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 Post subject: Assassin 298
PostPosted: Sat Aug 02, 2014 5:26 am 
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Grand Master
Grand Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
This has a score in SS of 'only' 1.30 - but I found it tougher than that. I feel like I missed something... I'll have another go and see what I can see.

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3x3::k:2566:4360:4360:4360:5914:5914:4882:4882:4882:2566:4360:5636:5636:5636:5914:2075:5392:5392:9217:9217:9217:5636:8963:8963:2075:1813:5392:2831:2831:9217:5636:8963:2324:2324:1813:5392:2831:3607:9217:9217:8963:6914:6914:1813:4366:5649:3607:2070:2070:8963:6405:6914:4366:4366:5649:3607:3096:8963:8963:6405:6914:6914:6914:5649:5649:3096:4121:6405:6405:6405:6921:1543:3347:3347:3347:4121:4121:6921:6921:6921:1543:


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 Post subject: Re: Assassin 298
PostPosted: Sat Aug 02, 2014 3:16 pm 
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Grand Master
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for this week's Assassin, wellbeback! It took me quite some time to solve it though the moves weren't particular difficult.
A298 Walkthrough:
1. R123
a) Outies R1 = 24(3) = {789} locked for R2; 7 also locked for N1
b) 23(3) = {689} locked for N2; 6 also locked for R1
c) 19(3) = 7{39/48} since {289} blocked by R1C56 = (689) -> 7 locked for R1+N3
d) 10(2) = [19/28/37]
e) 5 locked in 17(4) @ R1 = 5{129/138/147/237}; R1C23 <> 8,9 since R2C2 = (789)
f) 8(2) <> 1
g) 7(3) = {124} locked for C8
h) Outies N3 = 10(3) = 1{27/45} since R45C8 = (124) -> R4C9 = (57); 1 locked for C8+N6
i) 1 locked in 21(4) @ N3 = 15{69/78} since R2C8+R4C9 = (3567); R3C9 = (89); R2C9 = 1

2. C789 !
a) 6(2) = {24} locked for C9+N9
b) 17(3) = 3{59/68} -> 3 locked for N6
c) Innies N36 = 18(3) = {279/459/468} since {567} blocked by R4C9 = (57)
d) ! Using Innies N36: 1 locked in Innies C7 @ C7 = 19(4) = 18{37/46} -> 8 locked for C7 since 16{39/57} blocked by Killer pairs (36,56) of 8(2) and {1459} blocked by Killer pair (49) of Innies N36
e) 8 locked in 17(3) @ N6 = {368} locked for N6
f) 9 locked in 27(6) @ N6 = 129{348/357/456} for 27(6)
g) 9(2) = {27/45}
h) Killer pair (57) locked in 9(2) + R4C9 for R4

3. R456+N1
a) 36(6) = 789{156/246/345} -> 7 locked for R5
b) 11(3) <> 5 because {24}5 blocked by Killer pair (24) of 9(2)
c) Hidden Killer pair (89) in 36(6) @ N1 since R2C12 must have 7
d) Innies N47 = 18(3) <> 1 because {189} blocked by Killer pair (89) in R3C123
e) Innies N47 = 18(3) <> 4,8 because (378,459) are Killer triples of 12(2) and {468} blocked by Killer pair (68) of 11(3)

4. R456 !
a) ! Hidden Killer pair (48) in each of Outies N7 and 11(3) for N4 since they can only have one of them -> 11(3) = 1{28/46} -> 1 locked for N4
b) Outies N7 = 16(3) = {349/358/457} <> 2,6 since {268} blocked by Killer pair (68) of 11(3) and other combos eliminated by step 4a
c) 1 locked in R6C456 @ R6 for N5
d) 27(6) = 129{348/357/456} -> R7C7 = 1

5. R123+N4 !
a) ! R45C3 <> 6 since it sees all 6 of N1
b) Innies N47 = 18(3) = 9{27/36} -> 9 locked for C3+N4+36(6) since R4C3 = (239)
c) Hidden Single: R3C9 = 9 @ R3
d) 21(4) = {1569} -> R4C9 = 5, R2C8 = 6
e) 19(3) = {478} -> R1C7 = 4; 8 locked for R1
f) 6 locked in 36(6) @ R3 = 6789{15/24} for 36(6)

6. N4679
a) Innies N47 = 18(3) = {279} locked for C3+N4 since R45C3 <> 3,6
b) 11(3) = {146} locked for N4
c) 14(3) = {356} -> R7C2 = 6; 3,5 locked for C2+N4
d) R6C1 = 8, R6C8 = 3, R6C9 = 6, R5C9 = 8, R1C9 = 7, R1C8 = 8
e) 8(2) = [71] -> R6C3 = 7, R6C4 = 1
f) 27(6) = {123579} since R7C9 = 3 -> R7C9 = 3, R7C8 = 7, R5C6 = 5; 2 locked for C7+N6
g) 27(4) = {5679} since R89C8 = (59) -> R9C7 = 6; R9C6 = 7
h) 12(2) = {48} locked for C3+N7
i) 13(3) = {139}

7. Rest is singles.

Rating:
1.25 - Hard 1.25. I used some Hidden Killer pairs and Killer triples.


Last edited by Afmob on Sun Aug 10, 2014 5:55 am, edited 2 times in total.

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 Post subject: Re: Assassin 298
PostPosted: Wed Aug 06, 2014 4:18 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks wellbeback for an interesting and challenging Assassin. I didn't realise this puzzle had been posted until after Afmob had solved it (maybe I should visit this site more than once per day? ;) ), then it took me a while to find the breakthrough but while checking my walkthrough I found a flawed step so had to re-work from there and, surprisingly, found an easier way to finish it.

In the Assassin 297 thread, Ed wrote Interesting that Andrew considers Locking-out cages as very routine. They feel that way to me too:
I used a couple of them for this puzzle, also an interesting CCC/IOU.

Here is my walkthrough for Assassin 298:
Prelims

a) R12C1 = {19/28/37/46}, no 5
b) R23C7 = {17/26/35}, no 4,8,9
c) R4C67 = {18/27/36/45}, no 9
d) R6C34 = {17/26/35}, no 4,8,9
e) R78C3 = {39/48/57}, no 1,2,6
f) R89C9 = {15/24}
g) 23(3) cage at R1C5 = {689}
h) 19(3) cage at R1C7 = {289/379/469/478/568}, no 1
i) 7(3) cage at R3C8 = {124}
j) 11(3) cage at R4C1 = {128/137/146/236/245}, no 9
k) 27(4) cage at R8C8 = {3789/4689/5679}, no 1,2

Steps resulting from Prelims
1a. Naked triple {689} in 23(3) cage at R1C5, locked for N2
1b. Naked triple {124} in 7(3) cage at R3C8, locked for C8

2. 19(3) cage at R1C7 = {379/478} (cannot be {289/469/568} which clash with 23(3) cage at R1C5, ALS block), no 2,5,6, 7 locked for R1 and N3, clean-up: no 3 in R2C1, no 1 in R23C7
2a. Killer triple 6,8,9 in 23(3) cage at R1C5 and 19(3) cage, locked for R1, clean-up: no 1,2,4 in R2C1
2b. 6 in R1 only in R1C56, locked for N2

3. 45 rule on N3 3 outies R4C89 + R5C8 = 10 = {127/145} (cannot be {136/235} because 3,5,6 only in R4C9) -> R4C9 = {57}, 1 in R45C8, locked for C8 and N6, clean-up: no 8 in R4C6

4. 45 rule on R1 3 outies R2C126 = 24 = {789}, locked for R2, 7 also locked for N1, clean-up: no 4 in R1C1

5. Hidden killer pair 8,9 in 19(3) cage at R1C7 and R3C9 for N3, 19(3) cage contains one of 8,9 -> R3C9 = {89}
5a. R2C9 = 1 (hidden single in N3), clean-up: no 5 in R89C9
5b. Naked pair {24} in R89C9, locked for C9 and N9
5c. Hidden killer pair 5,6 in R23C7 and R2C8 for N3, R23C7 contains one of 5,6 -> R2C8 = {56}

6. 17(3) cage at R5C9 = {359/368}, no 7, 3 locked for N6, clean-up: no 6 in R4C6

7. 5 in R1 only in 17(4) cage at R1C2 = {1259/1358/1457/2357}
7a. 7 in N1 only in R12C1 = [37] or in 17(4) cage = {1457/2357} -> 17(4) cage = {1259/1457/2357} (cannot be {1358}, locking-out cages), no 8 in R2C2

8. 45 rule on N7 1 outie R6C1 = 1 innie R7C2 + 2, no 1,2 in R6C1, no 8,9 in R7C2

9. 45 rule on N47 3 innies R456C3 = 18 = {189/279/369/468/567} (cannot be {378/459} which clash with R78C3)
9a. 1 of {189} must be in R6C3 -> no 1 in R45C3

10. 4 in R2 only in R2C345, locked for 22(5) cage at R2C3, no 4 in R34C4
10a. 22(5) cage = {12469/13459/13468/23458/23467} (cannot be {12478} because 1,7,8 only in R34C4)
10b. 8,9 of {12469/13459/13468/23458} must be in R4C4 -> no 1,5 in R4C4

11. 45 rule on R9 3 outies R8C489 = 17 = {269/278/458/467} (cannot be {179/359/368} because R8C9 only contains 2,4), no 1,3
11a. R8C9 = {24} -> no 2,4 in R8C4

12. 36(6) cage at R3C1 must contain 7 in R45C3 + R5C4, CPE no 7 in R5C12
12a. Hidden killer pair 8,9 in R3C123 and R3C9 for R3, R3C9 = {89} -> R3C123 must contain one of 8,9
12b. R456C3 (step 9) = {279/369/468/567} (cannot be {189} because R45C3 cannot contain both of 8,9 since one of 8,9 must be in R3C123), no 1, clean-up: no 7 in R6C4
[I originally saw this elimination as R456C3 (step 9) = {279/369/468/567} (cannot be {189} because R6C34 = [17] clashes with the only remaining position for 7 in the 36(6) cage, killer combo clash), no 1, clean-up: no 7 in R6C4]
12c. 11(3) cage at R4C1 = {128/137/146/245} (cannot be {236} which clashes with R456C3)

13. 45 rule on C1234 2 outies R29C5 = 1 innie R7C4 + 1
13a. Max R29C5 = 10, no 9 in R9C5

14. 45 rule on N36 3 innies R456C7 = 18 = {279/459/468} (cannot be {567} which clashes with R4C9)
14a. 2 in C7 only in R23C7 = {26} or in R456C7 = {279} -> R456C7 = {279/459} (cannot be {468}, locking-out cages), no 6,8 in R456C7, 9 locked for C7 and N6, clean-up: no 1,3 in R4C6
14b. Killer pair 5,7 in R456C7 and R4C9, locked for N6

15. Killer pair 5,7 in R4C67 and R4C9, locked for R4
15a. 11(3) cage at R4C1 (step 12c) = {128/146} (cannot be {245} which clashes with R4C67), no 3,5, 1 locked for N4
15b. R456C3 (step 12b) = {279/369/567} (cannot be {468} which clashes with 11(3) cage), no 4,8
15c. Killer pair 2,6 in 11(3) cage and R456C3, locked for N4, clean-up: no 4 in R7C2 (step 8)

16. 45 rule on R12 4 remaining innies R2C3458 = 1 outie R3C7 + 12, IOU R2C345 cannot total 12
[I originally saw this are 45 rule on R12 5 remaining innies R2C34578 = 20
R2C78 cannot total 8, which would clash with R23C7 (CCC) -> R2C345 cannot total 12
Where there’s a CCC there’s usually an IOU, and vice versa.]
16a. 22(5) cage at R2C3 (step 10a) = {13468/23458/23467} (cannot be {12469/13459} because R2C345 = {246/345} would total 12), no 9 in R4C4
16b. 8 of {13468/23458} must be in R4C4, 3 of {23467} must be in R2C345 (R2C345 cannot be {246} which totals 12) -> no 3 in R4C4
16c. 1,7 of {13468/23467} must be in R3C4, 2 of {23458} must be in R2C345 (R2C345 cannot be {345} which totals 12) -> no 2 in R3C4
[This CCC/IOU seems to crack the puzzle; the rest is a lot easier with step 20b giving the final breakthrough.]

17. R4C35 = {39} (hidden pair in R4)
17a. Naked pair {39} in R4C35, CPE no 3,9 in R5C4
17b. R456C3 (step 15b) = {279/369} (cannot be {567} because R4C3 only contains 3,9), no 5, 9 locked for C3, N4 and 36(6) cage at R3C1, clean-up: no 3 in R6C4, no 7 in R7C2 (step 8), no 3 in R78C3
17c. 36(6) cage at R3C1 must contain 7 in R5C34, locked for R5

18. R3C9 = 9 (hidden single in R3)
18a. 19(3) cage at R1C7 (step 2) = {478} (only remaining combination) -> R1C7 = 4, R1C89 = {78}, locked for R1, R3C8 = 2, clean-up: no 6 in R23C7
18b. Naked pair {35} in R23C7, locked for C7 and N3 -> R2C8 = 6
18c. Naked triple {279} in R456C7, locked for C7 and N6 -> R4C9 = 5
18d. Naked triple {168} in R789C7, locked for N9
18e. 7 in R4 only in R4C67 = {27}, locked for R4

19. 6,8 in R3 only in R3C123, locked for N1 and 36(6) cage at R3C1, no 6,8 in R5C34, clean-up: no 2 in R1C1

20. 9 in C7 only in R56C7, locked for 27(6) cage at R5C6, no 9 in R5C6 + R7C8
20a. 27(6) cage contains 1,9 = {123489/123579/124569}
20b. Caged X-Wing for 2 in 27(6) cage and R4C67, no other 2 in C6 and N5, clean-up: no 6 in R6C3

21. R456C3 (step 17b) = {279} (only remaining combination) -> R4C3 = 9, R56C3 = {27}, locked for C3 and N4, clean-up: no 5 in R6C4, no 5 in R7C2 (step 8), no 5 in R78C3
21a. Naked pair {48} in R78C3, locked for C3 and N7
21b. 11(3) cage at R4C1 (step 15a) = {146} (only remaining combination), locked for N4, clean-up: no 2 in R7C2 (step 8)

22. 14(3) cage at R5C2 = {158/356}, 5 locked for C2 and N4
22a. 1,6 only in R7C2 -> R7C2 = {16}

23. Naked pair {38} in R6C18, locked for R6 -> R6C2 = 5, R6C9 = 6, R6C4 = 1 -> R6C3 = 7, R5C3 = 2, R56C7 = [92], R4C67 = [27]

24. R4C4 = 8 (hidden single in R4) -> 22(5) cage at R2C3 (step 16a) = {23458} (only remaining combination) -> R2C45 = {24}, locked for N2
24a. Naked pair {35} in R13C4, locked for C4 and N2

25. R3C12 = {48} (hidden pair in R3), locked for 36(6) cage at R3C1 -> R5C4 = 7

26. R5C56 = {56} (hidden pair in N5), locked for R5

27. 27(6) cage at R5C6 (step 20a) = {123579} (only remaining combination) -> R5C6 = 5, R7C7 = 1, R7C89 = {37}, locked for R7 and N9
27a. R7C2 = 6, R5C2 = 3 (cage sum), R6C1 = 8, R3C1 = 4, R5C1 = 1, R1C1 = 3 -> R2C1 = 7, R2C2 = 9

28. R9C3 = 3 (hidden single in C3) -> R9C12 = 10 = [91]

and the rest is naked singles.

Rating Comment:
Although none of my steps are technically harder than Easy 1.5, I'll rate my walkthrough for A298 at 1.5 because I found it difficult to find the breakthrough steps.


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 Post subject: Re: Assassin 298
PostPosted: Mon Aug 11, 2014 2:58 am 
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Grand Master
Grand Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Well done and thanks guys. I haven't got anything better. I wished I had found your moves (Afmob 3e) (Andrew 15b). Would have helped me enormously!
I kept looking for some clever move around innies and outies and placements on column 5 - but failed.


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