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 Post subject: Assassin 295
PostPosted: Thu Jun 26, 2014 4:13 pm 
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Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Assassin 295

SS gives it 1.3.

Image


JS Code:
3x3::k:4097:4097:2306:2306:5891:5636:5636:3845:3845:4097:4097:4097:8202:5636:5891:5636:3848:3848:4105:8202:8202:8202:5891:5891:3851:3848:3848:4105:4105:8202:8202:5891:9997:3851:8732:8732:6415:6415:9997:9997:9997:9997:9997:8732:8732:6415:6415:8221:9997:3857:2318:2318:8732:8732:5396:5396:8221:3857:3857:5644:5644:5644:8732:5396:5396:8221:3857:4894:5644:5401:5401:5401:1306:1306:8221:8221:4894:4894:4894:5401:5401:

Solution:
348157269
162489573
597632814
921546738
673298451
485713692
754321986
816974325
239865147


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PostPosted: Sat Jun 28, 2014 11:55 am 
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Grand Master
Grand Master

Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for the new Assassin, HATMAN! I found this Killer harder than SudokuSolver suggests, so there is probably an easier way to solve this Killer. Despite the technical difficulty my walkthrough is rather short.

Edit: Using Ed's suggestion I've further optimized my walkthrough with step 3g.
A295 Walkthrough:
1. R123 !
a) 16(5) = {12346} locked for N1
b) ! Killer quad (6789) locked in 15(4) + both 15(2) for N3
c) 22(4) must have two of (6789) -> R1C6+R2C5 = (6789)
d) 9 locked in R3C123 @ N1 for R3
e) 15(2) @ C7: R4C7 <> 6
f) Innies N3 = 15(3) <> 1 and <> {267} since R12C7 <> 6,7,8
g) 1 locked in 15(4) @ N3 = 1{239/248/257/347} <> 6 since {1356} blocked by Killer pair (35) of Innies N3

2. R123 !
a) Outies N3 = 22(2+1) = 7+{69/78} / 8+{68} / 9+{67}
b) ! Consider placement of 6 in R3 -> Outies N3 = 7+{78} / 9+{67}
- i) 6 in R3C456 locked for N2 -> Outies N3 = 7+{78}
- ii) R3C7 = 6 -> R4C7 = 9 -> Outies N3 = 9+{67}
-> 7 locked in Outies N3 for N2
c) 15(2): R3C7 <> 7
d) Killer pair (68) locked in 15(2) + R3C7 for N3
e) 8 locked in R2C456 @ R2 for N2
f) Killer pair (67) locked in 15(2) + R1C6 for R1
g) 9(2) = [54/81]
h) 16(5) = {12346} -> 6 locked for R2

3. R123 !
a) 7 locked in 22(4) @ N2 = 7{258/348/456}
b) ! Consider placement of 9(2) -> 22(4) <> 6
- i) 9(2) = [81] -> 15(2) @ R1 = {69}
- ii) 9(2) = [54] -> 22(4) <> {4567}
c) R1C6 = 7, R2C5 = 8
d) 15(2) @ R1 = {69} locked for R1+N3
e) R3C7 = 8 -> R4C7 = 7
f) Innies+Outies C12: -7 = R2C3 - R3C2 -> R3C2 = 9, R2C3 = 2
g) Naked pair (57) locked in R3C13 for R3+N1
h) R1C3 = 8 -> R1C4 = 1

4. C123
a) Innies N7 = 19(3) = 9{37/46} -> 9 locked C3+N7+32(5)
b) 32(5) = 89{267/357/456} -> R9C4 = 8
c) Outie N7 = R6C3 = 5
d) R3C3 = 7, R3C1 = 5
e) 32(5) = {45689} -> 4,6 locked for N7+C3
f) 3 locked in R45C3 @ C3 for N4
g) 16(3) = {259} -> R4C2 = 2, R4C1 = 9

5. N125
a) Naked pair (34) locked in R1C12 for R1+N1
b) 22(4) = {2578} -> R2C7 = 5, R1C7 = 2
c) 32(6) = 5679{14/23} -> R4C4 = 5, R3C4 = 6
d) 32(6) = {145679} -> R2C4 = 4, R4C3 = 1
e) 23(5) = {23459} -> R1C5 = 5, R2C6 = 9, R4C5 = 4; 3 locked for R3
f) 39(7) = {2346789} -> R5C3 = 3, R5C7 = 4; 2,6,7,8,9 locked for N5
g) 9(2) = {36} -> R6C6 = 3, R6C7 = 6
h) R6C5 = 1

6. N89
a) Innie N89 = R7C9 = 6
b) Innies+Outies C89: -5 = R8C7 - R7C8: R8C7 = 3, R7C8 = 8
c) 22(4) = {1489} -> R7C7 = 9; 1,4 locked for N8

7. Rest is singles.

Rating:
(Hard?) 1.5. I used two Killer quads and two small forcing chains.


Last edited by Afmob on Sun Jun 29, 2014 9:03 pm, edited 7 times in total.

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 Post subject: Re: Assassin 295
PostPosted: Sun Jun 29, 2014 5:43 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Much easier than recent ones and very quick to crack with an optimizing approach. No gimme though! Last time I could crack an Assassin in 9 of my steps was A284, another one of HATMAN's puzzles. More please!! Haven't looked in detail at Afmob's solution except to see that mine is very different.

Playthrough is probably a better description of Andrew's WTs (with all the looking steps) but heard the term recently in a gaming context and thought that was the way this puzzle felt! Thanks for the fun respite HATMAN!

Playthrough A295
29 steps:
Preliminaries
Cage 5(2) n7 - cells only uses 1234
Cage 15(2) n36 - cells only uses 6789
Cage 15(2) n3 - cells only uses 6789
Cage 9(2) n12 - cells do not use 9
Cage 9(2) n56 - cells do not use 9
Cage 16(5) n1 - cells ={12346}
Cage 32(5) n478 - cells do not use 1

1. 16(5) = {12346}: all locked for n1
1a. r1c4 = (124)

2. 9 in n1 only in r3: locked for r3
2a. no 6 in r4c7

3. Combined half cage 15(2)n3+r3c7 = {78}+[6] or {69}+(78): must have 6, 6 locked for n3

4. 15(4)n3 = {1239/1248/1257/1347}
4a. must have 1, 1 locked for n3

5. "45" on n3: 3 innies r123c7 = 15 and must have 6,7,8 for r3c7
5a. = {258/267/348/357/456}(no 9)
5b. but {267} blocked by 15(2)n3 = 6/7
5c. h15(3) = {258/348/357/456}

The key
6. Combined cage 9(2)+15(2) in r1 = [54]+{78} or 15(2)n3 = {69} ie, [54] in r1c34 or {69} in r1c89
6a. from 5c. h15(3)r123c7 = {258/348/357/456}
6b. but {456} as {45}[6] only, blocked by 9(2)+15(2)r1
6c. h15(3)r123c7 = {258/348/357}(no 6)
6d. -> 15(2)r3c7 = {78} only: both locked for c7
6e. no 1,2 in r6c6

7. 6 in n3 only in 15(2) = {69} only: both locked for r1 and 9 for n3

8. 6 in n1 only in r2: locked for r2

9. from 5c. h15(3)r123c7 = {258/348/357} -> r12c7 = {25/34/35}
9a. -> 22(4)r1c6 = {2578/3478}(no 1,9)
9b. must have both {78} -> r1c6+r2c5 = {78}: both locked for n2
9b. r2c5+r1c6 = 15 -> r12c7 = 7 (cage sum) -> r3c7 = 8 (h15(3)r123c7), r4c7 = 7

Cracked. Missing routine clean-up.
10. Naked triple {579} in r3c123: 5 & 7 locked for n1 and r3
10a. -> r1c34 = [81], r1c6 = 7, r2c5 = 8

11. "45" on c12: 1 innie r3c2 - 7 = 1 outie r2c3
11a. ->r3c2 = 9, r2c3 = 2

12. Naked pair {34} in r1c12: both locked for r1 and n1

13. r12c7 = 7 (cage sum) = [25] only permutation, r1c5 = 5

14. Hidden single 9 in n2 -> r2c6 = 9

15. 32(5)r6c3 = {26789/35789/45689}: must have 8 -> r9c4 = 8

16. "45" on n7: 1 remaining outie r6c3 = [5], r3c13 = [57]

17. "45" on n7: 3 innies r789c3 = 19 = {469} only: all locked for c3 and n7
17a. 5(2)n7 = {23} only: locked for n7 and r9

18. Naked pair {13} in r45c3: both locked for n4

19. r4c12 = 11 (cage sum) = [92] only permutation
19a. r9c12 = [23], r1c12 = [34]

20. 32(6)r2c4 must have two of {134} for r2c4+r4c3 -> {145679} only valid combination -> r4c4 = 5, r3c4 = 6, r4c3 = 1, r2c4 = 4
20a. r5c3 = 3

21. r3c56 = {23} = 5 -> r4c5 = 4 (cage sum)

22. 3 in n5 only in r6: locked for r6

23. 39(7)r5c3 = {1356789/2346789}: must have 7 & 8 which are only in n5: locked for n5 [edit: no 5 is available so the first combo is not valid. Missed that since I was just focusing on getting the next step to work. Thanks Afmob!]

24. 9(2)r6c6 = [36] only permutation, r3c56 = [32]

25. Hidden killer pair 1,2 in n5: 39(7) can't have more than one of 1,2 (step 22) -> r6c5 must have (12)
25a. also no 1 in r5c7

26. "45" on n6: 1 remaining innie r5c7 + 2 = 1 outie r7c9
26a. -> r5c7 = 4, r7c9 = 6, r1c89 = [69]

27. Naked triple {139} in r789c7: all locked for n9

28. "45" on c89: 1 innie r7c8 - 5 = 1 outie r8c7
28a. -> r7c8 = 8, r8c7 = 3

29. 22(4)r7c6 = {1489} only combination -> r7c7 = 9, r78c6 = {14} both locked for n8 and c7

[edit: deleted a couple of redundant steps since Afmob noticed it is all singles from here already.]
etc
Cheers
Ed


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 Post subject: Re: Assassin 295
PostPosted: Sun Jul 06, 2014 4:02 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Phew! That was a hard Assassin! There were times when I though I'd never finish it.

After the first few steps, I had several sessions when I only managed to find one more step and it was only when I found step 18 yesterday and step 24 today that I made real progress again. My lack of progress may have been partly due to watching the World Cup football, particularly after it reached the knock-out stages.

Ed wrote:
Much easier than recent ones and very quick to crack ... No gimme though!
As you will see if you go through my walkthrough, I felt the complete opposite!

Congratulations Ed for solving this Assassin using only one forcing chain (step 6) !

Here is my walkthrough for Assassin 295:
Prelims

a) R1C34 = {18/27/36/45}, no 9
b) R1C89 = {69/78}
c) R34C7 = {69/78}
d) R6C67 = {18/27/36/45}, no 9
e) R9C12 = {14/23}
f) 16(5) cage at R1C1 = {12346}
g) 32(5) cage at R6C3 = {26789/35789/45689}, no 1

1. 16(5) cage at R1C1 = {12346}, locked for N1, clean-up: R1C4 = {124}
1a. 9 in N1 only in R3C123, locked for R3, clean-up: no 6 in R4C7

2. 45 rule on C12 1 innie R3C2 = 1 outie R2C3 + 7 -> R2C3 = {12}, R3C2 = {89}

3. 45 rule on C89 1 innie R7C8 = 1 outie R8C7 + 5, R7C8 = {6789}, R8C7 = {1234}

4. 45 rule on N3 3 innies R123C7 = 15 = {258/348/357/456} (cannot be {159/249} because R3C7 only contains 6,7,8, cannot be {168/267} which clash with R1C89), no 1,9
4a. R3C7 = {678} -> no 6,7,8 in R12C7

5. 45 rule on N3 3(2+1) outies R1C6 + R2C5 + R4C7 = 22
5a. Min R1C6 + R2C5 = 13, no 1,2,3 in R1C6 + R2C5

6. R123C7 (step 4) = {258/348/357/456} -> R12C7 = {25/34/35/45}
6a. 22(4) cage at R1C6 = {2569/2578/3469/3478/3568/4567} -> R1C6 + R2C5 = {67/68/69/78}, no 4,5

7. 45 rule on N7 2 outies R6C3 + R9C4 = 13 = {49/58/67}, no 1,2,3

8. 45 rule on R789 2 outies R6C35 = 1 innie R7C9
8a. Min R6C35 = 5 -> min R7C9 = 5
8b. Max R6C35 = 9, no 9 in R6C3, no 6,7,8,9 in R6C5, clean-up: no 4 in R9C4 (step 7)

9. 34(7) cage at R4C8 must contain 1, locked for N6, clean-up: no 8 in R6C6
9a. 1 in C7 only in R789C7, locked for N9

10. 45 rule on N47 2(1+1) outies R3C1 + R9C4 = 2 innies R45C3 + 9
10a. Max R3C1 + R9C4 = 18 -> max R45C3 = 9, no 9 in R45C3

[It took me a long time to spot …]
11. 32(5) cage at R6C3 = {26789/45689} (cannot be {35789} which clashes with R13C3, ALS block), no 3
11a. {26789} must be 6{289}7 (other permutations clash with R13C3), no 7 in R6789C3, clean-up: no 6 in R9C4 (step 7)
11b. 32(5) cage = {26789/45689}, 6 locked for C3

12. 3 in C3 only in R45C3, locked for N4
12a. Hidden killer triple 1,2,4 in R2C3, R45C3 and 32(5) cage at R6C3 for C3, R2C3 = {12}, 32(5) cage contains one of 2,4 -> R45C3 must contain one of 1,2,4 and also contains 3 -> R45C3 = {13/23/34}, no 5,7,8
12b. 7 in C3 only in R13C3, locked for N1

13. 16(3) cage at R3C1 = {169/178/259/268/457}
13a. 8 of {178/268} must be in R3C1 -> no 8 in R4C12
[Can also eliminate {178} combination = 8{17}, which clashes with R2C3 + R3C2 = [18] because R2C3 = 1 is hidden single in C3, but I’ll leave this for now as it doesn’t give any extra candidate eliminations.]

14. 45 rule on N7 3 innies R789C3 = 19 = {289/469/568}
14a. 32(5) cage at R6C3 = {26789/45689}
14b. 45 rule on N4 3 innies R456C3 = 1 outie R3C1 + 4
14c. Consider placements for 5 in N1
5 in R13C3 => R789C3 = {289/469}
or R3C1 = 5 => R456C3 = 9 = {135} (cannot be {234} which clashes with 16(3) cage at R3C1 = 5{29/47}) => R789C3 = {289/469}
-> R789C3 = {289/469}, no 5, 9 locked for C3 and N7
14d. R789C3 = {289/469} -> R6C1 + R9C4 = [58/67/85], no 4 in R6C1, no 9 in R9C4
14e. Killer pair 2,4 in R789C3 and R9C12, locked for N7
14f. 9 in R3 only in R3C12, CPE no 9 in R4C2

15. Consider placements for R1C3
R1C3 = 5 => naked triple {789} in R3C123, locked for R3
or R1C3 = {78} => R1C89 = {69} (cannot be {78} which clashes with R1C3), locked for N3 => R3C7 = {78} => naked quad {5789} in R3C1237, locked for R3
-> no 7,8 in R3C45689
15a. R1C3 = 5 => naked triple {789} in R3C123, locked for R3 => R3C7 = 6 => R1C89 = {78}, locked for R1
or R1C3 = {78} => naked quad {6789} in R1C3689, locked for R1
-> no 7,8 in R1C5

16. Consider combinations for R1C89 = {69/78}
R1C89 = {69}, locked for N3
or R1C89 = {78}, locked for N3 => R3C7 = 6
-> no 6 in 15(4) cage at R2C8

17. Consider combinations for R1C6 + R2C5 (step 6a) = {67/68/69/78}
R1C6 + R2C5 = {67/68/69}, 6 locked for N2
or R1C6 + R2C5 = {78} => R1C89 = {69} (cannot be {78} which clashes with R1C3), locked for R1 => 6 in N1 only in R2C12, locked for R2
-> no 6 in R1C5 + R2C46

[At last something more promising …]
18. 15(4) cage at R2C8 = {1239/1248/1257/1347}
18a. Consider placements for R1C3
R1C3 = 5 => R1C4 = 4 => R12C7 cannot contain both of 4,5 => 15(4) cage must contain at least one of 4,5 = {1248/1257/1347}
or R1C4 = {78} => R1C89 = {69} (cannot be {78} which clashes with R1C3), locked for N3
-> 15(4) cage = {1248/1257/1347}, no 9
18b. 9 in N3 only in R1C89 = {69}, locked for R1 and N3, clean-up: no 9 in R4C7
18c. 6 in N1 only in R2C12, locked for R2
18d. Naked pair {78} in R34C7, locked for C7, clean-up: no 1,2 in R6C6

19. R1C36 = {78} (hidden pair in R1), clean-up: no 4 in R1C4
19a. 5 in N1 only in R3C13, locked for R3

20. 22(4) cage at R1C6 (step 6a) = {2578/3478} -> R1C6 + R2C5 = {78}, locked for N2, R12C7 = {25/34}

21. R6C35 = R7C9 (step 8)
21a. Min R6C35 = 6 -> min R7C9 = 6
21b. Max R6C35 = 9, no 5 in R6C5

22. 45 rule on N6 3 innies R456C7 = 1 outie R7C9 + 11
22a. The value in R7C9 must be in R456C7 (because the rest of N6 is the 34(7) cage at R4C8) -> the remaining two values in R456C7 must total 11, 9 is only in R5C7 -> no 2 in R5C7

23. 39(7) cage at R4C6 = {1356789/2346789}, 7,8 locked for N5, clean-up: no 2 in R6C7

[I ought to have spotted this immediately after step 20, but then I wouldn’t have found the interesting step 22a.]
24. 15(4) cage at R2C8 (step 18a) = {1257/1347} (cannot be {1248} which clashes with R12C7), no 8, 7 locked for R2 and N3 -> R34C7 = [87], R3C2 = 9, R2C3 = 2 (step 2), R3C13 = [57], R1C3 = 8 -> R1C4 = 1, R1C6 = 7, R2C5 = 8, clean-up: no 5 in R1C7 (step 20)
24a. Naked pair {34} in R1C12, locked for R1 and N1 -> R1C7 = 2, R2C7 = 5 (cage sum), R1C5 = 5, clean-up: no 4 in R6C6

25. Naked triple {469} in R789C3, locked for C3 and N7 -> R6C3 = 5, R9C4 = 8 (cage sum), clean-up: no 4 in R6C7, no 1 in R9C12
25a. Naked pair {13} in R45C3, locked for N4
25b. Naked pair {36} in R6C67, locked for R6

26. R3C1 = 5 -> R4C12 = 11 = [92], R9C12 = [23]

27. Two values in R456C7 must total 11 (step 22a), R4C7 = 7 -> R5C7 = 4
27a. 39(7) cage at R4C6 = {2346789} (only remaining combination), no 1,5 -> R45C3 = [13]

28. R6C35 = R7C9 (step 8), R6C3 = 5, R6C5 = 1 (hidden single in N6) -> R7C9 = 6, R1C89 = [69]
28a. Naked triple {139} in R789C7, locked for C7 and N9 -> R6C67 = [36]

29. 45 rule on N9 3 remaining innies R7C78 + R9C7 = 18 = {189} (only possible combination, cannot be {378} because 7,8 only in R7C8) -> R7C8 = 8
29a. R8C7 = 3 (hidden single in C7)

30. R4C45 = [54] (hidden pair in N5)
30a. R1C5 = 5, R2C6 = 9, R4C5 = 4 -> R3C56 = 5 = [32]

31. R4C89 = [38], R45C6 = [68], R6C89 = [92], R6C4 = 7, R23C4 = [46]

32. R7C4 = 3 (hidden single in C4), R6C5 = 1 -> R7C5 = 2 (hidden single in R7), R8C4 = 9 (cage sum)

33. R89C5 = {67} = 13 -> R9C67 = 6 = [51]

and the rest is naked singles.

Rating Comment:
I'll rate my walkthrough for A295 at least Hard 1.5. I used several forcing chains, although at least one could have been omitted if I'd found step 18 sooner.


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