims

a) R1C34 = {49/58/67}, no 1,2,3
b) R1C78 = {12}
c) R4C45 = {15/24}
d) R45C8 = {59/68}
e) R5C12 = {29/38/47/56}, no 1
f) R6C67 = {49/58/67}, no 1,2,3
g) R78C6 = {79}
h) R9C12 = {14/23}
i) 21(3) cage at R2C1 = {489/579/678}, no 1,2,3
j) 9(3) cage at R4C6 = {126/135/234}, no 7,8,9

Steps resulting from Prelims
1a. Naked pair {12} in R1C78, locked for R1 and N3
1b. Naked pair {79} in R78C6, locked for C6 and N8, clean-up: no 4,6 in R6C7

2. 45 rule on R9 3 innies R9C389 = 1 outie R8C5 + 21
2a. Max R9C389 = 24 -> max R8C5 = 3
2b. Min R9C389 = 22, no 1,2,3,4, must contain 9, locked for R9
2c. Min R9C89 = 13 -> max R8C8 = 4

3. 45 rule on R9 1 innie R9C3 = 2 outies R8C58 + 4
3a. Min R8C58 = 3 -> min R9C3 = 7

4. 45 rule on R12 2 innies R2C13 = 17 = {89}, locked for R2 and N1, clean-up: no 4,5 in R1C4
4a. 16(3) cage at R1C1 = {367} (only remaining combination, cannot be {457} which clashes with R1C3 + R3C1, ALS block), locked for N1, clean-up: no 6,7 in R1C4

5. R3C23 = {12} (hidden pair in N1), locked for R3
5a. Max R3C2 = 2 -> min R4C23 = 12, no 1,2 in R4C23
5b. Min R23C3 = 9 -> max R3C4 = 5

6. 21(3) cage at R2C1 = {489/579} (cannot be {678} because R3C1 only contains 4,5), no 6, 9 locked for C1, clean-up: no 2 in R5C2
6a. R2C1 = {45} -> no 4,5 in R4C1

7. 16(3) cage at R3C5 = {349/358/367} (cannot be {457} which clashes with R3C1), 3 locked for R3
7a. Naked pair {45} in R3C14, locked for R3 -> 16(3) cage = {367}, locked for R3
7b. Naked pair {89} in R3C89, locked for N3 and 29(5) cage at R3C8, no 8,9 in R456C9
7c. Killer pair 8,9 in R3C8 and R45C8, locked for C8
7d. Max R89C8 = 11 -> min R9C9 = 6

8. Hidden killer pair 8,9 in R45C8 and R6C7 for N6, R45C8 contains one of 8,9 -> R6C7 = {89}, clean-up: R6C6 = {45}
8a. Killer pair 4,5 in R4C45 and R6C6, locked for N5

9. 45 rule on N3 1 remaining innie R3C7 = 1 outie R2C6 + 5 -> R2C6 = {12}, R3C7 = {67}
9a. 3 in R3 only in R3C56, locked for N2

10. 14(3) cage at R2C3 = [815/824] (cannot be [914] which clashes with 21(3) cage at R2C1, combo blocker) -> R2C3 = 8, R2C1 = 9

11. 45 rule on N7 1 innie R7C2 = 1 outie R6C1 + 3, no 7,8 in R6C1, no 1,2,3 in R7C2
11a. 1 in C1 only in R6789C1, CPE no 1 in R8C2

12. 9(3) cage at R4C6 = {126/135/234}
12a. 6 of {126} must be in R4C7 (R4C67 cannot be {12} which clashes with R4C45, R45C7 cannot be {12} which clashes with R1C7), no 6 in R4C6 + R5C7

13. R3C89 = {89} = 17 -> R456C9 = 12
13a. 45 rule on N6 (using R456C9 = 12) 2 innies R6C78 = 1 outie R4C6 + 10
13b. Min R6C78 = 11, no 1 in R6C8
13c. Max R4C6 = 3 -> max R6C78 = 13, no 6,7 in R6C8
13d. 7 in N6 only in R456C9, locked for C9
13e. R456C9 = 12 = {147/237}, no 5,6
13f. 9(3) cage at R4C6 = {126/135} (cannot be {234} which clashes with R456C9), no 4
13g. 9(3) cage = {126/135}, CPE no 1 in R4C9
13h. Killer pair 5,6 in 9(3) cage and R45C8, locked for N6
13i. 4 in N6 only in R456C9 + R5C8, CPE no 4 in R78C9

14. 45 rule on N9 1 innie R9C7 = 1 outie R6C8 -> R9C7 = {234}

15. 17(3) cage at R8C8 = {269/278/359/368/458/467} (cannot be {179} which clashes with R9C3), no 1

16. R456C9 (step 13e) = {147/237}, 9(3) cage (step 13g) = {126/135}
16a. 45 rule on R1234 4 outies R5C789 + R6C9 = 16 = {1249/1267/1348/1357/1456/2356} (cannot be {1258} because R456C9 cannot contain both of 1,2, cannot be {2347} which clashes with R6C8)
16b. R5C789 + R6C9 cannot be {1267} = [16]{27} because R5C78 + R456C9 = [16]3{27} clashes with 9(3) cage and R5C789 + R6C9 = [26]{17} clashes with 9(3) cage
R5C789 + R6C9 cannot be {1357} = [15]{37} because R5C78 + R456C9 = [15]2{37} clashes with 9(3) cage and R5C789 + R6C9 = [35]{17} clashes with 9(3) cage
-> R5C789 + R6C9 = {1249/1348/1456/2356}, no 7

17. R4C9 = 7 (hidden single in N6), R4C1 = 8, R3C1 = 4 (cage sum), R1C3 = 5 -> R1C4 = 8, R3C4 = 5, R3C3 = 1 (cage sum)
17a. R3C2 = 2 -> R4C23 = 12 = {39}, locked for R4 and N4
17b. R1C5 = 9 (hidden single in N2)
Clean-ups omitted from here.

18. 4 in R4 only in R4C45 = {24}, locked for R4 and N5 -> R4C6 = 1, R2C6 = 2, R6C6 = 5 -> R6C7 = 8
18a. R5C8 = 9 (hidden single in N6) -> R4C8 = 5, R4C7 = 6, R5C7 = 2 (cage sum), R1C78 = [12], R3C89 = [89]
18b. Naked pair {34} in R68C8, locked for C8
18c. R3C7 = 7, R2C8 = 6, R79C8 = [17], R9C3 = 9, R4C23 = [93]

19. R9C8 = 7 -> R8C8 + R9C9 = 10 = [46], R9C7 = 3, R6C8 = 3
19a. Naked pair {59} in R78C7, locked for C7 and N9 -> R2C7 = 4, R12C9 = [35]
19b. Naked pair {67} in R1C12, locked for R1 and N1 -> R1C6 = 4, R2C2 = 3, R9C6 = 8

20. 19(5) cage at R8C5 = {12358} (only remaining combination) -> R9C5 = 5, R8C5 + R9C4 = {12}, locked for N8
20a. R9C2 = 4 (hidden single in R9) -> R9C1 = 1

21. 35(7) cage at R5C3 must contain 5 -> R7C2 = 5, R6C1 = 2 (step 11)
21a. R5C1 = 5 (hidden single in C1) -> R5C2 = 6

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A291 at very(?) Hard 1.25 because of the clashes I used in step 16b
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Ed
 Post subject: Re: Assassin 291
PostPosted: Wed May 07, 2014 6:33 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1043
Location: Sydney, Australia
Loved Afmob's whole solution and the start of Andrew's, especially step 10. I stayed in the early areas that both of them worked in so looks like my steps 18 & 20 are the big difference. I've used Andrew's start. [Big thanks to Andrew for a clarification]

Alt cracker for A291
8 more steps:
download the attached file and open with SudokuSolver or paste the following candidates into A291 in SudokuSolver: 
.-------------------------------.-------------------------------.-------------------------------.
| 367       367       45        | 89        456789    4568      | 12        12        3456      |
| 9         367       8         | 124567    124567    12        | 34567     34567     3456      |
| 45        12        12        | 45        367       36        | 67        89        89        |
:-------------------------------+-------------------------------+-------------------------------:
| 78        3456789   345679    | 1245      1245      123       | 12356     5689      2347      |
| 2345678   3456789   12345679  | 1236789   1236789   12368     | 1235      5689      12347     |
| 123456    123456789 12345679  | 1236789   1236789   45        | 89        234       12347     |
:-------------------------------+-------------------------------+-------------------------------:
| 12345678  456789    12345679  | 1234568   1234568   79        | 123456789 1234567   1235689   |
| 12345678  23456789  12345679  | 1234568   123       79        | 123456789 1234      1235689   |
| 1234      1234      79        | 1234568   1234568   1234568   | 234       567       689       |
'-------------------------------.-------------------------------.-------------------------------'
End Andrew's step 14 above.
15. "45" on r123: (remembering h17(2)r3c89) 3 outies r4c123 = 20(3)
15a. must have 7 or 8 for r4c1 = {389/479/578}(no 6)

16. 6 in r4 only in n6: locked for n6
16a. no 8 in r4c8

17. 8 in r4 only in n4: locked for n4
17a. no 3 in 11(2)n4

18. "45" on n6: (remembering h17(2)r3c89): 2 outies r46c6 - 3 = 1 innie r6c8
18. r6c6 & r6c8 cannot be equal since they are in the same row -> the Innie/outie difference of 3 cannot be in r4c6
18a. -> no 3 in r4c6 (IOU)

19. Killer pair 1,2 in 6(2)n5 and r4c6: both locked for r4 and n5

20. "45" on r1234:(remembering h17(2)r3c89) -> 2 outies r5c78 - 4 = 1 innie r4c9
20a. r4c9 = (347) -> r5c78 = 7,8,11
20b. -> no 1,5 in r5c7

21. 9(3)r4c6 must have 1 -> r4c6 = 1
21a. -> 6(2)n5 = {24} only: 4 locked for r4 & n5

Missing clean-up
22. r6c6 = 5, r6c7 = 8, 14(2)n6 = {59} only, 5 locked for c8 and n6, r45c7 = [62](only permutation) -> h12(3)r456c9 (step 13e) = {147} only: locked for c9 and n6, r4c9 = 7, r4c1 = 8 -> r4c23 = {39} (h20(3)r4c123), r3c2 (cage sum)

Cracked. Last combos, single innies/outies or cage sums etc left.


Attachments:
A291 ANDREW WT end step 14.ssv [119.76 KiB]
Downloaded 620 times
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