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 Post subject: Assassin 349
PostPosted: Mon Apr 30, 2018 7:03 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 767
Location: Sydney, Australia
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Was a bit worried about the boxy cage structure but ended up yielding a nice puzzle! I used two advanced tricks - both very Assassin worthy. Are a bit complicated and hard to find so I found this a very resistant puzzle. Perfect for 10 years of Assassins here! Gets a SudokuSolver score of 1.50. JSudoku uses a couple of fish.

Will post A350 mid-month.
code:
3x3::k:2560:4353:4353:4353:3842:6147:6147:2820:2820:5381:2560:2566:2566:3842:6147:6147:2820:2820:5381:2560:8711:8711:8711:8711:8711:3848:2569:5381:2560:8711:3338:4875:4875:8711:3848:2569:3084:3084:5645:5645:3338:4875:4875:1806:1806:2575:2064:8977:5645:5645:3338:8977:6930:4883:2575:2064:8977:8977:8977:8977:8977:6930:4883:5396:5396:4629:4629:2326:1559:1559:6930:4883:5396:5396:4629:4629:2326:3096:3096:3096:6930:
solution:
Code:
+-------+-------+-------+
| 1 8 5 | 4 7 9 | 6 3 2 |
| 9 3 4 | 6 8 2 | 7 5 1 |
| 7 2 6 | 3 1 5 | 9 8 4 |
+-------+-------+-------+
| 5 4 2 | 1 9 3 | 8 7 6 |
| 3 9 8 | 7 4 6 | 1 2 5 |
| 6 1 7 | 2 5 8 | 3 4 9 |
+-------+-------+-------+
| 4 7 9 | 8 2 1 | 5 6 3 |
| 8 6 1 | 5 3 4 | 2 9 7 |
| 2 5 3 | 9 6 7 | 4 1 8 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 349
PostPosted: Sun May 13, 2018 9:02 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 767
Location: Sydney, Australia
Don't get to post the first WT very often!
A349 WT:
Thanks to Andrew for some corrections. Preliminaries courtesy of SudokuSolver
Cage 6(2) n89 - cells only uses 1245
Cage 15(2) n2 - cells only uses 6789
Cage 15(2) n36 - cells only uses 6789
Cage 7(2) n6 - cells do not use 789
Cage 8(2) n47 - cells do not use 489
Cage 12(2) n4 - cells do not use 126
Cage 9(2) n8 - cells do not use 9
Cage 10(2) n12 - cells do not use 5
Cage 10(2) n36 - cells do not use 5
Cage 10(2) n47 - cells do not use 5
Cage 21(3) n14 - cells do not use 123
Cage 19(3) n69 - cells do not use 1
Cage 10(4) n14 - cells ={1234}
Cage 11(4) n3 - cells ={1235}
Cage 27(4) n69 - cells do not use 12

No routine clean-up done unless stated.
1. "45" on c12: 1 innie r1c2 = 8
1a. -> r1c34 = 9 = {27/36/45}(no 1,9)

2. "45" on c89: 1 innie r9c8 = 1

3. 11(4)n3 = {1235}: all locked for n3 and 1 for c9
3a. no 9 in 10(2)r3c9
3b. no 7,8 in r4c9

4. "45' on r89: 3 innies r8c89 + r9c9 = 24 = {789} only: all locked for n9

The first trick.
5. "45" on r1234: 3 innies r4c456 = 13 and must have one of 6,7,8,9
5a. 10(2)r3c9 must have one of 6,7,8
5b. 15(2)r3c8 must have two of 6,7,8,9
5c. 34(7)r3c3 must have three of 6,7,8,9
5d. -> r34c1 can only have one of 6,7,8,9 for c34
5e. -> {678} blocked from 21(3)r2c1
5f. = {489/579}(no 6)
5g. must have 9: locked for c1
5h. must have 4 or 5 in r34c1 (only room for one of 6,7,8,9)
5i. -> r2c1 = (79)

6. 6 in n1 only in c3: locked for c3

7. 6 in n4 only in r6: locked for r6

The second trick
8. 6 in n4 only in r6c12 -> r7c12 = [4] or [2]
8a. 21(3)r2c1 = [7]{59}/[948]/[9]{57}
8b. "45" on r12: 4 outies r34c1 + r34c2 = 18
8c. but [48]+{24} blocked by r7c12
8d. deleted
8e. -> r234c1 = {579} only; all locked for c1

9. Killer quad 1,2,3,4 in c2 in r234 + 8(2)r6c2: all locked for c2
9a. must have 4 which is only in r234c2 -> no 4 in r1c1

10. 12(2)n5c1 = [39] only permutation

11. 3 must be in 10(4)r1c1 only in r23c2: locked for c2 and n1
11a. no 5 in 8(2)r6c2

12. 5 in c2 only in 21(4) = {1578/2568}(no 4): 5 locked for n7, 8 locked for c1 and n7

13. 4 in c1 only in 10(2)r6c1 = {46} only: 6 locked for c1

14. 7(2)r5c8 = {25} only permutation: both locked for r5 and n6

15. "45" on n5: 2 outies r5c37 = 9 = {18} only: both locked for r5

16. naked triple {467} in r5c456: locked for n5
16a. naked triple {235} in r125c8: all locked for c8

17. deleted

18. 27(4)r6c8 = {4689} only combination -> r67c8 = [46], r8c8 + r9c9 = {89}: both locked for n9 -> r8c9 = 7
18a. r67c1 = [64]

19. r8c9 = 7 -> r67c9 = 12 = [93] only permutation
19a. r9c9 = 8, r8c8 = 9
19b. r34c9 = [46]
19c. r1c1 + r9c1 = [12], r8c1 = 8

20. "45" on r6789: 3 innies r6c456 = 15 = {258} only: all locked for r6 and n5
20a. naked triple {139} in r4c456: 1,3 locked for r4

21. 22(4)r5c3 = {2578} only valid combination
21a. r5c34 = [87], r6c45 = {25} -> r6c6 = 8
21b. -> r4c4 + r5c5 = 5 = [14] only

22. 8(2)r6c2 = {17} only: 7 locked for c2

23. r9c8 = 1 -> r9c78 = 11; but [65] blocked by r9c2
23a. = [74] only

24. 3 in n7 only in 18(4)r8c3 -> no 3 in r89c4

25. 3 in n8 only in 9(2)r8c5 = {36} only: both locked for c5 and n8

26. "45" on r12: 2 remaining innies r2c12 = 12 = [93] only permutation
Cheers
Ed


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 Post subject: Re: Assassin 349
PostPosted: Thu May 17, 2018 4:14 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 167
Location: California, out of London
Hi Ed - Thanks for the nice puzzle. Back from my vacation so here's my WT. I wrote it before looking at your WT and I see we used similar tricks although we applied them somewhat differently.

Mind you - I wouldn't call them 'tricks'. Perfectly acceptable techniques of the sort I love! :)

Assassin 349 WT:
1. Innies c12 -> r1c2 = 8
Innies r12 -> r1c1, r2c1, r2c2 = +13(3)
Since 10(4)r1c1 = {1234} -> Min r2c1 = 6.
-> r2c1 from (679)

2. 8(2)r6c2 contains one of (123)
-> r1c1 from (123)
-> 4 in r234c2
-> 12(2)r5c1 either {39} or {57}

3. Innies c89 -> r9c8 = 1
11(4)r1c8 = {1235}
-> 1 in r12c9
-> 7(2)r6c8 either {25} or {34}

4. -> Combined cages r5c1289 either [{39}{25}] or [{57}{34}]
-> Outies n5 = r5c37 = +9(2) = {18}
-> Innies r5 = r5c456 = +17(3) and includes a 6

Also Innies r1234 = r4c456 = +13(3)
-> r6c456 = +15(3)

5. Innies r89 = r8c8, r8c9, r9c9 = +24(3) = {789}
27(4)r6c8 must contain a 9
But r9c9 cannot be 9 since that would put remaining innies c9 = r125c9 = +7(3) = [{12}4] which puts 3 in c8 twice.
-> 9 in r68c8
-> 15(2)r3c8 = {78}
-> r89c9 = {78} and r8c8 = 9

6. 10(2)r3c9 can only be {46}
-> HS 9 in c9 -> r6c9 = 9
Also 6 in c8 only in r67c8
-> 27(4) either [{46}98] or [{56}97]

7! 34(7) must contain at least two of (678)
Since (678) already in r34 in r34c89 -> r34c1 has at most one of (678)
-> 21(3)r2c1 cannot be {678} - must have a 9.

Also 34(7) must have at least one of (48)
Since (48) already in r34 in r34c89 -> r34c1 has at most one of (48)
Since r2c1 also cannot be 4 or 8 -> 21(3)r2c1 cannot be {489}
-> 21(3)r2c1 = {579} with r2c1 from (79) and 5 in r34c1

8! Since 6 in n5 in r5c456 -> of the 6s in r34 one of them is in r34c9 and the other must be in the 34(7)
-> 5 is in the 34(7)
Since 5 also in r34c1 -> 5 nowhere else in r34
-> since 5 already in r5 in r5c1289 -> 5 in n5 in r6c456
Since 35(7) must also contain a 5 -> 5 nowhere else in r67
-> 27(4)r6c8 = [{46}98]

Puzzle cracked!
E.g., Continuing...

9. -> 19(3)r6c9 = [937]
Also since r4c9,r6c8 = {46} -> 7(2)r5c8 = {25}
-> 12(2)r5c1 = [39]
-> H13(3)r4c456 (must contain 9) = {139}
-> r5c456 = {467}
-> r6c456 = {258}
Also r6c7 = 3
-> r5c7 = 1
-> r5c3 = 8

Below is changed. Error spotted by Ed!
Second Edit: Now next two lines added.


NP r4c9,r6c8 = {46}
-> NP r4c78 = {78}
-> r4c123 = [5{24}] or [526]
-> Innies r12 (r1c1,r2c12) cannot be [274] - Can only be [193]
-> r3c1 = 7
-> r34c8 = [87]

Also
-> r34c2 = {24}
-> 8(2)r6c2 = {17}
-> r89c2 = {56}
-> r6789c1 = [6482]
-> r67c8 = [46]
-> r34c9 = [46]
etc.

Ed found an alternative and simpler ending...
Also 7 in r6 only in n4
->r4c1 = 5

Also 10(2)r6c1 = {46}
->r9c1 = 2
->r1c1 = 1
->Innies r12 = r2c12 = [93]
-> r3c1 = 7
-> r34c8 = [87]
etc.

This is the original ending which had an error
Also r6c123 = {167}
-> r4c123 = [5{24}]
-> Innies r12 = r1c1,r2c1,r2c2 = [193]
-> r3c1 = 7
-> r34c8 = [87]
etc.


Last edited by wellbeback on Tue May 22, 2018 6:12 pm, edited 3 times in total.

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 Post subject: Re: Assassin 349
PostPosted: Thu May 17, 2018 9:56 pm 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1601
Location: Lethbridge, Alberta, Canada
I've also been away on holiday; in my case only doing this puzzle after returning home.

My key breakthrough was very different from how Ed and wellbeback solved it.

Here is my walkthrough for Assassin 349:
Prelims

a) R12C5 = {69/78}
b) R2C34 = {19/28/37/46}, no 5
c) R34C8 = {69/78}
d) R34C9 = {19/28/37/46}, no 5
e) R5C12 = {39/48/57}, no 1,2,6
f) R5C89 = {16/25/34}, no 7,8,9
g) R67C1 = {19/28/37/46}, no 5
h) R67C2 = {17/26/35}, no 4,8,9
i) R89C5 = {18/27/36/45}, no 9
j) R8C67 = {15/24}
k) 21(3) cage at R2C1 = {489/579/678}, no 1,2,3
l) 19(3) cage at R6C9 = {289/379/469/478/568}, no 1
m) 10(4) cage at R1C1 = {1234}
n) 11(4) cage at R1C8 = {1235}
o) 27(4) cage at R6C8 = {3789/4689/5679}, no 1,2

Steps resulting from Prelims
1a. 10(4) cage at R1C1 = {1234}, CPE no 1,2,3,4 in R1C2
1b. 11(4) cage at R1C8 = {1235}, locked for N3, clean-up: no 7,8,9 in R4C9
1c. 27(4) cage at R6C8 = {3789/4689/5679}, CPE no 9 in R9C8

2. 45 rule on C12 1 innie R1C2 = 8, clean-up: no 2 in R2C4, no 7 in R2C5, no 4 in R5C1
2a. R1C34 = 9 = {27/36/45}, no 1,9

3. 45 rule on C89 1 innie R9C8 = 1, clean-up: no 6 in R5C9, no 8 in R8C5, no 5 in R8C6
3a. R9C67 = 11 = {29/38/47/56}
3b. 11(4) cage at R1C8 = {1235}, 1 locked for C9, clean-up: no 9 in R3C9, no 6 in R5C8

4. 45 rule on R89 3 innies R8C89 + R9C9 = 24 = {789}, locked for N9, clean-up: no 2,3,4 in R9C6 (step 3a)
4a. 27(4) cage at R6C8 = {3789/4689/5679}
4b. 3 of {3789} must be in R7C8 -> no 3 in R6C8
4c. 19(3) cage at R6C9 = {289/379/469/568} (cannot be {478} which clashes with R34C9)
4d. 2,3 of {289/379} must be in R7C9 -> no 2,3 in R6C9

5. 45 rule on R12 3 innies R1C1 + R2C12 = 13
5a. Max R1C1 + R2C2 = 7 -> min R2C1 = 6

6. Consider combinations for R5C89 = {25/34}
R5C89 = {25} => naked triple {235} in R125C8, locked for C8
or R5C89 = {34} => caged X-wing for 3 in 11(4) cage at R1C8 and R5C89, no other 3 in C89
-> no 3 in R7C8
[Alternatively this could be done by combined cages 11(4) cage at R1C8 and R5C89, the two-dimensional combined cage locking 3 for C8. I prefer the more elegant short forcing chain.]
6a. 27(4) cage at R6C8 = {4689/5679} -> R67C8 = {46/56}, 6 locked for C8, clean-up: no 9 in R34C8
6b. Naked pair {78} in R34C8, locked for C8 -> R8C8 = 9
6c. Naked pair {78} in R89C9, locked for C9, clean-up: no 2,3 in R4C9
6d. Naked pair {46} in R34C9, locked for C9, clean-up: no 3 in R5C8
6e. Killer triple 4,5,6 in R4C9, R5C89 and R6C8, locked for N6 -> R6C9 = 9, clean-up: no 1 in R7C1
6f. R6C9 = 9 -> R78C9 = 10 = [28/37]
6g. 3 in C8 only in R12C8, locked for N3
[After the key step 6, things are a lot easier.]

7. 45 rule on N5 2 outies R5C37 = 9 = {18/27}/[63], no 3,4,5,9 in R5C3
7a. R5C12 = {39/57}/[84], R5C89 = {25}/[43] -> combined cage R5C1289 = {39}{25}/{57}[43]/[84]{25}, 5 locked for R5
7b. R5C37 = {18}/[63] (cannot be {27} which clashes with combined cage R5C1289), no 2,7

8. Killer quad 1,2,3,4 in R234C2 and R67C2, locked for C2, 4 must be in R234C2 -> no 4 in R1C1, clean-up: no 8,9 in R5C1
8a. Killer pair 3,5 in R5C12 and R5C89, locked for R5, clean-up: no 6 in R5C3 (step 7b)
8b. Naked pair {18} in R5C37, locked for R5
8c. 6 in R5 only in R5C456, locked for N5
8d. Killer quad 1,2,3,5 in R1C1, R1C34 and R1C89, locked for R1

9. 24(4) cage at R1C6 = {2679/3489/3678/4569/4578} (cannot be {2589/3579} because 2,3,5 only in R2C6, cannot be {1689} = {69}[18] which clashes with R12C5), no 1
9a. 2,3,5 only in R2C6 -> R2C6 = {235}
9b. Hidden killer quad 6,7,8,9 in R2C1, R2C34, R2C5 and R2C7 for R2, R2C1 = {679}, R2C34 contain one of 6,7,8,9, R2C5 = {689} -> R2C7 must contain one of 6,7,8,9 -> no 4 in R2C7

10. 45 rule on R6789 3 innies R6C456 = 15 = {258/348/357}, no 1
10a. 1 in N5 only in R4C456, locked for R4
10b. 34(7) cage at R3C3 must contain 1, locked for R3
10c. R1C1 + R2C12 = 13 (step 5) must contain 1 for 10(4) cage at R1C1 -> R1C1 + R2C2 = {13}, locked for N1 and 10(4) cage, R2C1 = 9
10d. R2C1 = 9 -> R34C1 = 12 = [48]/{57}
10e. Caged X-Wing for 3 in R1C1 + R2C2 and 11(4) cage at R1C8, no other 3 in R12
10f. 3 in R3 only in R3C456, locked for 34(7) cage, no 3 in R4C37
10g. 34(7) cage contains 3 so must also contain 8 -> caged X-Wing for 8 in 34(7) cage and R34C8, no other 8 in R34
10h. Clean-ups: no 6 in R1C34 (step 2a), no 6 in R1C5, no 7 in R2C3, no 1,7 in R2C4, no 4 in R3C1, no 1 in R6C1

11. R2C7 = 7 (hidden single in R2), R34C8 = [87], R34C1 = [75], R5C1 = 3 -> R5C2 = 9, R1C1 = 1, R2C2 = 3
11a. Naked pair {25} in R2C68, locked for R2, clean-up: no 8 in R2C4
11b. R2C5 = 8 (hidden single in R2) -> R1C5 = 7, clean-up: no 2 in R1C34 (step 2a)
11c. Naked pair {45} in R1C34, locked for R1 -> R1C89 = [32], R2C89 = [51], R5C9 = 5 -> R5C8 = 2, R2C6 = 2
11d. R6C9 = 9, R7C9 = 3 -> R8C9 = 7 (cage sum), R9C9 = 8
11e. Clean-ups: no 5 in R7C2, no 1,2 in R8C5, no 4 in R8C7, no 2 in R9C5

12. Caged X-Wing for 4 in R34C2 and R34C9, no other 4 in R34
12a. R3C9 = 4 (hidden single in N3) -> R4C9 = 6, R34C2 = [24], R67C8 = [46], clean-up: no 6 in R6C2, no 5 in R9C6 (step 3a)
12b. Naked pair {17} in R67C2, locked for C2
12c. Naked pair {56} in R89C2, locked for N7
12d. R89C2 = {56} = 11 -> R89C1 = 10 = [82], R67C1 = [64]
12e. R9C7 = 4 (hidden single in C7), R9C8 = 1 -> R9C6 = 7 (cage sum), clean-up: no 5 in R8C5

13. R5C4 = 7 (hidden single in R5)
13a. R6C456 (step 10) = {258} (only remaining combination), locked for R6 and N5
13b. Naked pair {17} in R6C23, locked for R6 and N4 -> R45C3 = [28], R456C7 = [813]
13c. R4C4 = 1 (hidden single in R4) -> R5C5 + R6C6 = 12 = [48], R5C6 = 6, R1C67 = [96], R4C56 = [93], clean-up: no 5 in R9C5
13d. Naked pair {36} in R89C5, locked for C5 and N5
13e. R8C6 = 4 (hidden single in C6) -> R8C7 = 2

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A349 at Easy 1.5; I used a short forcing chain. As I commented after step 6, that could have been done using a two-dimensional combined cage, which might be rated a bit lower but I'm not sure that I would rate it lower.


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