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 Post subject: Assassin 149
PostPosted: Thu Apr 02, 2009 9:19 pm 
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Expert
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Joined: Sat Jan 17, 2009 8:30 am
Posts: 118
Location: france
This is a quite hard Assassin : I have had to use many little steps and the whole cage pattern before cracking it.
I have no V2, but I think this one will resist enough to keep you busy ...



Assassin 149

Image

Note that cells r46c5 form a cage 14(2).

Edit : thanks Ed for that nice picture !

PS code : 3x3::k:1536:1536:6914:6914:5636:5637:5637:2055:2055:5129:5129:6914:5636:5636:5636:5637:2320:2320:5129:1299:8212:6914:5636:5637:8212:3353:2320:1299:5660:4125:8212:3615:8212:4385:4130:3353:3876:5660:4125:4125:8212:4385:4385:4130:4908:3876:5660:4125:8212:3615:8212:4385:4130:4908:3876:3639:2360:5689:5689:5689:3132:3901:4908:3639:2360:1857:1857:5689:2884:2884:3132:3901:2360:4425:4425:4425:5689:3917:3917:3917:3132:

Solution :
Hidden Text:
429816753
856937421
731425986
268794135
593168247
174352698
985271364
612543879
347689512



SS (V3.3.0) Score : 1.71


Last edited by manu on Mon Apr 06, 2009 3:43 am, edited 2 times in total.

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PostPosted: Fri Apr 03, 2009 12:44 pm 
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Grand Master
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
That was different! :lol:

My original walkthrough was twice as long and I had some trouble getting into the puzzle and finding some place to start. But after that there were so many Killer subsets (especially hidden ones) I've found which made the solving really enjoyable. Thanks for this fun killer, manu!

A149 Walkthrough:

1. R789 !
a) Innies C12 = 8(3) = 1{25/34} -> 1 locked for N7
b) Innies C89 = 10(3) <> 8,9
c) Innies+Outies C89: 2 = R7C7 - R9C8 -> R7C7 <> 1,2
d) 1 locked in R7C456 @ R7 for N8
e) 7(2) <> 6
f) ! Innies+Outies C12: 1 = R7C3 - R9C2: R7C3 <> 6 and R9C2 <> 5 since (56) is a Killer pair of 14(2)
g) Hidden Quad (6789) in R7C12+R8C1+R9C3 for N7 -> R7C12+R8C1+R9C3 = (6789)
h) 14(2) = {68} locked for N7
i) 9(3) = 3{15/24} -> 3 locked for N7
j) Innies R789 = 13(2) = [76/94]

2. C789 !
a) Innies N3 = 28(4) = 89{47/56}
b) Hidden Killer pair (89) in R789C7 for N9 since 15(2) can only have of (89)
c) Innies N3 = 28(4): R3C8 = (89) since R123C7 can only have of (89) because of R789C7
d) 13(2) = [85/94]
e) 19(3) = {469/478/568} <> 2,3 because R7C9 = (46)
f) Killer pair (45) locked in R4C9 + 19(3) for C9
g) 8(2): R1C8 <> 3
h) 9(3): R2C8 <> 3 since 4,5 only possible there
i) 3 locked in R123C9 @ N3 for C9
j) ! Innies+Outies C89: 2 = R7C7 - R9C8: R7C7 <> 8,9 and R9C8 <> 6,7 since (68,79) are Killer pairs of 15(2)

3. C789 !
a) 12(3) = {147/156/237/246} because R9C9 <> 3,4,5
b) ! Killer pair (67) locked in 15(2) + 12(3) for N9
c) R7C9 = 4, R4C9 = 5 -> R3C8 = 8
d) Outies N6 = R5C6 = 8
e) Hidden Single: R6C9 = 8 @ N6 -> R5C9 = 7, R8C9 = 9 @ C9 -> R7C8 = 6
f) R7C2 = 8, R8C1 = 6
g) 11(2) = {38} -> R8C6 = 3, R8C7 = 8
h) 12(3) = {237} -> R9C9 = 2, R8C8 = 7, R7C7 = 3
i) 15(3) = {159} -> R9C6 = 9; 1,5 locked for R9
j) R9C2 = 4, R9C3 = 7 -> R9C4 = 6

4. N457
a) 9(3) = {135} -> R9C1 = 3, R7C3 = 5, R8C2 = 1
b) 5(2) = {23} -> R4C1 = 2, R3C2 = 3
c) 15(3) = {159} -> R7C1 = 9; 1,5 locked for C1+N4
d) Hidden Single: R4C3 = 8 @ N4
e) 16(4) = {1348} because R56C3 = (3469) -> R5C4 = 1; 4 locked for C3
f) 14(2) = {59} -> R4C5 = 9, R6C5 = 5
g) 32(7) = {1234679} -> R3C3 = 1, R3C7 = 9

5. R1
a) R1C1 = 4 -> R1C2 = 2
b) 8(2) = {35} -> R1C8 = 5, R1C9 = 3

6. Rest is singles.

Rating: 1.25 - (Hard) 1.25. I used lots of Killers pairs (Naked, Hidden or in combination with IOD).


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 Post subject: Re: Assassin 149
PostPosted: Sun Apr 05, 2009 8:36 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
I missed Afmob's neat step 1f. so took a slightly longer route to do the beginning. Did his step 2 ....differently. I'll give this puzzle a 1.5 rating since, as manu says, you have to consider the big picture of the puzzle (NOT a hint). Yet without many little eliminations, just lots of implied stuff. It's cracked from step 15. Really great puzzle. Thanks very much manu!

Please let me know of any corrections or clarifications. [Thanks Andrew!]

Walkthrough for Assassin 149

Prelims
i. 6(2)n1 = {15/24}
ii. 27(4)n1: no 1,2
iii. 8(2)n3: no 4,8,9
iv. 20(3)n1: no 1,2
v. 9(3)n3: no 7,8,9
vi. 5(2)n1 = {14/23}
vii. 13(2)n3: no 1,2,3
viii. 22(3)n4: no 1,2,3,4
ix. 14(2)r46c5 = {59/68}
x. 19(3)n6: no 1
xi. 14(2)n7 = {59/68}
xii. 9(3)n7: no 7,8,9
xiii. 15(2)n9 = {69/78}
xiv. 7(2)n7: no 7,8,9
xv. 11(2)n8: no 1

1. 22(3)n4 = 9{58/67}
1a. 9 locked for n4 & c2
1b. no 5 r8c1

2. "45" c12: 3 innies r8c2 + r9c12 = 8 = 1{25/34}(no 6..8)
2a. 1 locked for n7
2b. no 6 in r8c4

3. Hidden killer triple (789) in n7 since 14(2) = one of 8/9
3a. r7c1 & r9c3 = (789)

4. 15(3)n4 must have (789) in r7c1 and cannot have two of 7/8/9 because of the cage sum
4a. -> no 7 or 8 in r56c1

5. Hidden killer pair (78) in n4 since 22(3)n4 = one of 7/8 (step 1)
5a. -> 16(4)n4 must have 7/8 -> {1249/1456/2356} blocked

6. hidden killer triple (789) in n1. Like this. Since r456c3 = one of 7/8 (step 5a) and r9c3 = (789) -> r123c3 must have one of 7/8/9 for c3
6a. -> 20(3)n1 must have two of (789) for n1 = {389/479/578}(no 6)

7. 6 in n1 only in c3: 6 locked for c3

8. 6 in n7 only in 14(2) = {68}: 8 locked for n7

9. "45" n789: 2 innies r7c19 = 13 = [76/94]
9a. r7c9 = (46)

10. 19(3)n6 must have 4/6 in r7c9 = {469/478/568}(no 2,3) = one of 8/9 (important in a few steps)

11. "45" c89: 3 innies r8c9 + r9c89 = 10 = {127/136/145/235}(no 8,9)

12. Hidden killer pair (89) in c89 -> 13(2)n3 and 16(3)n6 must have 8/9 for c89. Like this.
12a. 15(2)n9 = one of 8/9; 19(3)n6 = one of 8/9 (step 10); 16(3)n6 can have at most one of 8/9 because of the cage sum
12b. -> 13(2)n3 must have 8/9 for c89 = {49/58}(no 6,7)
12c. and 16(3)n6 must have 8/9 for c89 -> {367/457} blocked

13. Killer pair (89) in 16(3)n6 (step 12c) & 19(3)n6 (step 10): both locked for n6
13a. no (45) in r3c8

14. Killer pair (89) in 16(3)n6 (step 12c) & r3c8: both locked for c8
14a. no 6 or 7 in r8c9

15. h13(2)r7c19: [76] blocked by r7c8
15a. -> r7c19 = [94]
15b. r9c3 = 7
15c. r4c9 = 5
15d. no 3 in r1c8

Now just trying to get to singles so won't worry too much about cage cleanup.
16. r3c8 = 8 (cage sum)

17. "45" n6: 1 remaining outie r5c6 = 8
17a. 14(2)n5 = [95](last permutation)

18. r6c9 = 8 (hsingle n6)
18a. r5c9 = 7 (cage sum)

19. r8c9 = 9
19a. r7c8 = 6 (cage sum)

20. r7c2 = 8 -> r8c1 = 6

21. 16(3)n6 = {349}(last combination): 3 & 4 locked for n6 & c8

22. 12(3)n9 = {237}(last combination): all locked for n9

23. r8c67 = [38](last permutation)

24. 7(2)n7 = {25}(last combination): both locked for r8
24a. r8c8 = 7

25. "45" c89: 1 outie r7c7 - 2 = r9c8 = [31]
25a. r9c79 = [52]
25b. r9c6 = 9 (cage sum)

26. "45" n7: 2 remaining outies r89c4 = 11 = [56]
26a. r9c2 = 4 (cage sum)

27. 22(3)n4 = {679} (last combination): 7 locked for c2

28. r2c1 = 8 (hsingle c1)
28a. r2c2 + r3c1 = 12 = [57]

29. 6(2)n1 = [42] (last permutaion)
29a. r56c1 = 6 = [51]
29b. 5(2)n1 = [32]

30. r4c3 = 8 (hsingle n4)
30a. r56c3 = {34} = 7 -> r5c4 = 1(cage sum)

31. r1c89 = [53] (cage sum)

32. 32(7)n1 = {1234679} -> r3c37 = {19}: both locked for r3

32. r12c3 = {69}: both locked for n3 & 27(4) = 15 -> r13c4 = 12 = [84]

33. r3c37 = [19]

34. "45" n3: 2 remaining outies r13c6 = 11 = [65]

Rest is singles
Cheers
Ed


Last edited by Ed on Thu Apr 23, 2009 4:55 am, edited 2 times in total.

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 Post subject: Re: Assassin 149
PostPosted: Sun Apr 05, 2009 5:55 pm 
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Expert
Expert

Joined: Sat Jan 17, 2009 8:30 am
Posts: 118
Location: france
Thanks for these very different but elegant walkthroughs, Afmob and Ed ! I have followed another (slightly different) approach, so other WTs are yet possible ;)

Reading Afmob's and Ed's, I have finally wanted to re-try to make a V2 with the same cage pattern, and got the following. It might to be felt not much more difficult than V1 ; my solving path for V2 is shorter but however implies harder moves (a forcing chain, an ALS and killer subsets) which could explain the higher SSrating. See by yourself...

ASSASSIN 149 V2

Image


PS code :3x3::k:2816:2816:5378:5378:5636:5381:5381:3591:3591:2569:2569:5378:5636:5636:5636:5381:3600:3600:2569:2579:9236:5378:5636:5381:9236:2329:3600:2579:2588:6941:9236:2591:9236:4385:5410:2329:4388:2588:6941:6941:9236:4385:4385:5410:3372:4388:2588:6941:9236:2591:9236:4385:5410:3372:4388:2103:5432:5689:5689:5689:2876:2365:3372:2103:5432:2113:2113:5689:2884:2884:2876:2365:5432:3913:3913:3913:5689:4429:4429:4429:2876:

Solution :
Hidden Text:
9243751683
6548192718
7926435253
1497866487
5329171986
2543436217
8595726983
14891534672


SS Score : 2.16

PS : not yet solved the bad quality of the picture (??) Edit : thanks Ed !


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PostPosted: Mon Apr 06, 2009 9:00 pm 
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Grand Master
Grand Master

Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
It took me some time to find the important steps (especially those Hidden Killer pairs), so I decided to rate this Killer "hard 1.5" but I think the moves are probably in the 1.5 territory.

A149 V2 Walkthrough:

1. R789
a) Innies C12 = 24(3) = {789} locked for N7
b) Innies R789 = 13(2) = [49/58/67]
c) 8(2) @ R7C2 <> 1
d) Hidden Killer triple (123) in R89C3 for N7 since 8(2) can only have one of (23)
-> R89C3 = (123)
e) Innies R9 = 13(3): R9C58 <> 6,7,8,9 since R9C1 >= 7
f) 15(3) must have one of (456) -> R9C4 = (456)
g) 13(3): R56C9 <> 6,7,8,9 since R7C9 >= 7
h) Innies C89 = 10(3) <> 8,9

2. R789
a) 17(3) @ R9 <> 7{19/28} because they are blocked by R9C12 = (789) -> 17(3) <> 1
b) 4 locked in R7C13 @ N7 for R7
c) 9(2): R8C9 <> 5
d) Innies+Outies C89: 1 = R7C7 - R9C8 -> R7C7 <> 1,2; R9C8 <> 3
e) 11(3): R8C8+R9C9 <> 5 since R7C7 <> 2,4
f) Innies C89 = 10(3): R9C8 <> 4 because R8C8+R9C9 <> 5
g) Innies+Outies C89: 1 = R7C7 - R9C8: R7C7 <> 5
h) 17(3) @ R9: R9C67 <> 5 since R9C8 <> 3,4,8,9

3. N89 !
a) ! Hidden Killer pair (89) in R89C6 for N8 since 22(5) cannot have more than one of (89)
b) Innies+Outies N9: 3 = R89C6 - R7C9: R89C6 <= 12 = {28/29/38/39/48} <> 5,6,7
c) 11(2): R8C7 <> 4,5,6
d) 5 locked in R79C8 @ N9 for C8

4. C789
a) 21(3) = 8{49/67} -> 8 locked for C8+N6
b) 14(2) = [68/95]
c) Killer pair (69) locked in R1C8 + 21(3) for C8
d) Innies+Outies C89: 1 = R7C7 - R9C8: R7C7 <> 7
e) 9(2) @ R3C8 <> 1; R4C9 <> 3,4
f) Innies+Outies N6: 6 = R5C6+R7C9 - R4C9 -> R5C6 <> 6 (IOU @ C9)
g) Outies N6 = 15(1+1+1): R5C6 <> 7,8,9 since R3C8+R7C9 >= 9

5. C789 !
a) 17(3) = {269/359/458/467} since R9C8 = (257)
b) 17(3): R9C67 <> 2,7 because R9C8 = (257)
c) ! Outies C89 = 18(2+1) = 3+{69} / 4+{68} / 8+{46} / 9+{36} -> 6 locked for C7+N9
d) 17(4) = {1259/1349/1457/2357}
e) Killer pair (79) locked in 17(4) + 21(3) for N6
f) 9(2) @ N3: R3C8 <> 2
g) 14(3) = {149/167/239/248/257} since 5{18/36} blocked by Killer pairs (56,58) of 14(2)
and {347} blocked by R3C8 = (347)
h) Hidden Killer pair (12) in R123C7 for N3 since 14(3) must have exactly one of (12) -> R123C7 must have exactly one of (12)
i) Innies N9 = 25(4): R8C7 <> 2 since R9C8 <> 6,8,9

6. C789 !
a) ! Hidden Killer pair (12) in R456C7 for C7 since R123C7 can only have one of (12)
b) Killer pair (12) locked in R456C7 + 13(3) for N6
c) ! Consider placement of R4C9 -> 21(3) <> 6
- i) R4C9 = 5 -> R1C9 = 8 -> R1C8 = 6
- ii) R4C9 = 6
d) Hidden Single: R4C9 = 6 @ N6 -> R3C8 = 3, R1C8 = 6 @ N3 -> R1C9 = 8
e) 21(3) = {489} locked for C8+N6
f) 13(3) = 1{39/57} -> 1 locked for C9+N6
g) 9(2) @ N9 <> 1,3
h) Hidden Single: R8C8 = 1 @ N9, R9C3 = 1 @ N7
i) 14(3) = {257} locked for N3; 5 also locked for C9
j) 13(3) = {139} -> R7C9 = 9; 3 locked for C9+N6

7. C789
a) 17(4) = {2357} since R456C7 = (257) -> R5C6 = 3; 7 locked for C7
c) 11(2) = {38} -> R8C6 = 8, R8C7 = 3
d) R8C3 = 2 -> R8C4 = 6, R8C1 = 5 -> R7C2 = 3

8. C123
a) 15(3) = {159} -> R9C2 = 9, R9C4 = 5
b) R8C2 = 7, R9C1 = 8 -> R7C3 = 6, R7C1 = 4
c) Hidden Single: R3C2 = 8 @ C2 -> R4C1 = 2
d) 17(3) = {467} -> 6,7 locked for C1+N4
e) 27(4) = {3789} -> R5C4 = 7; 3,9 locked for C3
f) 36(7) = {1245789} -> R3C3 = 7
g) 21(4) = {3459} -> R1C4 = 3, R3C4 = 9
h) R3C1 = 1, R3C7 = 4

9. Rest is singles.

Rating: Hard 1.5. I used Hidden Killer pairs and a small forcing chain.


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 Post subject: Re: Assassin 149
PostPosted: Thu Apr 09, 2009 6:43 pm 
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Expert
Expert

Joined: Sat Jan 17, 2009 8:30 am
Posts: 118
Location: france
Here is how I have solved V2 :

Assassin V2 Walkthrough


Hidden Text:
1)Innies for c12 : r8c2+r9c1+r9c2 =24 → naked triple {789} locked for n7
a) combinations of cage 8(2) at n7 : {26/35} → no 1 and contains one of (56) (important for step 3) )
b) Combinations of cage 21(3) at n7 : {489/579/678} → r7c3=(456)

2)Innies for r789 : r7c1+r7c9=13 : combinations for the hidden cage 13(2) at r7 : [49/58/67] and r7c1=(456)

3)Killer triple {456} locked for n7 at cage 8(2) and cells r7c13 → r8c3,r9c3=(123)
with 1 locked at r89c3 for n7 and c3

4)Innies and outies for n4 : r5c4+r7c1=9+r4c1
a) r5c4<>9 since r4c1 sees r7c1
b) cage 27(4) at n4 must contain digit 9 → 9 locked for n4 and c3 at r456c3
c) Max r5c4+r7c1=8+6=14 → Max r4c1=14-9=5 : r4c1=(1234) r3c2=(6789)

5)Innies for r9 : r9c1+r9c5+r9c9=13
a) Only one combination for r9c159 with digit 9 : {139}. We deduce the following implication : r9c1=9 → r9c59={13} → r9c3=2 (important for step 6)

The following is the key-step : it will enable to find directly all combinations of
n147

6)Digit 9 is locked for n1 at cage 11(2) or cell r3c2. Forcing chain :
(i) If 9 is locked at cage 11(2), 11(2)={29} so 2 is locked for c3 and n7 at r89c3
(ii) If r3c2=9, r9c1=9 (HS for n7) → r9c3=2 from step 5)a)
a) → 2 is locked for c3 and n7 at r89c3
b) Hidden pair {12} at r89c3 locked for c3 and n7.
c) cage 8(2) at n7 : {35} (last combination)
d) Naked pair : r7c13={46} locked for r7

7)Cell r7c2=(35) blocks combination {235} for cage 10(2) at n4.
a) 1 is locked at cage 10(2) for n4 and c2
b) r4c1<>1, r3c2<>9 → (step 6) 9 is locked for for n1 at cage 11(2). 11(2)={29} locked for n1 and r1
c) Combination of cage 14(2) at n3 : {68} locked for n3 and r1.


8)a) ALS : r1389c2=(26789). We deduce that cage 10(3) at n4 cannot be {127}. Remaining combinations 1{36/45} : no 2
b) Hidden single for c2 : r1c2=2 → r1c1=9
c) Killer pair {35} at cage 10(3) (at n4) and r7c2 , 35 locked for c2
d) Combinations of cage 10(2) at n1 : 1{36/45} with r2c2=(46) (cannot be 135) →
r23c1=(135)
e) Naked triple {135} at r238c1 locked for c1

The puzzle is cracked now ; the rest is quite easy.

9)a) Combinations of cage 17(3) at n4 : {278/467}
b) Cell r9c1=(78) blocks combination {278}→ 17(3) ={467} all locked for c1
c) r4c1=2, r3c2=8
d) r9c1=8, r89c2={79}

10) a) 8 and 9 are locked at cells r456c3 for n4
b) Combinations of cage 27(4) : {3789/4689} : no 5
c) 5 is locked for n4 at cage 10(3) : {145} locked for c2 an n4
d) Naked singles : r2c2=6 r7c2=3
e) Naked pair : r56c1={67}
f) Cage combination : r7c1=4, r23c1={13} locked for n1 and c1, r8c1=5, 27(4) = {3789} with r5c4=7
g) Hidden single for c3 : r7c3=6. Cage combination : r8c2=7, r8c34= [26].
R9c2=9, r9c34=[15]

11) a) Step 2 → r7c9=9. R56c9={13} locked for c9 and n6
b) Step 5 → r9c59=[32]
c) Combinations : cage11(2) at n8 =[83], cage 9(2) at n9 =[54], cage 11(3) at
n9=[812]

12) Combination of cage 20(3) at n6 : {489} ( because {678} is blocked by cell r1c8=(68) ) locked for n6 and c8 → 14(3) at n3=[68], r9c78=[67], r9c6=4 (cage combination).

13) Hidden single for c9 : r4c9=6 → r3c8=3

14) Cage combination : 17(4) at n6 : {2357} with r5c6=3

15) a) Cage combination : no 3 for cage 36(7) at n1 → combination {1245789}
b) Hidden single for n5 : r6c5=6 → r4c5=4
c) Digit 7 at cage 36(7) must be at r3c3 : r3c3=7

16) Naked pair : r12c3={45} → (cage combination) r13c4=[39]

17) Innies for n5 : r1c6 + r3c6= 11 → r13c6=[56]

18) The rest is singles


Cheers


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 Post subject: Re: Assassin 149
PostPosted: Sat Apr 25, 2009 3:23 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
A149 was the third successive Assassin that I went back to after being stuck at the time.

Even then I missed Afmob's first two ! steps, the third one follows from the second one. I also missed the key step 15 in Ed's walkthrough which I'm more annoyed that I missed.

On the basis that I'd rate both Afmob's and Ed's walkthroughs as Hard 1.25, I'll rate my walkthrough at 1.5 to Hard 1.5.

Here is my walkthrough for A149.

Prelims

a) R1C12 = {15/24}
b) R1C89 = {17/26/35}, no 4,8,9
c) R3C2 + R4C1 = {14/23}
d) R3C8 + R4C9 = {49/58/67}, no 1,2,3
e) R46C5 = {59/68}
f) R7C2 + R8C1 = {59/68}
g) R7C8 + R8C9 = {69/78}
h) R8C34 = {16/25/34}, no 7,8,9
i) R8C67 = {29/38/47/56}, no 1
j) 20(3) cage in N1 = {389/479/569/578}, no 1,2
k) 9(3) cage in N3 = {126/135/234}, no 7,8,9
l) R456C2 = {589/679}, 9 locked for C2 and N4, clean-up: no 5 in R8C1
m) R567C9 = {289/379/469/478/568}, no 1
n) 9(3) cage in N7 = {126/135/234}, no 7,8,9
o) 27(4) cage at R1C3 = {3789/4689/5679}, no 1,2

1. 45 rule on N3 4 innies R12C7 + R3C78 = 28 = {4789/5689}, no 1,2,3

2. 45 rule on R789 2 innies R7C19 = 13 = {49/58/67}, no 1,2,3

3. 45 rule on C12 1 outie R7C3 = 1 innie R9C2 + 1, no 1 in R7C3, no 6,7,8 in R9C2

4. 45 rule on C89 1 outie R7C7 = 1 innie R9C8 + 2, no 1,2 in R7C7, no 8,9 in R9C8
4a. 1 in R7 locked in R7C456, locked for N8, clean-up: no 6 in R8C3

5. 45 rule on N9 2 outies R89C6 = 1 innie R7C9 + 8
5a. Min R7C9 = 4 -> min R89C6 = 12, no 2, clean-up: no 9 in R8C7

6. 45 rule on C12 3 innies R8C2 + R9C12 = 8 = {125/134}, no 6, 1 locked for N7, clean-up: no 6 in R8C4

7. 45 rule on C89 3 innies R8C8 + R9C89 = 10 = {127/136/145/235}, no 8,9
[My “killer brain” had been asleep; I really ought to have spotted steps 6 and 7 earlier even though they are less obvious than the innies-outies in steps 3 and 4.]

8. Combined cage R4567C2 = 27,28,30 = {5679/5689/6789}, 6 locked for C2
[Step 11 shows that this step wasn’t needed but I saw it first so I’ll leave it in.]

9. Hidden killer triple 7,8,9 in R7C1, R7C2 + R8C1 and R9C3 for N7 -> R7C1 = {789}, R9C3 = {789}, clean-up: no 7,8,9 in R7C9 (step 2)
9a. Max R7C9 = 6 -> min R56C9 = 13, no 2,3

10. R567C1 = {159/168/249/258/267/348/357} (cannot be {456} because R7C1 only contains 7,8,9)
10a. R7C1 = {789} -> no 7,8 in R56C1

11. Double hidden killer triple 7,8,9 in 20(3) cage in N1, R456C2, R7C1 and R7C2 + R8C1 for C12 -> 20(3) cage in N1 must contain two of 7,8,9 = {389/479/578}, no 6
11a. 6 in N1 locked in R123C3, locked for C3, clean-up: no 5 in R9C2 (step 3)
11b. 6 locked in R123C3, CPE no 6 in R3C4

12. 6 in N7 locked in R7C2 + R8C1 = {68}, locked for N7, clean-up: no 5 in R7C9 (step 2)
12a. Killer pair 6,8 in R456C2 and R7C2, locked for C2

13. 9(3) cage in N7 = {135/234}, 3 locked for N7, clean-up: no 4 in R7C3 (step 3), no 4 in R8C4
13a. R8C2 + R9C12 (step 6) = {125/134}
13b. 2 of {125} must be in R9C2 (R8C2 + R9C1 cannot be {25} which clashes with combinations of 9(3) cage), no 2 in R8C2 + R9C1

14. 45 rule on N4 3 outies R3C2 + R5C4 + R7C1 = 13
14a. Min R7C1 + R3C2 = 8 -> max R5C4 = 5

15. Double hidden killer pair 8,9 in R3C8 + R4C9, R456C8, R56C9 and R7C8 + R8C9 for C89 -> R56C9 and R7C8 + R8C9 can each only contain one of 8,9 -> R3C8 + R4C9 and R456C8 must each contain one of 8,9
15a. R3C8 + R4C9 = {49/58}, no 6,7
15b. Killer pair 8,9 in R456C8 and R56C9, locked for N6, clean-up: no 4,5 in R3C2
15c. Killer pair 4,5 in R4C9 and R567C9, locked for C9, clean-up: no 3 in R1C8
15d. Hidden killer pair 8,9 in R56C9 and R8C9 for C9 -> R8C9 = {89}, clean-up: no 8,9 in R7C8

16. 9(3) cage in N3 = {126/135/234}
16a. 4,5 of {135/234} must be in R2C8 -> no 3 in R2C8
16b. 3 in N3 locked in R123C9, locked for C9

17. 45 rule on N6 3 outies R3C8 + R5C6 + R7C9 = 20
17a. Max R3C8 + R7C9 = 15 -> min R5C6 = 5
17b. Min R3C8 + R7C9 = 12 -> max R5C6 = 8

18. R7C8 + R8C9 = R7C2 + R8C1 + 1 -> R8C9 cannot be 1 more than R8C1
18a. R8C19 = [68/69] (cannot be [89]) -> R8C1 = 6, R7C2 = 8, clean-up: no 5 in R456C2, no 5 in R8C67, no 6 in R9C8 (step 4)
[With hindsight step 23 could have been done after step 17; then there would only be one difficult move in my walkthrough.]

19. Naked triple {679} in R456C2, locked for C2 and N4
19a. 8 in N4 locked in R456C3, locked for C3
19b. 16(4) cage at R4C3 = {1258/1348}, CPE no 1 in R5C1

20. 8 in N1 locked in 20(3) cage = {389/578}, no 4
20a. R2C2 = {35} -> no 3,5 in R23C1

21. Combined cage R8C3467 = 18 = {2349/2358/2457}, 2 locked for R8

22. R9C234 = {179/269/278/467} (cannot be {359/368} because R9C2 only contains 1,2,4, cannot be {458} because R9C3 only contains 7,9), no 3,5
22a. R9C2 = {124} -> no 2,4 in R9C4

23. R567C9 = {469/478/568}
23a. {568} => R7C9 = 6 => R7C8 = 7 => R8C9 = 8 clashes with {568}
23b. -> R567C9 = {469/478}, no 5, 4 locked for C9 -> R4C9 = 5, R3C8 = 8, clean-up: no 9 in R6C5
23c. 9 in N3 locked in R123C7, locked for C7
[Ed’s step 15 was a much simpler way to get this result.
R7C19 (step 2) = 13 = [94] (cannot be [76] which clashes with R7C8).
This could have been done after step 15.]

24. R2C1 = 8 (hidden single in C1)

25. R8C9 = 9 (hidden single in N9), R7C8 = 6, R7C9 = 4, R56C9 = {78} (step 23), locked for C9 and N6, R7C1 = 9 (step 2), R9C3 = 7, R3C1 = 7, R2C2 = 5 (step 11), clean-up: no 1 in R1C12, no 1 in R1C8, no 2 in R1C9, no 7 in R8C6, no 2 in R8C7
25a. R7C1 = 9 -> R56C1 = 6 = [51] (cannot be {24} which clashes with R1C1), clean-up: no 4 in R3C2

26. Naked pair {24} in R1C12, locked for R1 and N1, clean-up: no 6 in R1C9, no 3 in R4C1
26a. 3 in N4 locked in R456C3, locked for C3 and 16(4) cage at R4C3

27. R3C23 = [31] (hidden singles in N1), R4C1 = 2, R1C12 = [42], R9C1 = 3

28. Naked pair {69} in R12C3, locked for 27(4) cage at R1C3
28a. R12C3 = {69} = 15 -> R13C4 = 12 = [75/84]

29. 12(3) cage in N9 = {237} (only remaining combination) -> R9C9 = 2, R7C7 + R8C8 = {37}, locked for N9 -> R8C7 = 8, R8C6 = 3, R8C8 = 7, R7C7 = 3, R1C8 = 5, R1C9 = 3, R23C9 = [16], R2C8 = 2 (step 16), clean-up: no 4 in R8C3
28a. Naked pair {25} in R8C34, locked for R8 -> R8C5 = 4, R89C2 = [14], R7C3 = 5 (step 13), R8C34 = [25], R9C4 = 6 (step 22)
28b. R9C78 = [51] -> R9C6 = 9 (cage sum), R9C5 = 8, clean-up: no 6 in R46C5
28c. R46C5 = [95], R3C45 = [42], R3C6 = 5, R3C7 = 9, R12C7 = [74], R1C4 = 8, R1C6 = 6 (cage sum)

29. R5C4 = 1 (hidden single in N5)

and the rest is naked singles


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 Post subject: Re: Assassin 149
PostPosted: Mon Feb 15, 2010 5:07 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
A149 V2 was the next puzzle that I went back to in my backlog. I see from that I'd found the original A149 hard and hadn't tried V2 until a few days ago.

My solving path is different from both Afmob's and manu's walkthroughs. I was struggling until I found step 24 which used a "clone" although only after the two cells had been simplified. Even though it was a puzzle by manu, the cage pattern didn't look as if it would lead to a "clone" so I hadn't been looking for one.

Rating Comment:
I'll agree with Afmob's rating of Hard 1.5 for A149 V2. I think my hardest steps have the same difficulty level as the hardest steps in Afmob's and manu's walkthroughs.

Here is my walkthrough for A149 V2.

Prelims

a) R1C12 = {29/38/47/56}, no 1
b) R1C89 = {59/68}
c) R3C2 + R4C1 = {19/28/37/46}, no 5
d) R3C8 + R4C9 = {18/27/36/45}, no 9
e) R46C5 = {19/28/37/46}, no 5
f) R7C2 + R8C1 = {17/26/35}, no 4,8,9
g) R7C8 + R8C9 = {18/27/36/45}, no 9
h) R8C34 = {17/26/35}, no 4,8,9
i) R8C67 = {29/38/47/56}, no 1
j) 10(3) cage in N1 = {127/136/145/235}, no 8,9
k) 10(3) cage in N4 = {127/136/145/235}, no 8,9
l) 21(3) cage in N6 = {489/579/678}, no 1,2,3
m) 21(3) cage in N7 = {489/579/678}, no 1,2,3
n) 11(3) cage in N9 = {128/137/146/236/245}, no 9
o) 27(4) cage at R4C3 = {3789/4689/5679}, no 1,2

1. R1C12 = {29/38/47} (cannot be {56} which clashes with R1C89), no 5,6

2. 45 rule on R789 2 innies R7C19 = 13 = {49/58/67}, no 1,2,3

3. 45 rule on C12 1 innie R9C2 = 1 outie R7C3 + 3, R7C3 = {456}, R9C2 = {789}
3a. 21(3) cage in N7 = {489/579/678}
3b. R7C3 = {456} -> no 4,5,6 in R8C2 + R9C1
3c. Naked triple {789} in R8C2 + R9C12, locked for N7, clean-up: no 1 in R7C2 + R8C1, no 4,5,6 in R7C9 (step 2), no 1 in R8C4
[See comment after step 21.]
3d. 1 in N7 only in R89C3, locked for C3
3e. 1 in R1 only in R1C4567, CPE no 1 in R3C6

4. Killer triple 4,5,6 in R7C1, R7C3 and R7C2 + R8C1, locked for N7, clean-up: no 2,3 in R8C4
4a. 4 in N7 only in R7C13, locked for R7, clean-up: no 5 in R8C9

5. 45 rule on C89 1 outie R7C7 = 1 innie R9C8 + 1, no 1 in R7C7, no 3,8,9 in R9C8

6. 15(3) cage at R9C2 = {159/168/249/258/267/348/357} (cannot be {456} because R9C2 only contains 7,8,9)
6a. 4,5,6 only in R9C4 -> R9C4 = {456}

7. 45 rule in R9 3 innies R9C159 = 13 = {139/148/157/238/247} (cannot be {256/346} because R9C1 only contains 7,8,9), no 6
7a. R9C1 = {789} -> no 7,8,9 in R9C59

8. Hidden killer triple 7,8,9 in R9C1, R9C2 and 17(3) cage at R9C6 for R9 -> 17(3) cage at R9C6 must contain one of 7,8,9
8a. 17(3) cage at R9C6 = {269/359/368/458/467} (cannot be {179/278} which contain two of 7,8,9), no 1, clean-up: no 2 in R7C7 (step 5)
[Alternatively 17(3) cage at R9C6 cannot be {179/278} which clash with R9C12, ALS block.]

9. 10(3) cage in N1 and 10(3) cage at R4C2 cannot both be {235} (R456C2 = {235} would clash with R2C2 = {235}) -> at least one of these 10(3) cages must contain 1, CPE no 1 in R3C2, clean-up: no 9 in R4C1
[With hindsight I could have got the elimination in step 9 from simpler steps, either by simplifying the 17(3) cage at R5C1 or by using step 10, but I’ve kept step 9 as an interesting step.]
9a. 1 in N1 only in 10(3) cage = {127/136/145}
9b. 45 rule on N1 4 innies R12C3 + R3C23 = 24 = {2589/2679/3678/4569/4578} (cannot be {3489/3579} which clash with R1C12)
[I originally used a hidden killer triple in N1, 4 innies must contain one of 2,3,4, but found that wasn’t necessary.]

10. 45 rule on N4 3(1+1+1) outies R3C2 + R5C4 + R7C1 = 19
10a. Max R7C1 = 6 -> min R3C2 + R5C4 = 13, no 2,3 in R3C2, no 3 in R5C4, clean-up: no 7,8 in R4C1

11. 45 rule on N4 2(1+1) outies R5C4 + R7C1 = 1 innie R4C1 + 9, IOU no 9 in R5C4
11a. 9 in 27(4) cage at R4C3 only in R456C3, locked for C3 and N4
11b. Max R5C4 + R7C1 = 14 -> no 6 in R4C1, clean-up: no 4 in R3C2

12. 17(3) cage at R5C1 = {368/458/467} (cannot be {278} because R7C1 only contains 4,5,6), no 1,2
12a. Min R7C9 = 7 -> max R56C9 = 6, no 6,7,8,9 in R56C9

13. 45 rule on N6 2(1+1) outies R5C6 + R7C9 = 1 innie R4C9 + 6, IOU no 6 in R5C6
13a. Min R5C6 + R7C9 = 8 -> min R4C9 = 2, clean-up: no 8 in R3C8
13b. Max R4C9 = 8 -> max R5C6 + R7C9 = 14 -> max R5C6 = 7

14. R12C3 + R3C23 (step 9b) = {2589/2679/3678/4578} (cannot be {4569} which clashes with R7C3)
14a. 10(3) cage in N1 (step 9a) = {136/145} (cannot be {127} which clashes with R12C3 + R3C23), no 2,7

15. Hidden killer triple 7,8,9 in R1C1, 17(3) cage at R5C1 and R9C1 for C1, 17(3) cage at R5C1 contains one of 7,8, R9C1 = {789} -> R1C1 = {789}, clean-up: no 7,8,9 in R1C2

16. 11(3) cage in N9 = {128/137/146/236/245}
16a. 5 of {245} must be in R7C7 -> no 5 in R8C8 + R9C9
16b. 8 of {128} must be in R7C7 -> no 8 in R8C8

17. 2 in C1 only in R48C1 -> no 7 in 10(3) cage at R4C2
17a. R4C1 = 2 => R3C2 = 8 => naked triple {789} in R389C2, locked for C2
R8C1 = 2 => R7C2 = 6 => naked quad {6789} in R3C789C2, locked for C2
[I got the idea for this step having just completed Human Solvable 7.]
17b. -> 10(3) cage at R4C2 = {136/145/235}
17c. Hidden killer pair 1,2 in R4C1 and 10(3) cage at R4C2 for N4 -> R4C1 = {12}, clean-up: R3C2 = {89}
17d. 7 in C2 only in R89C2, locked for N7

18. R5C4 + R7C1 = R4C1 + 9 (step 11)
18a. Max R4C1 = 2 -> max R5C4 + R7C1 = 11, max R5C4 = 7

19. R9C159 (step 7) = {139/148/238}, no 5
19a. 15(3) cage at R9C2 (step 6) = {159/258/267/357} (cannot be {168/249/348} which clash with R9C159), no 4

20. 45 rule on N47 3 outies R589C4 = 1 innie R4C1 + 16
20a. R4C1 = {12} -> R589C4 = 17,18 = {467/567}, 6,7 locked for C4

21. R7C7 + R8C8 + R9C9 = 11, R7C7 = R9C8 + 1 (step 5) -> R8C8 + R9C89 = 10 = {127/136/145/235}
21a. 5,6 of {136/145} must be in R9C8 -> no 6 in R8C8, no 4 in R9C8, clean-up: no 5 in R7C7 (step 5)
[It was only when I looked at my posted A149 walkthrough, after I’d finished this puzzle without looking at that earlier walkthrough, that I realised that step 21 was actually 45 rule on C89 3 innies R8C8 + R9C89 = 10. The same applies for step 3c which is more directly 45 rule on C12 3 innies R8C2 + R9C12 = 24. :oops: I also missed these innies when I solved A149.]

22. 17(3) cage at R9C6 (step 8a) = {269/359/458/467} (cannot be {368} which clashes with R9C159)
22a. 5 of {359/458} must be in R9C8 -> no 5 in R9C67

23. 1 in N8 only in 22(5) cage = {12379/12469/12478/13459/13468} (cannot be {12568/13567} which clash with R9C4)
23a. Killer triple 5,6,7 in 22(5) cage, R8C4 and R9C4, locked for N8, clean-up: no 4,5,6 in R8C7

24. R3C2 + R89C2 = {89} + {789}, R89C2 + R9C1 = {789} + {89} -> R3C2 = R9C1
[That had been there since step 17c but I’ve only just spotted how to use it.]
24a. R4C1 + R3C2 = [19/28] -> R49C1 = [19/28] = 10
24b. 45 rule on C1 4 remaining innies R1238C1 = 18 = {1359/2367/2457} (cannot be {1269/1278} which clash with R4C1, cannot be {1368/1458/2349} which clash with R49C1, cannot be {1467/3456} which clash with 17(3) cage at R5C1, cannot be {2358} which clashes with combinations for 10(3) cage in N1), no 8, clean-up: no 3 in R1C2
24c. 2 of {2367} must be in R8C1 -> no 6 in R8C1, clean-up: no 2 in R7C2
24d. R23C1 = {13/15/36/45} -> R2C2 = {146}

25. 6 in N7 only in R7C123, locked for R7, clean-up: no 3 in R8C9
[While checking I found that I’d missed a couple of clean-ups for R9C8 and later missed a placement for R9C8 after fixing R7C7. I’ve left them out rather than re-working later steps.]

26. 11(3) cage in N9 = {128/137}, no 4, 1 locked for N9, clean-up: no 8 in R7C8 + R8C9
26a. R7C8 + R8C9 = [36/54] (cannot be {27} which clashes with 11(3) cage), no 2,7

27. Naked quad {3456} in R7C1238, locked for R7
27a. 11(3) cage in N9 (step 26) = {128/137}
27b. R7C7 = {78} -> no 7 in R8C8
27c. 1,2 in R7 only in R7C456, locked for N8, clean-up: no 9 in R8C7

28. R9C159 (step 19) = {139/148/238}
28a. 1,2 only in R9C9 -> R9C9 = {12}

29. 13(3) cage at R5C9 = {139/148/157/238/247} (cannot be {256/346} because R7C9 only contains 7,8,9), no 6
29a. Killer pair 1,2 in R56C9 and R9C9, locked for C9, clean-up: no 7 in R3C8

30. 9 in N9 only in R7C9 + R9C7
30a. 45 rule on N9 4 innies R7C9 + R8C7 + R9C78 = 25 = {2689/3679/4579} (cannot be {3589} which clashes with R7C8)
30b. 45 rule on N9 2 innies R7C9 + R8C7 = 1 outie R9C6 + 8
30c. R9C6 = {3489} -> R7C9 + R8C7 = 11,12,16,17 = [92/93/97/98] (cannot be [83] which clashes with the 11(3) cage) -> R7C9 = 9, R7C1 = 4 (step 2), clean-up: no 5 in R1C8
[I originally did this step using interactions between the combinations for R7C9 + R8C7 + R9C78 and the permutations for R9C78 in 17(3) cage at R9C6. Then I realised that using the second 45 rule on N9 was much simpler.]

31. R7C9 = 9 -> R56C9 (step 29) = {13}, locked for C9 and N6 -> R9C9 = 2, clean-up: no 6 in R3C8, no 9 in R8C6
31a. R8C8 = 1 (hidden single in N9), R7C7 = 8 (step 26), clean-up: no 8 in R4C9, no 7 in R8C4, no 3 in R8C6
31b. R9C3 = 1 (hidden single in N7)

32. 21(3) cage in N7 = {579/678} -> R8C2 = 7, R8C7 = 3, R8C6 = 8, R7C8 = 5, R8C3 = 2, R8C1 = 5, R8C4 = 6, R8C9 = 4, R8C5 = 9, R7C3 = 6, R9C1 = 8, R7C2 = 3, R9C24 = [95], R3C2 = 8, R4C1 = 2, clean-up: no 1 in R4C5, no 1,8 in R6C5

33. R7C1 = 4 -> R56C1 = 13 = {67} (only remaining combination), locked for C1 and N4 -> R1C1 = 9, R1C2 = 2, clean-up: no 5 in R1C9
33a. Naked triple {145} in R456C2, locked for C2 and N4 -> R2C2 = 6
33b. Naked triple {389} in R456C3, locked for C3, R5C4 = 7 (cage sum), R56C1 = [67], clean-up: no 3 in R46C5
33c. Naked triple {457} in R123C3, CPE no 4 in R3C4

34. R9C78 = {67} = 13 -> R9C6 = 4, R9C5 = 3

35. Naked pair {68} in R1C89, locked for R1 and N3
35a. Naked pair {57} in R23C9, locked for C9 and N3 -> R4C9 = 6, R3C8 = 3, R23C1 = [31], R1C89 = [68], R9C78 = [67], clean-up: no 4 in R6C5

36. Naked triple {489} in R456C8, locked for C8 and N6 -> R2C8 = 2

37. Naked pair {25} in R56C7, locked for C7 and 17(4) cage at R4C7 -> R4C7 = 7, R5C6 = 3 (cage sum), R56C9 = [13]
37a. R4C3 = 3 (hidden single in N4)

38. 36(7) cage at R3C3 = {1245789} -> R3C3 = 7, R23C9 = [75]

39. R6C5 = 6 (hidden single in N5), R4C5 = 4, R3C5 = 2, R3C4 = 9, R3C6 = 6, R3C7 = 4, R12C7 = [19], R1C6 = 5 (cage sum)

and the rest is naked singles.


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