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 Post subject: Assassin 357
PostPosted: Sat Sep 01, 2018 8:05 am 
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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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a357.JPG
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NOTE: 1-9 cannot repeat on the diagonals.

Assassin 357
I found this quite a difficult puzzle. Some steps took some finding and seemed to be a lot of critical ones. But still enjoyed it a lot. SudokuSolver gives it 1.45. No trouble for JSudoku.

I have a bit of a bank of Assassins so will post every 10 days for a while. Hope I can keep up with WTs!

code:
3x3:d:k:2048:5121:5121:2306:2306:3843:3843:6404:6404:2048:5121:2053:2053:3843:3843:6404:6404:3846:4103:4103:2053:5640:5640:5129:5129:6404:3846:4103:3338:3338:5640:8971:8971:5129:5900:3846:6413:3338:5134:8971:8971:8971:5129:5900:3846:6413:3338:5134:8971:8971:4623:5900:5900:4112:6413:6929:5134:5134:4623:4623:3858:4112:4112:6413:6929:6929:4883:4883:3858:3858:4372:2325:6929:6929:4883:4883:2582:2582:4372:4372:2325:
solution:
Code:
+-------+-------+-------+
| 5 4 7 | 8 1 6 | 3 2 9 |
| 3 9 1 | 5 4 2 | 7 6 8 |
| 6 8 2 | 9 7 3 | 5 1 4 |
+-------+-------+-------+
| 2 3 4 | 6 5 7 | 8 9 1 |
| 7 1 6 | 3 8 9 | 4 5 2 |
| 8 5 9 | 1 2 4 | 6 3 7 |
+-------+-------+-------+
| 9 7 3 | 2 6 8 | 1 4 5 |
| 1 2 8 | 4 3 5 | 9 7 6 |
| 4 6 5 | 7 9 1 | 2 8 3 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 357
PostPosted: Sat Sep 08, 2018 8:06 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 767
Location: Sydney, Australia
Here's how I did it.

Assassin 357
WT:
Preliminaries
Cage 8(2) n1 - cells do not use 489
Cage 9(2) n9 - cells do not use 9
Cage 9(2) n2 - cells do not use 9
Cage 10(2) n8 - cells do not use 5
Cage 8(3) n12 - cells do not use 6789
Cage 22(3) n25 - cells do not use 1234
Cage 20(3) n1 - cells do not use 12
Cage 13(4) n4 - cells do not use 89

1. "45" on n5: 2 innies r4c4 + r6c6 = 10 (no 5)
1a. r6c6 = (1234)

2. "45" on n9: 2 outies r6c9 + r8c6 = 12 (no 1,2)

3. "45" on n1478: 2 outies r2c4 + r6c6 = 1 innie r8c6 + 4
3a. since one innie & 1 outie see each other -> no 4 in r2c4 (IOU)
3b. max. 2 outies = 9 -> max. r8c6 = 5
3c. min. r8c6 = 3 -> min. 2 outies = 7 -> min. r2c4 = 3, min. r6c6 = 2
3d. no 9 in r4c4 (h10(2))
3e. r6c9 = (789) (h12(2))

4. 22(3)r3c4 must have 9 which is only in r3c45: 9 locked for n2 and r3

5. 8(3)r2c3 = {125/134}: must have 1: 1 locked for n1 and c3
5a. must have 3/5 for r2c4 but can't have both 3,5 -> no 3,5 in r23c3

6. "45" on n1: 2 outies r2c4 + r4c1 = 7 = [34/52]

7. 16(3)r3c1 must have 2/4 for r4c1 = {268/457}(no 3)
7a. can't have both 2,4 -> no 2,4 in r3c12
7b. r3c12 = {68/57} = 6 or 7

One of the hidden steps
8. "45" on n1: 1 outie r2c4 + 9 = 2 innies r3c12 = [3]{57}/[5]{68}
8a. must have 5 in the innies or outie -> no 5 in r2c12 nor r3c456

9. 22(3)r3c4 = {679} only (no 8) = 6 or 7 in r3
9a. no 2 in r6c6 (h10(2))

10. Killer pair 6,7 in r3c1245: both locked for r3

The next hidden step
11. "45" on n1478: 2 outies r2c4 + r6c6 = 1 innie r8c6 + 4
11a. = [343/534/545]: must have 4 in r69c6: 4 locked for c6, and also no 4 in r7c7 nor r8c8 since they see both those 4s through D\ (CPE)

12. "45" on r12: 2 outies r3c38 + 5 = 1 innie r2c9
12a. -> r3c38 = 3/4 = {12}/[13] only: 1 locked for r3 and no 1 in r8c8 since it see both those cells through D\ (CPE)
12b. & r2c9 = (89) only

Tricky one
13. "45" on r12: 5 outies r3c389 + r45c9 = 10
13a. = [132]+{13}/{12}[4]+{12}
13b. r3c9 = (24),
13c. r45c9 = {123}
13d. 15(4)r2c9 = [92]{13}/[84]{12}: must have 1&2, both locked for c9, 1 locked for n6

14. 4 in r3 only in n3: 4 locked for n3

15. from step 13d. r23c9 = [92]/[84] -> 25(5)n3: {12589/23578} blocked
15a. = {12679/13579/13678/23569} = 8 or 9
15b. killer pair 8,9 with r2c9: both locked for n3

16. "45" on c789: 1 innie r1c7 + 5 = 2 outies r38c6
16a. r38c6 cannot sum to 10 -> no 5 in r1c7

Final cracker
17. "45" on n3: 4 innies r13c7 + r23c9 = 20, must have 4 for n3 and remembering that r23c9 = [92]/[84] -> must have both {29} or both {48}
17a. = {1478/2459/2468/3458}
17b. 5 in {2459} must be in r3c7, 3 other combinations only have both {48} -> 4 must go in r23c9
17c. -> no 4 in r3c7
17d. -> r3c9 = 4, r2c9 = 8, r45c9 = {12} only: 2 locked for n6
17e. no 4 in r8c6 (h12(2)r6c9+r8c6)

18. "45" on r12: 2 remaining outies r3c38 = 3 = {12} only: 2 locked for r3
18a. no 1,2 in r8c8 since it sees both these

19. r23c9 = 12 -> r13c7 = 8 = [35] only permutation
19a. 5 placed for d/

20. r6c6 = 4 (hidden single in c4): placed for D\
20a. r4c4 = 6 (h10(2)): placed for D\

21. "45" on c789: 2 remaining outies r38c6 = 8 = [35] only permutation
21a. -> r6c9 = 7 (h12(2))

22. "45" on c1: 1 outie r3c2 - 4 = 1 innie r9c1
22a. r9c1 = (234)

Very straightforward to the end now. Don't forget the diagonals!
Cheers
Ed


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 Post subject: Re: Assassin 357
PostPosted: Tue Sep 11, 2018 12:44 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1601
Location: Lethbridge, Alberta, Canada
Thanks Ed for another nice Assassin.

"I have a bit of a bank of Assassins so will post every 10 days for a while. Hope I can keep up with WTs!"
I always give priority to Assassins, except when I'm already working on another puzzle. I was already working on one of HATMAN's MeanDoku NCs when Assassin 356 appeared, and on another one when Assassin 357 was posted.

I was surprised that Ed and I used several different 45s to solve this Assassin.
Loved Ed's step 3:
It made really good progress at getting into the puzzle. My step 2, with the extension of it in step 7, gave me a good start. Then it was my 45s on 4 nonets in steps 9 and 10 which broke the puzzle open for me.

Here is my walkthrough for Assassin 357:
Prelims

a) R12C1 = {17/26/35}, no 4,8,9
b) R1C45 = {18/27/36/45}, no 9
c) R89C9 = {18/27/36/45}, no 9
d) R9C56 = {19/28/37/46}, no 5
e) 20(3) cage at R1C2 = {389/479/569/578}, no 1,2
f) 8(3) cage at R2C3 = {125/134}
g) 22(3) cage at R3C4 = {589/679}
h) 13(4) cage at R4C2 = {1237/1246/1345}, no 8,9

Steps resulting from Prelims
1a. 8(3) cage at R2C3 = {125/134}, CPE no 1 in R2C1, clean-up: no 7 in R1C1
1b. 13(4) cage at R4C2 = {1237/1246/1345}, 1 locked for N4

[The first key 45.]
2. 45 rule on R12 1 innie R2C9 = 2 outies R3C38 + 5
2a. Min R3C38 = 3 -> min R2C9 = 8
2b. Max R3C38 = 4 -> R3C38 = {12/13}, 1 locked for R3
[I overlooked no 1 in R8C8, CPE using D\]
2c. R2C9 = {89} -> 15(4) cage at R2C9 = {1239/1248}, no 5,6,7, 1,2 locked for C9, 1 also locked for N6,clean-up: no 7,8 in R89C9
2d. R2C9 = {89} -> no 8,9 in R345C9
2e. Killer pair 3,4 in 15(4) cage and R89C9, locked for C9
2f. 16(3) cage at R6C9 must contain one of 1,2,3,4 -> R7C8 = {1234}

3. 45 rule on C12 3 outies R148C3 = 19 = {289/379/469/478/568}, no 1
3a. 2 of {289} must be in R4C3 -> no 2 in R8C3
3b. 13(4) cage at R4C2 = {1237/1246/1345}, 1 locked for C2

4. 45 rule on N5 2 innies R4C4 + R6C6 = 10 = [64/73/82/91]
4a. 18(3) cage at R6C6 = {189/279/369/378/459/468} (cannot be {567} because R6C6 only contains 1,2,3,4)
4b. R6C6 = {1234} -> no 1,2,3,4 in R7C56

5a. 45 rule on N1 2(1+1) outies R2C4 + R4C1 = 7 = [16/25/34/43/52]
5b. 45 rule on N9 2(1+1) outies R6C9 + R8C6 = 12 = [57/66/75/84/93]
5c. 45 rule on C1 1 outie R3C2 = 1 innie R9C1 + 4, no 2,3,4 in R3C2, no 6,7,8,9 in R9C1
5d. 45 rule on C9 1 innie R1C9 = 1 outie R8C8 + 5, no 5 in R1C9
5e. 16(3) cage at R6C9 = {178/259/268/367/457} (cannot be {349} because 3,4 only in R7C8, cannot be {358} which clashes with R89C9, cannot be {169} which clashes with R1C9 + R7C8 = [61])
5f. 16(3) cage at R3C1 = {259/268/349/358/457} (cannot be {367} which clashes with R12C1)
[At this stage I can’t see any direct possibilities for the combined cages 8(2) at R1C1 and 16(3) at R3C1, or 16(3) at R6C9 and 9(2) at R8C9.]

6. 45 rule on R89 2 outies R7C27 = 1 innie R8C1 + 7, no 7 in R7C7 (IOU)

[Taking step 2 further …]
7. 15(4) cage at R2C9 (step 2c) = {1239/1248}
7a. R2C9 + R3C389 = 9{13}2/8{12}4, 2 locked for R3, no 3 in R3C9
7b. 4 of {1248} must be in R3C9 -> no 4 in R45C9
7c. 16(3) cage at R3C1 (step 5f) = {259/268/349/358/457}
7d. {268} must be {68}2 -> no 6 in R4C1, clean-up: no 1 in R2C4 (step 5a)
7e. 8(3) cage at R2C3 = {125/134}, 1 locked for C3 and N1, clean-up: no 7 in R2C1
7f. 16(3) cage at R3C1 = {268/349/358/457} (cannot be {259} which clashes with R12C1)
7g. 9 of {349} must be in R3C2 -> no 9 in R3C1
7h. R12C1 and 16(3) cage ‘see’ each other -> combined cage 16(3) cage + R12C1 = {268}{35}/{349}{26}/{358}{26}/{457}{26}, 2 locked for C1, clean-up: no 6 in R3C2 (step 5c)

8. 45 rule on N3 4 innies R13C7 + R23C9 = 20, R23C9 (step 7a) = [84/92] = 11,12 -> R13C7 = 8,9 = [17/26]/{35}/[18]{36/45}, no 7,8,9 in R1C7, no 9 in R3C7

[Another key 45 but a harder one to spot.]
9. 45 rule on N1236 2 outies R4C14 = 1 innie R6C9 + 1
9a. Min R4C14 = 8 -> min R6C9 = 7, clean-up: no 6,7 in R8C6 (step 5b)
9b. Max R4C14 = 10 -> no 5 in R4C1, no 9 in R4C4, clean-up: 2 in R2C4 (step 5a), no 1 in R6C6 (step 4)
9c. 22(3) cage at R3C4 = {589/679}, 9 locked for R3 and N2, clean-up: no 5 in R9C1 (step 5c)
9d. 8 of {589} must be in R4C4 -> no 8 in R3C45
9e. 8(3) cage at R2C3 = {125/134}
9f. 5 of {125} must be in R2C4 -> no 5 in R2C3
9g. 16(3) cage at R3C1 (step 7f) = {268/358/457}
9h. R4C1 = {234} -> no 3,4 in R3C1
9i. 1,2 in N2 only in R1C123 + R2C23, CPE no 1,2 in R1C7
9j. R13C7 (step 8) = 8,9 = {35/36/45}, no 7,8

[And a related 45.]
10. 45 rule on N1236 5(4+1) innies R3C1245 + R6C9 = 37
10a. Min R3C1245 = 28 must contain 8 -> 8 in R3C12, locked for R3 and N1
10b. 16(3) cage at R3C1 (step 9g) must contain 8 = {268/358}, no 4,7, clean-up: no 3 in R2C4 (step 5a)
10c. Killer pair 2,3 in R12C1 and R4C1, locked for C1
10d. 7 in N1 only in 20(3) cage at R1C2 = {479}, 4 locked for N1
10e. R148C3 (step 3) = {289/379/469/478} (cannot be {568} because R1C3 only contains 4,7,9), no 5

11. 7 in R3 only in R3C456, locked for N2, clean-up: no 2 in R1C45
11a. R1C45 and 15(4) cage at R1C6 ‘see’ each other -> combined cage R1C45 + 15(4) cage at R1C6 = 24(6) = {123468} (only remaining combination without 7,9), no 5, clean-up: no 4 in R1C45
11b. Caged X-Wing for 4 in 20(3) cage at R1C2 and 15(4) cage at R1C6, no other 4 in R12
[Cracked. The rest is straightforward.]
11c. R2C4 = 5 -> R23C3 = 3 = {12}, locked for C3 and N1, R12C1 = [53], 5 placed for D\, R3C12 = [68], R4C1 = 2, R9C1 = 4 (step 5c), placed for D/, clean-up: no 4,5 in R8C9, no 6 in R9C56
11d. Naked pair {36} in R89C9, locked for C9 and N9 -> R345C9 = [412], R2C9 = 8 (cage sum), clean-up: no 1 in R7C8 (step 5d), no 4 in R8C6 (step 5b)
11e. R3C45 = {79}, locked for R3, R4C4 = 6 (cage sum), R6C4 = 4 (step 4), both placed for D\ -> R89C9 = [63], 3 placed for D\, clean-up: no 3 in R1C5, no 7 in R9C56
11f. R2C5 = 4 (hidden single in N2), R3C6 = 3, clean-up: no 6 in R1C5
11g. Naked pair {18} in R1C45, locked for R1 and N2
11h. Naked pair {26} in R12C6, locked for C6 and 15(4) cage at R1C6, R1C7 = 3, R3C7 = 5, placed for D/, clean-up: no 8 in R9C5
11i. R8C4 = 5, R6C9 = 7 (step 5b), R1C9 = 9, placed for D/, R7C9 = 5, R7C8 = 4 (cage sum)
11j. R3C67 = [35] = 8 -> R45C7 = 12 = {48}, locked for C7 and N6
11k. Naked pair {47} in R1C23, locked for R1 and N1 -> R2C2 = 9, placed for D\
11l. Naked pair {12} in R3C3 + R7C7, locked for D\
11m. Naked pair {78} on D\, CPE no 7,8 in R8C5
11n. 13(4) cage at R4C2 = {1345}, locked for N4, 5 also locked for C2
11o. 7 in R4 only in R4C56, locked for N5 -> R5C5 = 8, placed for both diagonals, R4C6 = 7, placed for D/, R8C8 = 7, R1C45 = [81], clean-up: no 9 in R9C6
11p. R6C6 = 4 -> R7C56 = 14 = [68], R9C6 = 1 -> R9C5 = 9, R9C78 = [28], R7C7 = 1, placed for D\, R7C3 + R8C2 = [32], placed for D/

and the rest is naked singles, without using the diagonals.

Rating Comment:
I'll rate my WT for A357 at Easy 1.5. It felt like it ought to be 1.25 but technically the 'see each other' combined cages are in the 1.5 range.


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 Post subject: Re: Assassin 357
PostPosted: Sat Sep 15, 2018 8:31 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 167
Location: California, out of London
Excellent :)
We all saw important and non-obvious 45s and used them in interesting ways - and often different ones!

Here is how I did it...
Assassin 357 WT:
1. Innies - Outies r12 -> r2c9 = r3c3 + r3c8 + 5
-> r2c9, r3c38 from [8{12}] or [9{13}]
-> 15(3)r2c9 from [84{12}] or [92{13}]
I.e (12(3|4)) locked in r3 in r3c389

2. Whether 15(3)r2c9 = [84{12}] or [92{13}]
-> Max r456c9 = +12(3)
-> Min r45c7 = +10(2)
-> Max r3c67 = +10(2)
-> r3c67 = One of (34) and one of (567)
-> (1234) in r3 locked in r3c36789

3. Innies n5 -> r4c4 + r6c6 = +10(2) -> No 5
-> r3c45 cannot be {89}
Also r3c12 cannot be {89}
-> r3c12 = One of (89) and one of (567)
-> Max r4c1 = 3

4. 13(4)n4 must have a 1
-> Min r4c1 = 2
-> r4c1 from (23)
Outies n1 -> r4c1 + r2c4 = +7(2)
-> r2c4 from (54)

5! Breaks it!
Innies n2356 -> r2c4 + r6c6 + r6c9 = +16(3)
Outies n9 -> r6c9 + r8c6 = +12(2)
-> r6c6 + r6c9 cannot = +12(2)
-> r2c4 cannot be 4!
-> r2c4 = 5

6. Continuing
-> r4c1 = 2
Also r23c3 = {12}
-> 8(2)n1 = [53]
-> r3c12 = {68}
-> 20(3)n1 = {479}
Also 22(3)r3c4 = [{79}6]
-> r6c6 = 4
-> (Innies n2356) r6c9 = 7

7. More...
Also HS 5 in r3 -> r3c7 = 5
-> NS r3c6 = 3
-> 20(4)r3c6 = [35(48}]
-> r45c9 = [12]
-> r3c389 = [{12}4]
-> r2c9 = 8
-> 9(2)n9 = {36}
-> 16(3)r6c9 = [745]
-> r1c9 = 9
Also remaining Innie n3 -> r1c7 = 3
Also 20(3)n1 = [{47}9]

7. Even More...
13(4)n4 = {1345}
-> Since 20(3)n1 also contains a 4 -> One of r14c3 is a 4.
Outies c12 = r148c3 = +19(3)
This can only be [748]
Also remaining innies c1 = r39c1 = +10(2) = [64]
-> r3c2 = 8
Also NP r56c3 = {69}
-> 20(4)r5c3 = [{69}[32]
-> 25(4)c1 = [{78}[{19}]
-> Remaining Innie n7 -> r9c3 = 5

8. Yet More...
Outies n9 -> r8c6 = 5
-> r7c56 = {68}
Also HS r2c5 = 4
-> r12c6 = {26}
-> 9(2)n2 = {18}
Also 6 on D\ in r4c4 -> 9(2)n9 = [63]
Also 9 on D\ in r2c2 -> r78c7 = [19]
etc.


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