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Afmob
Expert

Joined: 22 Sep 2007
Posts: 103
Location: MV, Germany

 Posted: Fri Feb 01, 2008 5:17 pm    Post subject: Assassin 88 This assassin had a lot of Killer pairs/triples you could use to solve it. And it's quite stubborn in the end game (my first version was about 30% longer) but if you manage to find the right moves it can be solved in a not too long way. Edit: Andrew found an elimination in my wt which couldn't be applied at this stage. I fixed this mistake and changed the walkthrough from step 6 on. A88 Walkthrough: 1. R6789 a) Innies R89 = 11(3) <> 9; R8C58 <> 5,6,7,8 because R8C2 = (68) b) 23(3) = {689} locked N7, 9 locked for R7 c) Innies R789 = 12(4) = 12{36/45} -> 1,2 locked for R7 d) 9(2): R7C5 <> 3,4 e) Innies+Outies N7: 7 = R8C4 - R7C1 -> R7C1 = (12), R8C4 = (89) f) Killer pair (12) locked in R7C1 + 5(2) for C1+N7 g) Innies+Outies N9: 2 = R8C6 - R7C9 -> R8C6 <> 1,2,9 h) Innies+Outies : -2 = R5C19 - R6C5 -> R5C19 <> 7,8,9; -> R6C5 = (6789) and R5C9 <> 5,6 since R5C1 >= 3 2. C123 ! a) 29(4) = {5789} locked between C1+N4 -> R56C1 <> 5,7,8,9 b) R56C1 = 6{3/4} because {34} blocked by Killer pair (34) of 5(2) -> 6 locked for C1+N4 -> 6 locked in 15(4) = 36{15/24} -> 3 locked for N4 c) 15(4) must have 1 xor 2 and R7C1 = (12) -> R6C2 <> 1,2 d) ! 15(4): R6C2 <> 3 because R567C1 = {246} blocked by Killer pair (24) of 5(2) e) 3 locked in 15(4) for C1 f) 5(2) = {14} locked for C1+N7 g) 24(4) = {3579} -> R8C4 = 9 h) 15(4) = {2346} -> R6C2 = 4, R7C1 = 2 3. C123 a) 12(2) <> 5,7 since it's blocked by R89C3 = (357) b) 12(2): R3C3 <> 8,9 c) Innies C12 = 24(4) <> 1 because R9C2 = (357) d) 1 locked in R56C3 for C3 e) 10(3): R2C4 <> 4,6,7 because R12C3 <> 1 f) 10(3): R2C4 <> 2 because {35}2 blocked by R89C3 = (357) 4. R1234 a) Innies N2 = 10(2) = [19/37] b) Outies N1 = 23(3+1) and R2C4 = (13) -> R4C123 = 20/22(3) = 58{7/9} -> 5,8 locked for R4+N4; c) 5 locked in R4C12 @ 29(4) -> R23C1 <> 5 d) Innies = 9(3) = 2{16/34} -> 2 locked R4+N5 e) 9(2): R3C7 <> 1,4,7 5. C123 ! a) Killer triple (789) locked in 17(4) + R23C1 for N1 b) Innies C12 = 24(4): R5C2 <> 9 since R789C3 >= 17 c) 10(3) = {36/45}1 / {25}3 -> R12C3 must have 1 of (35) d) ! Killer triple {357} locked in R12C3+R89C3 for C3 e) 12(2) = {48} -> R3C3 = 4, R4C3 = 8 f) 29(4) = {5789} -> 8 locked for N1 g) 17(4) @ N5: R45C4 <> 2,7 because R5C3 <> 3,5 h) ! 2 locked in Innies C1234 = 16(3) = {268} locked for C4 6. N5+R56 a) Hidden Single: R6C4 = 7 @ C4 b) 12(3) = 7{14/23}; R7C4 <> 1 c) Hidden Single: R5C4 = 5 @ C5 e) 14(3) @ R4C5 = {149/239/248} f) Innies+Outies R6789: -2 = R5C19 - R6C5 -> R6C5 <> 8 because R5C1 = (36) -> R6C5 = 9; R5C19 = [34/61] g) 14(3) @ C5 = 9{14/23}; R4C5 <> 3 h) 25(4) = 68{29/47} because 79{18/36} blocked by Killer pair (79) of 17(4) 7. N5 a) Innies R1234 = 9(3): R4C4 <> 4 because 3 only possible there b) 17(4) = 25{19/37} -> 2 locked for R5+N4 c) 12(3) = {147} -> R6C3 = 1, R7C4 = 4 d) 14(3) @ R6C6 = 5{18/36} e) 14(3) @ R6C6: R7C6 <> 5 because R6C67 <> 1 and R6C1 = (36) blocks {36}5 8. R789 a) Innies = 12(4) = {1245} -> R7C9 = 5, R7C6 = 1 b) 14(2) = {68} locked for C9+N9 c) 12(3) = {237} -> R8C8 = 2; {37} locked for R7+N9 d) 9(2) = {36} -> R7C5 = 6, R8C5 = 3 e) 14(3) = {158} -> R6C6 = 8, R6C7 = 5 f) 15(3) = {258} locked for R9+N8 g) R8C6 = 7, R2C6 = 9 9. N36 a) 14(4) = 25{16/34} -> R6C9 = 2 b) 19(4) = {1369} -> R4C8 = 6; {139} locked for C9 c) R5C9 = 4, R6C8 = 3, R1C9 = 7 d) 19(3) = 9{28/46} e) 9(2) = [27/81] f) 6 locked in 19(3) = {469} -> 4 locked for C7+N3 10. N2 a) 17(3) = 8{36/45} -> 8 locked for R1+N2 11. Rest is singles. Rating: 1.25. I used some Killer triples.Last edited by Afmob on Tue Feb 05, 2008 11:49 am; edited 2 times in total
gary w

Joined: 07 Sep 2007
Posts: 84
Location: south wales

 Posted: Sun Feb 03, 2008 12:28 am    Post subject: I found this one rather harder than most recent assassins..at least it took me longer to do,about 3 hours or so.Having said that I didn't use any advanced moves mainly a lot of combo work c1 is where I made first placements given the restrictions imposed by the 29(4) cage..this also -> r4c8 combo work then shows that r5c2=2/7 and r5c23+r6c3={127} innies on r789=12(4)..very useful innies-outies c89 also used combo work on n456 then solved it but quite long-winded..couldn't really find a "neat" move for this one!! Regards Gary
Andrew
Grandmaster

Joined: 11 Aug 2006
Posts: 300
Location: Lethbridge, Alberta

Posted: Mon Feb 04, 2008 7:31 am    Post subject:

 Ruud wrote: This Assassin will give you a busy week ... or at least the weekend.

 Gary wrote: I found this one rather harder than most recent assassins..at least it took me longer to do,about 3 hours or so.Having said that I didn't use any advanced moves mainly a lot of combo work

It took me until the end of the weekend, working on and off, to solve A88.

Like Gary I had to do a lot of combo work. After the early steps, I initially found it hard to see which combos to work on but it eventually started to flow. Gary must be a quicker solver than I am; it took me much longer than 3 hours.

I guess I'll still rate A88 as 1.25 but definitely one of the hardest of that rating for me.

In Afmob's walkthrough, as well as the steps that were highlighted by !s, I think steps 5g and 5h were also key ones that removed the need for a lot of combo work. Step 5g looked difficult to spot but maybe that's because I work with an Excel spreadsheet and my only helper is Ruud's combination calculator. Looking again at my walkthrough, I did have the equivalent of step 5g in my step 21 but missed Afmob's step 5h which I think would have made my solving path a lot easier and shorter (this note has been edited to be consistent with changes in Afmob's walkthrough).

Here is my walkthrough, thanks Afmob for corrections to typos. I've also done some of my own tidying up, mainly taking account of eliminations that I missed when I was finishing my original solution late last night.

Prelims

a) R34C3 = {39/48/57}, no 1,2,6
b) R34C7 = {18/27/36/45}, no 9
c) R78C5 = {18/27/36/45}, no 9
d) R89C1 = {14/23}
e) R89C9 = {59/68}
f) 10(3) cage at R1C3 = {127/136/145/235}, no 8,9
g) 19(3) cage at R1C7 = {289/379/469/478/568}, no 1
h) 23(3) cage in N7 = {689}, locked for N7
i) 29(4) cage at R2C1 = {5789}, CPE no 5,7,8,9 in R56C1
j) 14(4) cage at R5C9 = {1238/1247/1256/1346/2345}, no 9

1. 45 rule on N7 1 outie R8C4 = 1 innie R7C1 + 7 -> R7C1 = {12}, R8C4 = {89}

2. Killer pair 1,2 in R7C1 and R89C1, locked for C1 and N7

3. R56C1 = {36/46} (cannot be {34} which clashes with R89C1), 6 locked for C1 and N4
3a. Killer pair 3,4 in R56C1 and R89C1, locked for C1
3b. 15(4) cage at R5C1 = {2346} (only remaining combination, cannot be {1356} because R567C1 = {36}1 clashes with R89C1), R7C1 = 2, R8C4 = 9 (step 1), 3,4 locked for N4, clean-up: no 8,9 in R3C3, no 7 in R8C5, no 3 in R89C1, no 5 in R9C9
[Alternatively 45 rule on C1 2 outies R46C2 = 1 outie R1C1, R1C1 must equal R4C4 -> R6C2 = 4 …]
3c. Naked pair {14} in R89C1, locked for C1 and N7
3d. R6C2 = 4 (hidden single in N4)
3e. 9 in N7 locked in R7C23, locked for R7
3f. R34C3 = [39/48] (cannot be {57} which clashes with R89C3)

At this stage there appears, at first sight, to be a CPE because R1234C1 and R4C2 are all {5789}. However R1C1 must equal R4C2 so there is no CPE.

4. 45 rule on N9 1 outie R8C6 = 1 innie R7C9 + 2, no 1,2,4 in R8C6, no 7,8 in R7C9

5. 45 rule on R89 3 innies R8C258 = 11 = {128/236} (cannot be {137/245} because R8C2 only contains 6,8, cannot be {146} which clashes with R8C1), no 4,5,7, 2 locked for R8, clean-up: no 4,5 in R7C5
5a. 6,8 must be in R8C2 -> no 6,8 in R8C58, clean-up: no 1,3 in R7C5

6. 45 rule on R789 3 remaining innies R7C469 = 10 = {136/145}, 1 locked for R7

7. 12(3) cage in N9 = {138/147/237/345} (cannot be {156} which clashes with R89C9, cannot be {246} which clashes with R7C469), no 6

8. 45 rule R1234 3 innies R4C456 = 9 = {126/135/234}, no 7,8,9
8a. Max R4C6 = 6 -> min R5C678 = 19, no 1

9. 45 rule on R6789 1 innie R6C5 = 2 outies R5C19 + 2
9a. Min R5C19 = 4 -> min R6C5 = 6
9b. Max R6C5 = 9 -> max R5C19 = 7, max R5C9 = 4
9c. R6C5 = {6789} -> R5C19 = [31/32/34/61] cannot be 6 -> no 3 in R5C9, no 8 in R6C5
9d. Min R6C5 = 6 -> max R45C5 = 8, no 8,9

10. 45 rule on C12 2 innies R59C2 = 1 outie R7C3 + 1, IOU no 1 in R5C2
10a. Max R7C3 = 9, max R59C2 = 10, min R9C2 = 3 -> max R5C2 = 7
10b. R7C3 = {689} -> R59C2 = 7,9,10 = [25/27/73], no 5 in R5C2
10c. 1 in N4 locked in R56C3, locked for C3

11. 45 rule on C89 2 innies R59C8 = 1 outie R7C7 + 10
11a. Min R7C7 = 3 -> min R59C8 = 13, no 1,2,3
11b. Max R59C8 = 17 -> max R7C7 = 7

12. 45 rule on N2 2 innies R2C46 = 10 = [19/28]/{37/46}, no 5, no 2 in R2C6

13. 10(3) cage at R1C3 = {127/136/235} (cannot be {145} because R12C3 = {45} => R3C3 = 3 clashes with R89C3), no 4, clean-up: no 6 in R2C6 (step 12)
13a. 1 of {127/136} must be in R2C4 -> no 6,7 in R2C4, clean-up: no 3,4 in R2C6 (step 12)
13b. 2 of {235} must be in R12C3 (R12C3 cannot be {35} which clashes with R89C3), no 2 in R2C4, clean-up: no 8 in R2C6 (step 12)

14. R3C3 = 4 (hidden single in C3), R4C3 = 8, clean-up: no 1 in R3C7, no 5 in R4C7
14a. 8 in N7 locked in R78C2, locked for C2

15. 45 rule on N1 2 innies R23C1 = 1 remaining outie R2C4 + 14
15a. R2C4 = {13} -> R23C1 = 15,17 = {78/89}, no 5, 8 locked for N1
15b. 5 in 29(4) cage locked in R4C12, locked for R4 and N4
15c. R4C456 (step 8) = {126/234}, 2 locked for R4 and N5, clean-up: no 7 in R3C7

16. 19(3) cage at R1C7 = {289/379/469/478} (cannot be {568} because R2C6 only contains 7,9), no 5

17. R1C456 = {269/278/368/458/467} (cannot be {179} which clashes with R2C6, cannot be {359} which clashes with R2C46), no 1

18. 17(4) cage at R1C1 = {1259/1367}
18a. 7 of {1367} must be in R1C1 -> no 7 in R123C2

19. Killer pair 7,9 in 17(4) cage at R1C1 and R23C1, locked for N1
[The elimination of 7 from R12C3 could have been done after step 15b using hidden killer pair 3,5 in R12C3 and R89C3.]
19a. 10(3) cage at R1C3 (step 13) = {136/235}, CPE no 3 in R2C2

20. 12(3) cage at R6C3 = {138/147/156/237/246}, cannot be {129} because 2,9 only in R6C3, cannot be {345} because no 3,4,5 in R6C3), no 9
20a. 1 of {138/156} must be in R6C3, 1 of {147} must be in R6C34 -> no 1 in R7C4
20b. 7,8 of {138/237} must be in R6C4 -> no 3 in R6C4

21. 17(4) cage at R4C4 = {1259/1268/1367/1457/2357} (cannot be {1349/1358} because R5C2 only contains 2,7, cannot be {2348/2456} because no 3,4,5,6,8 in R5C23)
21a. 1 of {1259} must be in R4C4, 1 of {1268/1367/1457} must be in R5C3 -> no 1 in R5C4
21b. 2 of {1259/1268} must be in R5C2, 2 of {2357} must be in R5C23 -> no 2 in R4C4
21c. 5 of {1457} must be in R5C4 -> no 4 in R5C4
21d. 5 of {1457} must be in R5C4, 7 of {2357} must be in R5C23 -> no 7 in R5C4

22. R456C5 = {149/239/257/347} (cannot be {167} which clashes with R78C5, cannot be {356} which clashes with 17(4) cage at R4C4), no 6
22a. R6C5 = {79} -> no 7 in R5C5

23. 45 rule on N8 3 innies R7C46 + R8C6 = 12 = {138/147/156/345}
23a. 1 of {156} must be in R7C6 -> no 6 in R7C6
23b. 1 of {138} must be in R7C6, {345} must be {45}3 (cannot be {34}5 which clashes with R7C469) -> no 3 in R7C6

24. R8C6 = R7C9 + 2 (step 4)
24a. 45 rule on N9 4 innies R7C9 + R8C7 + R9C78 = 19 = {1279/1459/1468/2359/2368/2467} (cannot be {1369/1567/2458} which clash with R89C9, cannot be {1378} because no 6 in 12(3) cage, cannot be {3457} because R7C9 = 3 or 5 gives repeated digit in 21(4) cage and R7C9 = 4 => R9C78 = {357} clashes with R9C23)
24b. 2 of {2359/2368} must be in R9C7 -> no 3 in R9C7
24c. 2 of {1279/2467} must be in R9C7 -> no 7 in R9C7
24d. Cannot be {1279} because R89C9 = {68}, 12(3) cage = {345} and R7C789 = {45}1 clashes with R7C6
24e. -> R7C9 + R8C7 + R9C78 = {1459/1468/2359/2368/2467}

25. 12(3) cage in N9 (step 7) = {138/147/237} (cannot be {345} which clashes with R7C9 + R8C7 + R9C78), no 5
25a. 1,2 of {138/237} must be in R8C8 -> no 3 in R8C8

26. 5 in R7 locked in R7C469 = {145}, locked for R7, clean-up: no 5,8 in R8C6 (step 4)
[Alternatively killer quad 6,7,8,9 in R7C235 and R7C78, locked for R7]

27. 3 in R7 locked in R7C78, locked for N9

28. R8C6 = R7C9 + 2 (step 4)
28a. 4 in N9 locked in R7C9 + R8C7 + R9C78 = {1459/1468} (cannot be {2467} because 4 must be in R7C9 giving repeated 6 in 21(4) cage), no 2,7, 1 locked for N9 -> R8C8 = 2, R7C78 = 10 = {37}
28b. Naked pair {37} in R7C78, locked for R7

29. 2 in R9 locked in R9C456 = {258/267}, no 1,3,4
29a. R7C46 + R8C6 (step 23) = {147/345} (cannot be {156} which clashes with R9C456), no 6, clean-up: no 4 in R7C9 (step 4)
29b. 3 in N8 locked in R8C56, locked for R8

30. Killer pair 5,7 in R9C23 and R9C456, locked for R9

31. 12(3) cage at R6C3 (step 20) = {147/156/246}, no 8
31a. 5 of {156} must be in R7C4 -> no 5 in R6C4

32. 14(3) cage at R6C6 = {149/158/248/257} (cannot be {167} which clashes with R6C34, cannot be {239} because R7C6 only contains 1,4,5, cannot be {347} which clashes with R6C1 + R6C34, cannot be {356} which clashes with R6C1), no 3,6
32a. 2 of {257} must be in R6C7 -> no 7 in R6C7

33. 14(4) cage at R5C9 = {1238/1247/1256/2345} (cannot be {1346} which clashes with R6C1), 2 locked in R56C9 for C9 and N6
33a. 4 of {1247} must be in R5C9 with 2 in R6C9 -> no 7 in R6C9
33b. 1 of {1238/1247} must be in R7C9
33c. {1256} = 1[62]5/2{56}1 (cannot be 2{16}5 which clashes with R6C34)
33d. combining steps 33b and 33c -> no 1 in R6C89

34. 14(3) cage at R6C6 (step 32) = {149/158}, no 7

35. 19(3) cage at R1C7 (step 16) = {289/379/469/478}
35a. 7 of {379/478} must be in R2C6 (cannot be R12C7 = {37} which clashes with R7C7) -> no 7 in R12C7

36. 14(4) cage at R5C9 (step 33) = {1247/1256/2345} (cannot be {1238} because R6C89 = {38} => R6C67 = {19} so cannot place 5 in R6), no 8
36a. 2 of {2345} must be in R6C9 (4 is in R5C9) -> no 3 in R6C9

37. 8 in R6 locked in R6C67 -> 14(3) cage at R6C6 (step 34) = {158}
37a. R6C5 = 9 (hidden single in R6), R45C5 = 5 = {14}/[23], no 3 in R4C5, no 5 in R5C5
37b. Killer pair 1,3 in R45C5 and R8C5, locked for C5
37b. R7C4 = 4 (hidden single in R7)

38. R6C5 = R5C19 + 2 (step 9)
38a. R6C5 = 9 -> R5C19 = 7 = [34/61], no 2 in R5C9

39. R6C9 = 2 (hidden single in C9)
39a. 14(4) cage at R5C9 (step 36) = {1247/1256/2345}
39b. 6 of {1256} must be in R6C8, 5 of {2345} must be in R7C9 -> no 5 in R6C8

40. 5 in R6 locked in R6C67 -> R6C67 = {58}, R7C6 = 1, R7C9 = 5, R8C5 = 3, R7C5 = 6, R8C6 = 7, R7C23 = [89], R8C23 = [65], R89C9 = [86], R2C6 = 9, R2C4 = 1 (step 12), clean-up: no 2 in R12C3 (step 19a)
40a. R6C3 = 1 (hidden single in R6), R6C4 = 7 (step 31)

41. Naked pair {36} in R12C3, locked for C3 and N1 -> R9C23 = [37], R5C23 = [72]
41a. R5C23 = 9 -> R45C4 = 8 = [35], R6C67 = [85], clean-up: no 6 in R3C7, no 4 in R4C7, no 2 in R4C5 (step 37a)

42. Naked pair {14} in R45C5, locked for C5 and N5 -> R45C6 = [26], R56C1 = [36], R6C8 = 3, R5C9 = 4 (step 36), R45C5 = [41], R7C78 = [37], R9C6 = 5, R3C6 = 3, R1C6 = 4, clean-up: no 6 in R2C7 (step 16), no 6 in R4C7

43. R4C7 = 7 (hidden single in C7), R3C7 = 2, clean-up: no 8 in R12C7 (step 16)
43a. R12C7 = [64], R12C3 = [36], R89C7 = [19], R9C8 = 4, R89C1 = [41], R5C78 = [89], R4C89 = [61]

44. R4C89 = 7 -> R23C9 = 12 = [39], R1C9 = 7
[Original step 44 deleted, step 44a renumbered.]

45. R1C6 = 6 -> R1C45 = 13 = [85]
[Original step 45 deleted, step 45a renumbered.]

and the rest is naked singles

Last edited by Andrew on Fri Feb 08, 2008 2:16 am; edited 1 time in total
gary w

Joined: 07 Sep 2007
Posts: 84
Location: south wales

 Posted: Wed Feb 06, 2008 11:53 pm    Post subject: Hi Andrew, It's not that I'm a particularly fast solver but that I don't normally keep a wt as I go along as this definitely slows me down.Of course it is then sometimes a problem when I wish to reconstruct my solution.Then again,you or Afmob or Mike will have written out more elegant wts than I could manage anyway. Yes,I think I would rate no.88 as close to 1.5 ..quite a bit tougher than some other recent assassins. Regards Gary
Andrew
Grandmaster

Joined: 11 Aug 2006
Posts: 300
Location: Lethbridge, Alberta

 Posted: Fri Feb 08, 2008 2:26 am    Post subject: Gary That's a fair comment. In my case if I was just writing the walkthrough as I went along, like I used to do, then it didn't take much longer. However in the past few months I've been putting steps in the correct place if they were ones I felt that I ought to have spotted earlier; then I have to rework what I've done to check that it didn't affect the later steps. If that happens several times, as it does for some puzzles, it adds a lot to my solving time. I suppose I could wait until I finish and then put those steps in their correct place. However that's not the way I do it. What I try to produce is a combination of a semi-polished walkthrough and how I actually solved the puzzle. Afmob's and Mike's walkthroughs are, I think, more attempts to optimise the solution. In the case of A88, I did do some rework to insert steps but the main reason why I took a long time was because of the step that I missed, which I've mentioned in my earlier message. I think it would avoided a lot of my combo crunching.
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