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 Post subject: Assassin 309
PostPosted: Thu Feb 12, 2015 10:01 pm 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Fun one! Enjoyed this much more than the last Assassin. Nice meandering solution with just one advanced step. Hopefully Afmob will have more than one ! sub-step. SudokuSolver gives it 1.40

Assassin 309
Image
code: paste into solver:
3x3::k:4120:4120:4120:4353:4353:4098:4098:4355:4355:3092:4120:4356:4353:3333:3333:3334:4355:4355:3092:4356:4356:2331:2331:2312:3334:3334:3849:4106:4106:3354:2331:8715:2312:2312:1292:3849:4106:1293:3354:8715:8715:8715:6926:1292:5135:2832:1293:2833:2833:8715:6926:6926:5135:5135:2832:3090:3090:2833:6926:6926:4371:4371:1031:6165:6165:3090:1558:1558:3095:4371:6169:1031:6165:6165:2560:2560:3095:3095:6169:6169:6169:
solution:
+-------+-------+-------+
| 5 3 1 | 6 2 7 | 9 8 4 |
| 4 7 6 | 9 5 8 | 1 3 2 |
| 8 2 9 | 4 3 1 | 5 7 6 |
+-------+-------+-------+
| 7 6 8 | 2 4 5 | 3 1 9 |
| 3 1 5 | 7 9 6 | 2 4 8 |
| 9 4 2 | 1 8 3 | 6 5 7 |
+-------+-------+-------+
| 2 5 3 | 8 7 9 | 4 6 1 |
| 6 8 4 | 5 1 2 | 7 9 3 |
| 1 9 7 | 3 6 4 | 8 2 5 |
+-------+-------+-------+
Cheers
Ed


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PostPosted: Sat Feb 14, 2015 10:37 am 
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for the new Killer, Ed! My walkthrough has two '!' sub-steps but only one of them is technically difficult. My original walkthrough was quite long but after going through it six (!) times, I managed to cut it down to nearly half the size.

A309 Walkthrough:
1. N578 !
a) 34(5) = {46789} locked for N5
b) ! Innies+Outies N2356: 15 = R7C56 - R6C4 -> R6C4 = (12); R7C56 = 9{7/8} -> 9 locked for R7+N8+27(5)
c) Innies N8 = 27(4) = 9{378/468/567} <> 1,2
d) Innies N78 = 26(4): R7C1 <> 7,8 since R7C56 = (789) and R7C4 <> 2
e) Innies N7 = 9(2) = [27/36/54/63]
f) 10(2) <> 8

2. R6789
a) 4(2) = {13} locked for C9+N9
b) Innies R89 = 14(3): R8C3 <> 1,3 since R8C9 = (13)
c) Innies+Outies N4: R7C1 = R6C3 = (2356)
d) 11(3): R7C4 <> 5 since R6C34 <> 4
e) Innies N8 = 27(4) = 89{37/46} -> 8 locked for N8+R7

3. R6789 !
! a) 12(3) @ N7 <> {246} since it's a Killer triple of Innies N7
b) Killer pair (13) locked in 12(3) + R7C9 for R7
c) 8,9 locked in Innies N78 @ R7 = 26(4) = 89{27/45}
d) Innies+Outies N4: R7C1 = R6C3 = (25)
e) 11(3) = 2{18/45} -> 2 locked for R6
f) Innies N7 = 9(2) = [27/54]
g) 10(2) = [46/73]

4. C456
a) 16(2) = {79} locked for R1
b) Hidden pair (79) in R25C4 for C4 -> R25C4 = (79)
c) Naked pair (79) locked in R1C6+R2C4 for N2
d) 13(2) = {58} locked for R2+N2
e) Innies+Outies C1234: -1 = R138C5 - R5C4 -> R13C5 <> 6
f) 17(3) = 6{29/47} since R1C45 <> 7,9 -> R1C4 = 6
g) R9C4 = 3 -> R9C3 = 7

5. N457
a) Innie N7 = R7C1 = 2
b) Cage sum: R6C1 = 9
c) 13(2) = {58} locked for C3+N4
d) R6C3 = 2, R6C4 = 1 -> R7C4 = 8
e) 9(3) @ C4 = {234} since R3C4 = (24) -> R4C4 = 2, R3C4 = 4, R3C5 = 3
f) R1C5 = 2 -> R2C4 = 9, R1C6 = 7, R1C7 = 9
g) 12(3) = 5{16/34} -> R7C2 = 5; R7C3 = (13)

6. N136
a) 9 locked in 17(3) @ N1 = 9{17/26} -> R3C2 = (27); R3C3 = 9
b) Innie N3 = R3C9 = 6
c) Cage sum: R4C9 = 9
d) 20(3) = {578} locked for N6
e) 9(3) @ N6 = {135} -> R3C6 = 1, R4C7 = 3, R4C6 = 5
f) 13(3) = {157} since R3C78 <> 1,4 and 4{27} blocked by R3C2 = (27) -> R2C7 = 1; 5,7 locked for R3+N3

7. Rest is singles.

Rating:
1.25. I used a Killer triple combo elimination.


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 Post subject: Re: Assassin 309
PostPosted: Sat Feb 14, 2015 10:14 pm 
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Grand Master
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
My thanks as well Ed. When I finally spotted step 5 below, it simplified things for me.

Hidden Text:
0. 4(3)n9 = {13}
16(2)r1 = {79}
Innies n5 = +11 = {1235}

1. Innies n3 = +15 = [96] or [78]
-> r4c9 from (79)
-> 20(3)n6 not {479}
Max r56c9 = +15 -> Min r6c8 = 5
-> 20(3)n6 not {389}
-> 20(3)n6 from {578} or {569}
-> r456c7 = (6|8) + (14|23)

2. Innies n2 -> r3c456 = +6 or +8 -> {123} {125} {134}
-> Max rc45 = +7 -> Min r4c4 = 2. (Not 1)

3. Outies n47 = r679c4 = +12
-> Max r79c4 = +11
-> Min r7c56 = +16
-> r7c56 = {79} or {89} and r6c4 = 1 or 2

4. (Didn't like this step but couldn't see better).
Outies n478 -> r5c7 + r6c467 = +12
Only way 8 can be in there is if they are [1][128]
But that puts r4c7 = 4 and another 2 in c6 in r3c6
-> 8 not in n6 in r456c7
-> 20(3)n6 = {578}
-> 15(2)c9 = [69]
-> 16(2)r1 = [79]
-> r3c456 = +8 = {125} or {134}

5! Innies - Outies c1234 -> r5c4 = r138c5 + 1
-> r5c4 from (789) and r138c5 is max 8 -> Must include a 1
-> 1 in c5 in r3c5 or r8c5
Also Max r1c5 = 5
-> 6 in n2 in r12c4
-> 6 in n8 in 12(3)n8
-> 3 in n8 in r79c4
-> 3 in n5 in r46c6
-> 3 in n2 in r13c5

6. Implications from that...
r4c4 from (25)
-> Only possibilities for 9(3)r3c4 are [432] or [135] -> r3c5 = 3
-> HS 1 in c5 -> r8c5 = 1
-> 6(2)n8 = [51]
-> 9(3)r3c4 = [432]
-> r3c6 = 1 and r6c4 = 1
-> 9(3)r3c6 = [153]
-> r6c6 = 3
Also r7c56 = [79]
-> r79c4 = {38}
Also HS 7 in n5 -> r5c4 = 7
-> r1c5 = 2
-> r12c4 = [69]
-> 13(2)n2 = [58]

7. More implications
5(2)n6 = {14}
r56c7 = {26}
Also HS 1 in n3 -> r2c7 = 1
-> r3c78 = {57}
Also 7 in n6 in r6c89
-> 11(3)r6c3 cannot be [713]
-> 11(3)r6c3 = [218]
-> 10(2)r9 = [73]
-> Innies n7 -> 11(2)c1 = [92]
-> Also 5(2)n4 = [14]
-> HS 3 n4/r5 -> r5c1 = 3
-> HS 5 n4 -> r5c3 = 5
-> r4c3 = 8
-> r4c12 = {67}
Also HS 7 c9 -> r6c9 = 7
etc.

My 100th post! I'm an Expert! :)
CPFC 1 - 2 LFC. :cry:


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 Post subject: Re: Assassin 309
PostPosted: Mon Feb 16, 2015 5:01 am 
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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 latest Assassin. It took me a while, at one time I wondered what to do next but when I found some more steps they weren't technically difficult.

Here is my walkthrough for Assassin 309:
Thanks Afmob for pointing out the extra elimination in step 24a and that I could simplify step 25.
Prelims

a) R1C67 = {79}
b) R23C1 = {39/48/57}, no 1,2,6
c) R2C56 = {49/58/67}, no 1,2,3
d) R34C9 = {69/78}
e) R45C3 = {49/58/67}, no 1,2,3
f) R45C8 = {14/23}
g) R56C2 = {14/23}
h) R67C1 = {29/38/47/56}, no 1
i) R78C9 = {13}
j) R8C45 = {15/24}
k) R9C34 = {19/28/37/46}, no 5
l) 9(3) cage at R3C4 = {126/135/234}, no 7,8,9
m) 9(3) cage at R3C6 = {126/135/234}, no 7,8,9
n) 20(3) cage at R5C9 = {389/479/569/578}, no 1,2
o) 11(3) cage at R6C3 = {128/137/146/236/245}, no 9
p) 34(5) cage at R4C5 = {46789}

Steps resulting from Prelims
1a. Naked pair {79} in R1C67, locked for R1
1b. Naked pair {13} in R78C9, locked for C9 and N9
1c. Naked quint {46789} in 34(5) cage at R4C5, locked for N5

2. 45 rule on N3 2 innies R1C7 + R3C9 = 15 = [78/96], clean-up: no 6,8 in R4C9

3. 45 rule on N4 2 innies R6C13 = 11 = {38/47/56}/[92], no 2 in R6C1, no 1 in R6C3, clean-up: no 9 in R7C1

4. 45 rule on N7 2 innies R7C1 + R9C3 = 9 = {27/36}/[54/81], no 4 in R7C1, no 8,9 in R9C3, clean-up: no 7 in R6C1, no 4 in R6C3 (step 3), no 1,2 in R9C4

5. 20(3) cage at R5C9 = {569/578} (cannot be {389} which clashes with R34C9, cannot be {479} which clashes with R4C9), no 3,4, 5 locked for N6
5a. Killer pair 7,9 in R4C9 and 20(3) cage, locked for N6

6. 12(3) cage at R8C6 = {138/156/237/246} (cannot be {129/147/345} which clash with R8C45), no 9
6a. Killer pair 1,2 in R8C45 and 12(3) cage, locked for N8

7. 45 rule on R89 3 innies R8C379 = 14 = {158/167/239/347/356} (cannot be {149/257} which clash with R8C45, cannot be {248} because R8C9 only contains 1,3)
7a. R8C9 = {13} -> no 1,3 in R8C3

8. 12(3) cage at R7C2 = {129/147/156/237/246/345} (cannot be {138} which clashes with R7C9 and there’s no 1,3 in R8C3), no 8

9. 45 rule on N2 1 outie R1C7 = 3 innies R3C456 + 1, R1C7 = {79} -> R3C456 = 6,8 = {123/125/134}, no 6, 1 locked for R3 and N2

10. 9(3) cage at R3C4 = {135/234}, CPE no 3 in R12C4

11. 11(3) cage at R6C3 = {128/137/146/236/245}
11a. 8 of {128} must be in R7C4 (because 1,2 only in R6C34) -> no 8 in R6C3, clean-up: no 3 in R6C1 (step 3), no 8 in R7C1, no 1 in R9C3 (step 4), no 9 in R9C4
11b. 4 of {245} must be in R7C4 -> no 5 in R7C4
11c. 9 in N8 only in R7C56, locked for R7

[I originally used 45 rule on C123 next, but this step is more powerful]
12. 45 rule on N478 1 outie R6C4 = 2 innies R7C56 + 15
12a. Max R7C56 = 17 -> max R6C4 = 2
12b. R6C4 = {12} -> R7C56 = 16,17 = {79/89}

13. 45 rule on N8 4 innies R7C456 + R9C4 = 27 = {3789/4689}, 8 locked for N8

14. Deleted.

15. 17(3) cage at R7C7 = {269/278/458/467}
15a. 2 of {269/278} must be in R7C78 (R7C78 cannot be {78} which clashes with R7C56, ALS block), no 2 in R8C7

16. 45 rule on R89 R8C379 (step 7) = {158/167/239/347/356}
16a. 2 of {239} must be in R8C3 -> no 9 in R8C3

17. 8,9 in N7 only in 24(4) cage at R8C1 = {1689/2589/3489}, no 7

18. R7C1 + R9C3 (step 4) = {27/36}/[54]
18a. 12(3) cage at R7C2 (step 8) = {147/156/237/345} (cannot be {246} which clashes with R7C1 + R9C3)
18b. Killer pair 1,3 in 12(3) cage at R7C9, locked for R7, clean-up: no 8 in R6C1, no 3 in R6C3 (step 3), no 6 in R9C3 (step 4), no 4 in R9C4

19. 45 rule on C123 3 outies R679C4 = 12 = {138/246} (cannot be {147} because R7C456 + R9C4, step 13, cannot contain both of 4,7, cannot be {237} = [273] because 11(3) cage at R6C3 cannot be [227]), no 7 in R79C4, clean-up: no 3 in R9C3, no 6 in R7C1 (step 4), no 5 in R6C1, no 6 in R6C3 (step 3)

20. 11(3) cage at R6C3 (step 11) = {128/245} (cannot be {146} because 4,6 only in R7C4), no 6,7, 2 locked for R6, clean-up: no 3 in R5C2, no 4 in R6C1 (step 3), no 7 in R7C1, no 2 in R9C3 (step 4), no 8 in R9C4
20a. 8 in N8 only in R7C456, locked for R7

21. 12(3) cage at R7C2 (step 18a) = {156/237/345} (cannot be {147} which clashes with R9C3)
21a. 24(4) cage at R8C1 (step 17) = {1689/3489} (cannot be {2589} which clashes with 12(3) cage), no 2,5
[Alternatively killer pair 2,5 in R7C1 + R9C3 and 12(3) cage, locked for N7]

22. Deleted. I used combined cages and locking cages to make eliminations in C3, but they were unnecessary after I spotted step 24 and would have increased the rating of my walkthrough.

23. 16(3) cage at R4C1 = {178/358/367/457} (cannot be {169} which clashes with R6C1, cannot be {259} which clashes with R6C3, cannot be {268} which clashes with R6C13, cannot be {349} which clashes with R56C2), no 2,9
23a. Hidden killer pair 1,3 in 16(3) cage and R56C2 for N4, R56C2 contains one of 1,3 -> 16(3) cage must contain one of 1,3 = {178/358/367} (cannot be {457} which doesn’t contain 1 or 3), no 4

[Just spotted; this cracks the puzzle – no further clean-ups.]
24. 45 rule on N7 1 outie R6C1 = 1 innie R9C3 + 2 -> R6C1 + R9C3 = [64/97]
24a. R45C3 = {58} (cannot be {49/67} which clashes with R6C1 + R9C3, IOD clash), locked for C3 and N4
[Thanks Afmob for pointing out that the IOD clash also eliminated {67}.]


25. R6C1 = 9 (hidden single in N4) -> R7C1 = 2, R9C3 = 7 (step 4) -> R9C4 = 3, R6C3 = 2 (step 3), R6C4 = 1, R7C4 = 8 (cage sum), clean-up: no 3 in R23C1, no 4 in R5C2, no 3 in R6C2, no 5 in R8C5
25a. Deleted
25b. R56C2 = [14], clean-up: no 4 in R4C8
25c. Naked pair {79} in R7C56, 7 locked for R7 and N8

26. 9(3) cage at R3C4 (step 10) = {234} (only remaining combination, cannot be {135} because 1,3 only in R3C5) -> R3C5 = 3, R34C4 = [42], R8C4 = 5 -> R8C5 = 1, R78C9 = [13], R1C4 = 6
26a. R3C6 = 1 (hidden single in R3)
26b. R1C5 = 2 (hidden single in N2), R2C4 = 9 (cage sum), R1C67 = [79], R3C9 = 6 (step 2), R4C9 = 9, R7C56 = [79]
26c. Naked pair {35} in R46C6, locked for C6 -> R2C56 = [58]

27. R9C1 = 1 (hidden single in N7) -> 24(4) cage at R8C1 (step 17) = {1689}, 6 locked for N7

28. R8C3 = 4, R7C23 = [53]
28a. Naked pair {46} in R7C78, locked for N7, R8C7 = 7 (cage sum)

29. R3C6 = 1 -> R4C67 = 8 = [53]
29a. R6C6 = 3, R7C56 = [79] = 16 -> R56C7 = 8 = [26]

30. R1C3 = 1, R23C3 = [69], R3C2 = 2 (cage sum)

31. 13(3) cage at R2C7 = {157} (only possible combination) -> R2C7 = 1, R3C78 = [57], R3C1 = 8 -> R2C1 = 4

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A309 at 1.25. I thought about Easy 1.25 but the IOD clash which cracked the puzzle probably deserves the full 1.25.

wellbeback wrote:
My 100th post! I'm an Expert! :)
CPFC 1 - 2 LFC. :cry:
Congratulations on your 100th post! :applause:
A pity that Palace are out of the FA Cup. Now they can concentrate of the Premier League and try to move up a few places for a solid mid-table position.


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 Post subject: Re:
PostPosted: Sun Feb 22, 2015 2:32 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Afmob wrote:
My original walkthrough was quite long but after going through it six (!) times, I managed to cut it down to nearly half the size.
I average 5 times through a puzzle when I post a WT. The first couple are trying to solve it differently, then optimising, then checking my WT. We must be bonkers!! My optimised solution for this puzzle is also much shorter than when I first did it.

My way is closest to Andrew's since he used my key advanced step (my 4e). Particularly enjoyed his 24.

This turned out to be a really good puzzle with 4 distinct ways to do it and made you guys really think.

This is how I got started. I missed the really neat "45" the other 3 used but my way is simple enough to not need it.

Start to A309
15 steps:
Preliminaries courtesy of SudokuSolver
Cage 4(2) n9 - cells ={13}
Cage 16(2) n23 - cells ={79}
Cage 5(2) n4 - cells only uses 1234
Cage 5(2) n6 - cells only uses 1234
Cage 6(2) n8 - cells only uses 1245
Cage 15(2) n36 - cells only uses 6789
Cage 12(2) n1 - cells do not use 126
Cage 13(2) n4 - cells do not use 123
Cage 13(2) n2 - cells do not use 123
Cage 10(2) n78 - cells do not use 5
Cage 11(2) n47 - cells do not use 1
Cage 9(3) n25 - cells do not use 789
Cage 9(3) n256 - cells do not use 789
Cage 20(3) n6 - cells do not use 12
Cage 11(3) n458 - cells do not use 9
Cage 34(5) n5 - cells ={46789}

1. 16(2)r1c6 = {79}: both locked for r1
1a. 34(5)n5 = {46789} only: all locked for n5

2. 17(3)n2: {179} blocked by r1c6 = (79)
2a. {278} blocked by 13(3)={49} only and r1c6 = 9 only
2b. 17(3) = {269/359/368/458/467}(no 1): note, can't have more than one of 7,8,9

3. "45" on n8: 4 innies r7c456+r9c4 = 27 = {3789/4689/5679}(no 1,2): note, can't have both 4 & 7
3a. no 8,9 in r9c3

4. "45" on n47: 3 outies r679c4 = 12: ie, can't have more than one of 7,8,9
4a. ->Hidden killer triple 7,8,9 in c4 since 17(3)n2 can't have more than one of 7,8,9 (step 2)
4b. -> r5c4 = (789)
4c. & h12(3)r679c4 must have one of 7,8,9 = {129/138/147/237}(no 5,6)
4d. but {129} blocked by no 1,2 in r79c4
4e. and {147} as [1]{47} only, blocked by r79c4 cannot be both 4 & 7 (step 3)
4f. = {138/237}(no 4,9)
4g. must have 3: 3 locked for c4
4h. no 1,4,6 in r9c3

5. 6 in c4 only in n2: locked for n2
5a. 13(2)n2 = {49/58}(no 7): must have 5 or 9

6. 9(3)r3c4 = {126/135/234}: must have 3 or 6 in n2 (no eliminations yet)

7. 17(3)n2 = {269/359/368/458/467}(step 2b)
7a. but {359} blocked by 13(2)(step 5a)
7b. and {368} blocked by 9(3)r3c4 (step 6)
7c. = {269/458/467}(no 3)

8. "45" on n4: 1 innie r6c3 = 1 outie r7c1: no 1,9
8a. no 2 in r6c1

9. 11(3)r6c3: combo's with 3 are {137/236}: {137} must have 1 in r6c4, {236} = [623] only -> no 3 in r6c4

10. 3 in c4 only in r79c4 in h27(4) = {3789} only (step 3): all locked for n8

11. Hidden single 3 in c5 -> r3c5 = 3
11a. -> r34c4 = 6 = {15}/[42](no 2,6 in r3c4)
11b. no 9 in r2c1

12. "45" on n2: 3 remaining innies r1c6+r3c46 = 12, must have 7 or 9 for r1c6 = {129/147}(no 5)
12a. must have 1: 1 locked for r3
12b. no 1 in r4c4 (sp6(2)r34c4)

13. 6 in c4 only in 17(3)n2 = {269/467}(no 5,8)

Missing clean-ups
14. 5 & 8 in n2 only in 13(2) = {58} only: both locked for r2

15. "45" on c1234: 1 innie r5c4 - 4 = 2 remaining outies r18c5
15a. -> r18c5 = [21/41] = 3 or 5 -> r5c4 = (79)
15b. -> r8c5 = 1, r8c4 = 5, r34c4 = [42](sp6(2)r34c4), r1c45 = [62], r2c4 = 9 (cage sum)

On from there.

Cheers
Ed


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