Hi Gary
Check Mike's step 31. They all get eliminated in that step.
greetings
Para
Assassin 68
assassin 68 v2
Thanks Para..of course! It was almost 2am by the time I'ld got to the end of the wt.I'll need to be a bit sharper to do number 69!
Gary
Gary
So many things to do! I only started Assassin 68 yesterday evening and wrapped it up today.
Gary's post about this puzzle can be put more clearly as
r6c9+r7c6=9, r6c9, r7c6 <> 9
Min r4c789 = 6
Min r56c7 = 13
-> Max r6c9 = 7 -> r7c6 <> 1
I've only had a glance at Cathy's and Para's walkthoughs; I'll look at them properly later.
Edit. I've now worked through Cathy's and Para's walkthoughs. Although we did some things in a different order, Para's and my walkthroughs are very similar. If I'd gone through his one first I probably wouldn't have posted mine. Still, having posted it, there's no point in deleting it. Also I see that Ed has already quoted all three walkthroughs in his ratings thread.
One interesting thought. Para composed his Transformer-Xs. Cathy had solved Transformer Lite before she solved A68, which may have made it easier for her to solve A68. I haven't yet tried either Transformer-X but my solution for A68 was remarkably similar to Para's one.
I'll rate it as 1.25. I found it a difficult cage pattern because I didn't find any innies/outies that helped; maybe they will be more help for the variants with their different cage totals. Fortunately there was enough help from other steps.
Here is my walkthrough for Assassin 68
1. R12C5 = {49/58/67}, no 1,2,3
2. R67C5 = {15/24}
3. R89C1 = {19/28/37/46}, no 5
4. R89C9 = {14/23}
5. 10(3) cage at R1C6 = {127/136/145/235}, no 8,9
6. 22(3) cage at R5C7 = 9{58/67}, CPE no 9 in R6C89
7. 19(3) cage at R5C8 = {289/379/469/478/568}, no 1
8. 11(3) cage at R6C1 = {128/137/146/236/245}, no 9
9. 19(3) cage at R6C9 = {289/379/469/478/568}, no 1
10. 11(3) cage at R7C3 = {128/137/146/236/245}, no 9
11. R8C456 = {389/479/569/578}, no 1,2
12. 26(4) cage at R3C3 = {2789/3689/4589/4679/5678}, no 1
13. 14(4) cage at R3C7 = {1238/1247/1256/1346/2345}, no 9
14. 1 in N6 locked in R4C789, locked for R4
15. 3 in C5 locked in R34589C5
15a. 45 rule on C5 5 innies R34589C5 = 26 = {13589/13679/23489/23678} (cannot be {23579/34568} which clash with R67C5)
16. 45 rule on N8 3 innies R7C456 = 8 = 1{25/34}, 1 locked for R7 and N8
17. R9C456 = {269/278/359/368/467} (cannot be {458} which clashes with R7C456)
18. 45 rule on R89 2 innies R8C37 = 5 = {14/23}
19. 11(3) cage at R7C3 (step 10) = {128/137/146/236/245}
19a. 7 of {137} and 6 of {236} must be in R7C3 -> no 3 in R7C3
20. 45 rule on R1234 3 outies R5C456 = 10 = {127/136/145/235}, no 8,9
21. 45 rule on C12 2 outies R19C3 = 6 = {15/24}
22. 17(3) cage in N7, max R9C3 = 5 -> min R89C2 = 12, no 1,2
23. 45 rule on C89 2 outies R19C7 = 13 = {49/58/67}, no 1,2,3
24. 45 rule on C1234 3 innies R389C4 = 20 = {389/479/569/578}, no 1,2
25. 45 rule on N7 2 outies R6C1 + R7C4 = 4 = {13/22}
26. 11(3) cage at R7C3 (step 10) = {128/137/146/236/245}
26a. Max R7C4 + R8C3 = 7 -> no 2 in R7C3
26b. 6 of {146} and 5 of {245} must be in R7C3 -> no 4 in R7C3
[Alternatively R7C3 cannot be 4 which would make the 11(3) cage [434])
27. 45 rule on N9 2 outies R6C9 + R7C6 = 9, no 2,3 in R6C9
28. 9 in R7 locked in R7C789, locked for N9, clean-up: no 4 in R1C7 (step 23)
29. 14(3) cage at R7C6 = {149/158/239/248/257/347/356} (cannot be {167} because 6,7 only in R7C7)
29a. Max R7C6 + R8C7 = 9 -> no 2,3,4 in R7C7
29b. 6,7,8 of {356/257/158} must be in R7C7 -> no 5 in R7C7
[Alternatively R7C7 cannot be 5 which would make the 14(3) cage [554])
30. 16(3) cage in N9 = {178/268/358/367/457}
30a. Killer quad {1234) in R8C7, R89C9 and 16(3) cage -> no 2,3,4 in R7C89
[This could have been done after step 18 but I didn’t see it then. It probably didn’t make much difference that I didn’t see it until now.]
31. 19(3) cage at R6C9 = {469/478/568}
31a. 4 of {478} must be in R6C9 -> no 7 in R6C9, clean-up: no 2 in R7C6 (step 27)
32. 45 rule on N7 4 innies R7C123 + R8C3 = 18 = {1278/1458/1467/2358/2367/2457/3456} (cannot be {1368} which clashes with R89C1)
32a. R8C3 = {1234}, R7C3 = {5678} -> R7C12 must contain one of 5,6,7,8
32b. Killer quint {56789} in R7C12, R7C3, R7C789 -> no 5 in R7C56, clean-up: no 2 in R7C45 (step 16), no 2 in R6C1 (step 25), no 1,4 in R6C5, no 4 in R6C9 (step 27)
33. 19(3) cage at R6C9 (step 31) = {568} (only remaining combination)
34. R7C7 = 9 (hidden single in R7), clean-up: no 4 in R9C7 (step 23)
34a. R7C6 + R8C7 = 5 = [14/32/41], no 3 in R8C7
35. R6C6 = 9 (only remaining place for 9 in 22(3) cage)
36. Naked quad {5678} in R1569C7, locked for C7
37. Naked triple {134} in R7C456, locked for R7 and N8
38. 2 in N8 locked in R9C56, locked for R9, clean-up: no 4 in R1C3 (step 21), no 8 in R8C1, no 3 in R8C9
38a. R9C456 = 2{69/78}, no 5
39. 5 in N8 locked in R8C456, locked for R8
39a. R8C456 = 5{69/78}
40. 2 in R7 locked in R7C12, locked for N7, clean-up: no 8 in R9C1
40a. 11(3) cage at R6C1 (step 8) = {128/236}, no 5,7
41. R7C3 = 7 (hidden single in R7), clean-up: no 3 in R89C1
41a. R7C4 + R8C3 = 4 = {13}, no 4 [Forgot to clean-up for R8C7. If I’d remembered, R67C5 would have been fixed two moves earlier.]
42. 5 in R7 locked in R7C89, locked for N9 and 19(3) cage at R6C9 -> no 5 in R6C9, clean-up: no 8 in R1C7 (step 23)
43. 16(3) cage in N9 = {178/268/367}, no 4
44. 45 rule on R789 3 outies R6C159 = 11 = {128/236} = 2{18/36} -> R6C5 = 2, R7C5 = 4, clean-up: no 9 in R12C5, no 1 in R8C6 (step 34a)
45. R9C6 = 2 (hidden single in R9)
46. 2 in N2 locked in R12C4, locked for 13(3) cage at R1C4 -> no 2 in R2C3
46a. 13(3) cage = 2{38/47/56}, no 1,9
46b. 7 only in R12C4 -> no 4 in R12C4
47. 5 in N7 locked in R9C23
47a. 17(3) cage = {359/458}, no 1,6, clean-up: no 5 in R1C3 (step 21)
48. R5C456 (step 20) = {136/145}, no 7, 1 locked for R5 and N5
49. R56C7 = {58/67}, R6C9 = {68}
49a. Killer pair {68} in R56C7 and R6C9, locked for N6
50. 19(3) cage in N6 = {379} (only remaining combination), locked for N6, clean-up: no 6 in R56C7
51. Naked pair {58} in R56C7, locked for C7 and N6 -> R6C9 = 6, R6C1 = 3 (step 44), R6C8 = 7
52. R9C7 = 7 (hidden single in N9), R1C7 = 6, clean-up: no 7 in R2C5, no 8 in R9C45 (step 38a)
52a. R89C8 = 9 = {18/36}, no 2
53. Naked pair {58} in R7C89, locked for R7 and N9, clean-up: no 1 in R89C8 (step 52a)
54. Naked pair {36} in R89C8, locked for C8 and N9, clean-up: no 2 in R8C9 -> R5C89 = [93], clean-up: no 6 in R5C456 (step 48), no 2 in R8C9
55. Naked pair {14} in R89C9, locked for C9 and N9 -> R4C9 = 2, R8C7 = 2, R7C6 = 3 (step 34a), R7C4 = 1, R8C3 = 3, clean-up: no 9 in 17(3) cage in N7 (step 47a)
56. 17(3) cage in N7 = {458}, locked for N7, clean-up: no 6 in R89C1
57. Naked pair {19} in R89C1, locked for C1
58. Naked pair {69} in R9C45, locked for R9 and N8 -> R89C1 = [91], R89C8 = [63], R89C9 = [14], R9C23 = [85], R8C2 = 4, R1C3 = 1 (step 21)
59. Naked triple {145} in R5C456, locked for R5 and N5 -> R56C7 = [85], R6C4 = 8, R56C3 = 6 = [24], R6C2 = 1, clean-up: no 6,7 in R12C4 (step 46a)
60. Naked pair {67} in R5C12, locked for N4
61. 6 in C3 locked in R23C3, locked for N1
62. 14(4) cage at R3C7 = {1346} (only remaining combination), no 5,7 -> R4C6 = 6, R3C7 = 3
60. 26(4) cage at R3C3 = {4589/4679/5678} (cannot be {3689} because R5C4 only contains 4,5), no 3 -> R4C4 = 7, R4C5 = 3, R8C4 = 5
60a. 26(4) cage = {4679/5678} = 67{49/58} -> R3C3 = 6, R2C3 = 8, R4C3 = 9, R5C4 = 4, R5C56 = [51], R4C12 = [85], R3C4 = 9, R9C45 = [69], R2C5 = 6, R1C5 = 7, R8C56 = [87], R3C5 = 1
61. Naked pair {45} in R23C6, locked for C6 -> R3C6 = 8, R2C7 = 1, R4C78 = [41]
62. R4C12 = [85] -> R23C1 = 11 = {47}
62a. Naked pair {47} in R23C1, locked for C1 and N1 -> R3C2 = 2, R1C1 = 5, R5C12 = [67], R7C12 = [26]
63. R4C89 = [12] -> R23C9 = 12 = {57}
63a. Naked pair {57}, locked for C9 and N3
and the rest is naked singles
I think I missed some hidden singles in the later steps but it probably didn't make much difference.
I'll try to find time to have a go at A68V1.5 (I'll probably "pass" on V2 and V3) and at least one of Para's Transformers.
Gary's post about this puzzle can be put more clearly as
r6c9+r7c6=9, r6c9, r7c6 <> 9
Min r4c789 = 6
Min r56c7 = 13
-> Max r6c9 = 7 -> r7c6 <> 1
I've only had a glance at Cathy's and Para's walkthoughs; I'll look at them properly later.
Edit. I've now worked through Cathy's and Para's walkthoughs. Although we did some things in a different order, Para's and my walkthroughs are very similar. If I'd gone through his one first I probably wouldn't have posted mine. Still, having posted it, there's no point in deleting it. Also I see that Ed has already quoted all three walkthroughs in his ratings thread.
One interesting thought. Para composed his Transformer-Xs. Cathy had solved Transformer Lite before she solved A68, which may have made it easier for her to solve A68. I haven't yet tried either Transformer-X but my solution for A68 was remarkably similar to Para's one.
I'll rate it as 1.25. I found it a difficult cage pattern because I didn't find any innies/outies that helped; maybe they will be more help for the variants with their different cage totals. Fortunately there was enough help from other steps.
Here is my walkthrough for Assassin 68
1. R12C5 = {49/58/67}, no 1,2,3
2. R67C5 = {15/24}
3. R89C1 = {19/28/37/46}, no 5
4. R89C9 = {14/23}
5. 10(3) cage at R1C6 = {127/136/145/235}, no 8,9
6. 22(3) cage at R5C7 = 9{58/67}, CPE no 9 in R6C89
7. 19(3) cage at R5C8 = {289/379/469/478/568}, no 1
8. 11(3) cage at R6C1 = {128/137/146/236/245}, no 9
9. 19(3) cage at R6C9 = {289/379/469/478/568}, no 1
10. 11(3) cage at R7C3 = {128/137/146/236/245}, no 9
11. R8C456 = {389/479/569/578}, no 1,2
12. 26(4) cage at R3C3 = {2789/3689/4589/4679/5678}, no 1
13. 14(4) cage at R3C7 = {1238/1247/1256/1346/2345}, no 9
14. 1 in N6 locked in R4C789, locked for R4
15. 3 in C5 locked in R34589C5
15a. 45 rule on C5 5 innies R34589C5 = 26 = {13589/13679/23489/23678} (cannot be {23579/34568} which clash with R67C5)
16. 45 rule on N8 3 innies R7C456 = 8 = 1{25/34}, 1 locked for R7 and N8
17. R9C456 = {269/278/359/368/467} (cannot be {458} which clashes with R7C456)
18. 45 rule on R89 2 innies R8C37 = 5 = {14/23}
19. 11(3) cage at R7C3 (step 10) = {128/137/146/236/245}
19a. 7 of {137} and 6 of {236} must be in R7C3 -> no 3 in R7C3
20. 45 rule on R1234 3 outies R5C456 = 10 = {127/136/145/235}, no 8,9
21. 45 rule on C12 2 outies R19C3 = 6 = {15/24}
22. 17(3) cage in N7, max R9C3 = 5 -> min R89C2 = 12, no 1,2
23. 45 rule on C89 2 outies R19C7 = 13 = {49/58/67}, no 1,2,3
24. 45 rule on C1234 3 innies R389C4 = 20 = {389/479/569/578}, no 1,2
25. 45 rule on N7 2 outies R6C1 + R7C4 = 4 = {13/22}
26. 11(3) cage at R7C3 (step 10) = {128/137/146/236/245}
26a. Max R7C4 + R8C3 = 7 -> no 2 in R7C3
26b. 6 of {146} and 5 of {245} must be in R7C3 -> no 4 in R7C3
[Alternatively R7C3 cannot be 4 which would make the 11(3) cage [434])
27. 45 rule on N9 2 outies R6C9 + R7C6 = 9, no 2,3 in R6C9
28. 9 in R7 locked in R7C789, locked for N9, clean-up: no 4 in R1C7 (step 23)
29. 14(3) cage at R7C6 = {149/158/239/248/257/347/356} (cannot be {167} because 6,7 only in R7C7)
29a. Max R7C6 + R8C7 = 9 -> no 2,3,4 in R7C7
29b. 6,7,8 of {356/257/158} must be in R7C7 -> no 5 in R7C7
[Alternatively R7C7 cannot be 5 which would make the 14(3) cage [554])
30. 16(3) cage in N9 = {178/268/358/367/457}
30a. Killer quad {1234) in R8C7, R89C9 and 16(3) cage -> no 2,3,4 in R7C89
[This could have been done after step 18 but I didn’t see it then. It probably didn’t make much difference that I didn’t see it until now.]
31. 19(3) cage at R6C9 = {469/478/568}
31a. 4 of {478} must be in R6C9 -> no 7 in R6C9, clean-up: no 2 in R7C6 (step 27)
32. 45 rule on N7 4 innies R7C123 + R8C3 = 18 = {1278/1458/1467/2358/2367/2457/3456} (cannot be {1368} which clashes with R89C1)
32a. R8C3 = {1234}, R7C3 = {5678} -> R7C12 must contain one of 5,6,7,8
32b. Killer quint {56789} in R7C12, R7C3, R7C789 -> no 5 in R7C56, clean-up: no 2 in R7C45 (step 16), no 2 in R6C1 (step 25), no 1,4 in R6C5, no 4 in R6C9 (step 27)
33. 19(3) cage at R6C9 (step 31) = {568} (only remaining combination)
34. R7C7 = 9 (hidden single in R7), clean-up: no 4 in R9C7 (step 23)
34a. R7C6 + R8C7 = 5 = [14/32/41], no 3 in R8C7
35. R6C6 = 9 (only remaining place for 9 in 22(3) cage)
36. Naked quad {5678} in R1569C7, locked for C7
37. Naked triple {134} in R7C456, locked for R7 and N8
38. 2 in N8 locked in R9C56, locked for R9, clean-up: no 4 in R1C3 (step 21), no 8 in R8C1, no 3 in R8C9
38a. R9C456 = 2{69/78}, no 5
39. 5 in N8 locked in R8C456, locked for R8
39a. R8C456 = 5{69/78}
40. 2 in R7 locked in R7C12, locked for N7, clean-up: no 8 in R9C1
40a. 11(3) cage at R6C1 (step 8) = {128/236}, no 5,7
41. R7C3 = 7 (hidden single in R7), clean-up: no 3 in R89C1
41a. R7C4 + R8C3 = 4 = {13}, no 4 [Forgot to clean-up for R8C7. If I’d remembered, R67C5 would have been fixed two moves earlier.]
42. 5 in R7 locked in R7C89, locked for N9 and 19(3) cage at R6C9 -> no 5 in R6C9, clean-up: no 8 in R1C7 (step 23)
43. 16(3) cage in N9 = {178/268/367}, no 4
44. 45 rule on R789 3 outies R6C159 = 11 = {128/236} = 2{18/36} -> R6C5 = 2, R7C5 = 4, clean-up: no 9 in R12C5, no 1 in R8C6 (step 34a)
45. R9C6 = 2 (hidden single in R9)
46. 2 in N2 locked in R12C4, locked for 13(3) cage at R1C4 -> no 2 in R2C3
46a. 13(3) cage = 2{38/47/56}, no 1,9
46b. 7 only in R12C4 -> no 4 in R12C4
47. 5 in N7 locked in R9C23
47a. 17(3) cage = {359/458}, no 1,6, clean-up: no 5 in R1C3 (step 21)
48. R5C456 (step 20) = {136/145}, no 7, 1 locked for R5 and N5
49. R56C7 = {58/67}, R6C9 = {68}
49a. Killer pair {68} in R56C7 and R6C9, locked for N6
50. 19(3) cage in N6 = {379} (only remaining combination), locked for N6, clean-up: no 6 in R56C7
51. Naked pair {58} in R56C7, locked for C7 and N6 -> R6C9 = 6, R6C1 = 3 (step 44), R6C8 = 7
52. R9C7 = 7 (hidden single in N9), R1C7 = 6, clean-up: no 7 in R2C5, no 8 in R9C45 (step 38a)
52a. R89C8 = 9 = {18/36}, no 2
53. Naked pair {58} in R7C89, locked for R7 and N9, clean-up: no 1 in R89C8 (step 52a)
54. Naked pair {36} in R89C8, locked for C8 and N9, clean-up: no 2 in R8C9 -> R5C89 = [93], clean-up: no 6 in R5C456 (step 48), no 2 in R8C9
55. Naked pair {14} in R89C9, locked for C9 and N9 -> R4C9 = 2, R8C7 = 2, R7C6 = 3 (step 34a), R7C4 = 1, R8C3 = 3, clean-up: no 9 in 17(3) cage in N7 (step 47a)
56. 17(3) cage in N7 = {458}, locked for N7, clean-up: no 6 in R89C1
57. Naked pair {19} in R89C1, locked for C1
58. Naked pair {69} in R9C45, locked for R9 and N8 -> R89C1 = [91], R89C8 = [63], R89C9 = [14], R9C23 = [85], R8C2 = 4, R1C3 = 1 (step 21)
59. Naked triple {145} in R5C456, locked for R5 and N5 -> R56C7 = [85], R6C4 = 8, R56C3 = 6 = [24], R6C2 = 1, clean-up: no 6,7 in R12C4 (step 46a)
60. Naked pair {67} in R5C12, locked for N4
61. 6 in C3 locked in R23C3, locked for N1
62. 14(4) cage at R3C7 = {1346} (only remaining combination), no 5,7 -> R4C6 = 6, R3C7 = 3
60. 26(4) cage at R3C3 = {4589/4679/5678} (cannot be {3689} because R5C4 only contains 4,5), no 3 -> R4C4 = 7, R4C5 = 3, R8C4 = 5
60a. 26(4) cage = {4679/5678} = 67{49/58} -> R3C3 = 6, R2C3 = 8, R4C3 = 9, R5C4 = 4, R5C56 = [51], R4C12 = [85], R3C4 = 9, R9C45 = [69], R2C5 = 6, R1C5 = 7, R8C56 = [87], R3C5 = 1
61. Naked pair {45} in R23C6, locked for C6 -> R3C6 = 8, R2C7 = 1, R4C78 = [41]
62. R4C12 = [85] -> R23C1 = 11 = {47}
62a. Naked pair {47} in R23C1, locked for C1 and N1 -> R3C2 = 2, R1C1 = 5, R5C12 = [67], R7C12 = [26]
63. R4C89 = [12] -> R23C9 = 12 = {57}
63a. Naked pair {57}, locked for C9 and N3
and the rest is naked singles
I think I missed some hidden singles in the later steps but it probably didn't make much difference.
I'll try to find time to have a go at A68V1.5 (I'll probably "pass" on V2 and V3) and at least one of Para's Transformers.
Last edited by Andrew on Tue Sep 25, 2007 12:21 am, edited 3 times in total.
Here's a very different way of tackling Assassin 68V2. Para and especially Mike found lots of things I missed: various '45's, implied subsets, combo conflicts and IOU's. Well done.
So mine is more combination pecking. Hopefully easy enough to follow. Still no-where near A60 RP Lite in difficulty. But a very nice 1.75! Sadly, my way doesn't help much with the V3.
Assassin 68 V2
Preliminaries
i. 24(3)n2 = {789}
ii. 9(2)n2: no 9
iii. 22(3)n2 = {589/679}
iv. 19(5)n3 must have 1: 1 locked for n3
v. 14(4)n1: no 9
vi. 10(3)n4: no 8 or 9
vii. 12(2)n5: no 1,2 or 6
viii. 14(2)n7 = {59/68}
ix. 11(3)n9: no 9
x. 15(2)n9 = {69/78}
1. 24(3)n2 = {789} -> no 7,8,9 in r2c56
1a. no 1 or 2 in r1c5
2. 22(3)n2 = 9{58/67} = [5/6..]
2a. r2c6 = {56} -> no 5/6 elsewhere in 22(3)n2 (step 2)
2b. 22(3) must have 9 -> no 9 r2c4
2b. Common Peer Elimination (CPE): r1c3 sees both 9's which must be in 24(3)n2 -> no 9 r1c3
2c. Generalized X-Wing 9 in 24(3) & 22(3)-> 9 locked for r12
3. naked triple {789} in r12c4 + r1c6: all locked for n2
3a. no 1 or 2 in r2c5
4. 9(2)n2 = {36/45} = [4/6,5/6..]
4a. Killer pair 5/6 with r2c6: both locked for n2
5. 1 & 2 in n2 only in r3: both locked for r3 and no 1 or 2 in r45c5
5a. 21(5) must have 3 of {1234} in r3c456 = 12{369/378/459} ({12468} blocked: clashes with [4/6] needed in 9(2)n2 which 'sees' each cell in 21(4))
5b. r45c5 = {69/78/59}(no 3,4) = [8/9..]
6. Naked Triple {789} r2c347: all locked for r2
7. deleted
8. {57} combo. in 12(2)n5 is blocked: forces r45c5 to {69} (step 5b) but {56} clashes with 5/6 needed in 9(2)n2
8a. 12(2)n5 = {39/48} = [8/9..]
8b. Killer pair {89} in r4567c5: locked for c5
8c. Killer pair {34} in 9(2) & 12(2): both locked for c5
9. "45" c12: r19c3 = h7(2): no 789
10. "45" c1234: r389c4 = h15(3)
10. max. r3c4 = 4 -> min. r89c4 = 11 (no 1)
11. "45" c89: r19c7 = h5(2) = {14/23}
12. "45" c6789: r389c6 = h8(3) = 1{25/34}
12a. 1 locked for c6
13. 1 in n5 only in c4: 1 locked for c4
13a. h15(3)r389c4 = {249/258/267/348/357/456}
14. "45" r9: r8c1289 = h19(4)
14a. min r8c19 = 11 -> max r8c28 = 8 (no 8,9)
15. "45" r89: r8c47 = h12(2) = {39/48/57} (no 1,2 or 6)
16. "45" r89: r7c3467 = h16(4)
17. "45" n8: r7c456 = h19(3) -> r7c5 = r7c37 + 3 (step 16)
17a. min r7c37 = {12} = 3 -> min r7c5 = 6
17b. r67c5 = [39/48]
17c. r7c5 = 8/9 -> r7c37 = 5/6 = {14/23/15/24}(no 6789}
17d. r7c37+r7c5 = {14/23}[8]/{15/24}[9]
18. 14(3)n8 = {149/158/167/239/248/257/356} ({347} clashes with h12(2)r8c37)
19. "45" r789: r6c159 = h16(3)
19a. max r6c5 = 4 -> min r6c19 = 12 (no 1,2)
20. "45" n78: 2 outies r6c15 - 5 = r7c6
20a. max r6c15 = [94] = 13 -> max r7c6 = 8. However this means 2 8's in r7c56
20b. -> r6c15 max = [93] = 12 -> max r7c6 = 7
20c. min. r6c9 = 4 (step 19)
20d. max r7c56 = [97] = 16 -> min r7c4 = 3 (step 17)
21. "45" n9: 2 outies = 11
Should have done this next one after 17b.
23. "45" r1234: r5c456 = h16(3) & remembering r45c5 = {59/68/78} (step 5b)
23a. r5c456 = {169/178/268/358/367/457} ({259} blocked by clash with r4c5;{349} blocked by r6c5)
23b. 1 only in r5c4 -> no 9 r5c4
24. "45" n1:r4c12 + 10 = r23c3
24a. min r4c12 = 3 -> min r23c3 = 13
24b. no 3 r3c3
24c. max r23c3 = 17 -> max r4c12 = 7
24d. r4c12, no 7,8
25. 12(3)n7 = {129/138/147/237/246/345}({156} blocked by 14(2))
26. A nice straight chain shows a complex hidden single 5 in r1234567C5. Here's how.
26a. r45c5 = {59/69/78} (step 5b) & 9(2) = [5/6..]
26b. -> r1245c5 = Killer pair 5/6 or r45c5 = {78} -> 12(2) = {39} -> 9(2) = {45}
26c. ->5 locked for c5
27. 12(3)n8 = {129/138/147/156/237/246} = [1/6/7..]({345} blocked by r9c5)
28. 14(3)n8 = {149/158/239/248/257/356} ({167} blocked by 12(3) step 27)
28a. 1 must be in r8c5 for {149/158} -> no 1 r8c6
28b. 4 must be in r8c6 for {149/248} -> no 4 r8c4
28c. 6 must be in r8c5 for {356} -> no 6 r8c4
29. deleted
30. deleted
31. deleted
32. OK - much more creative. Maybe this is a Killer AIC.
32a. when r3c4 = 4 -> 9(2)n2 = {36} -> r2c6 = 5 -> h8(3)r389c6 = [1]{34}
32b. this is useful for next step
33. h15(3)r389c4 = {249/258/267/348/357/456}
33a. = [294/4{29}/2{58}/276/384/357] ([4]{38} blocked by 3 in r89c6 step 32a; [456] blocked by {34} in r89c6 (step 32a- forces r8c5 = 6: 2 6's n8;[375] blocked by 14(3) must be [725] but 2 5s n8)
33b. no 3 r89c6;
34. h15(3)r389c4 = {249/258/267/348/357) = [7/8/9..]
34a. hidden killer triple 7/8/9 with r12c4: all locked for c4
35. h19(3)r7c456 = {379/469/478/568}(no 2)
35a. 3 in {379} only in r7c4 -> no 3 r7c6
36. 13(3)n7 = {139/148/157/238/247/256/346}
36a. 1 and 2 only in r7c3 -> no 5 r7c3
36b. r7c34 = [13/14/15/23/24/26/36/46]
37. "45" n9: 2 outies = 11
37a. min r7c6 = 4 -> max r6c9 = 7
38. "45" n7: 2 outies = 12
38a. max r7c4 = 6 -> min r6c1 = 6
39. h16(3)r6c159 = [934/835/637/745] = [3/5..] ([736] blocked by [55] forced into r7c46 steps 37, 38)
39a. no 6 r6c9 -> no 5 r7c6 (step 37)
39b. & following up on step 37, 38: h19(3)r7c456 = [397/496/694/586] = {379/469/568} = [3/6..]
39c. -> from step 36b.r7c34 = [13/14/15/23/24/26/36]([46] blocked by [694] in h19(3))
39d. no 4 r7c3
39e. max r7c34 = 9 -> min r8c3 = 4
39f. no 9 r8c7 (h12(2)r8c47)
40. 14(3)n8 = {149/158/239/248/257}(no 6) = [1/2..]({356} blocked by h19(3) step 39b)
41. 12(3)n8 = {138/147/156/237/246}(no 9) ({129} blocked by 14(3) step 40)
42. R89c5 must have 1/2 for c5 (but cannot have both)
42a. When 14(3)n8 = {257} -> 12(3)n8 can only be {138} = [813] -> r8c5 !=2 (step 42) -> 14(3) = [572]
42b. -> 7 must be in r8c5 when 14(3) = {257} -> no 7 r8c4
42c. no other combo with 7, & {257} cannot combine with any other combo's in 12(3)
42d. -> no 7 r8c4
43. from step 33. h15(3)r389c4 = [294/492/258/285/384/357](no 6 r9c4) ([276] blocked by r8c4)
44. 12(3)n8 = {138/147/156/237/246}
44a. 5 in {156} must be in r6c4 -> no 5 r9c6
45. h8(3)r389c6 = 1{25/34}.
45a. 5 in {125} only in r8c6 -> no 2 r8c6
46. 14(3)n8 = {149/158/239/248/257}
46a. 5 in {158/257} must be in r8c6
46b. no 5 r8c4
47. from step 43. h15(3)r389c4 = [294/492/285/384]
47a. no 2 r8c4; no 7,8 r9c4
48. 7 in c4 only in r12c4: 7 locked for n2 and not in r2c3
48. 14(3)n7 = {149/158/239/248}(no 7)
49. naked pair {12} r38c5: locked for c5
50. from 39c.r7c34 = [13/14/15/23/24/26/36]
50a. 13(3) = [139/148/157/247/265/364] ([238] combined with h12(2)r8c37 clashes with [3/4/8] needed in 14(3)n8;
50b. r7c34 = [13/14/15/24/26/36]
51. from 39b h19(3)r7c456 = [397/496/694/586]
51a. combining with 50b -> h16(4)r7c3467+r7c5 = [1375][9]/[1465][9]/[1564][8] ([2464][9]/[2644][9]/[3643][9] clash)
51b. -> r7c3 = 1 finally!
51c. r7c4 = {345}, r7c6 = {67}, r7c7 = {45}
51d. 13(3)n7 = [1][39/48/57]
51e. r8c3 = {789}
51f. r8c7 = {345}
51g. 15(3) = {357/456} = [753/654/645]
51h. r6c1: no 6 ("45"n7)
51i. r6c9: no 7 ("45"n9)
51j. r7c456 = [397/496/586] -> h16(3)r6c159 = [934/835/745]
52. 6 in c4 only in n5: 6 locked for n5
52a. r45c5 = {78/59}
53. from step 51g. r78c7 = [53/54/45]: 5 locked for n9 & c7
53a. = 8/9
54. "45"n9: 4 innies = 19 = 5{239/248/347}(no 6)
54a. from step 53, r7c89 = {29/28/37} (no 4)
54b. 15(3)n6 = {249/258/357}
55. 11(3)n9 must have 1 for n9 = 1{28/37/46}
56. 12(3)n7 = {237/246/345}
56. from 51d. r7c4 + r8c3 = [39/48/57]
57. deleted
58. c34: generalized swordfish (or is triple X-wing?) {789} in 24(3)n2(X3), r8c34(X2), 21(4)n1(X1)
58a. -> no 7 in 10(3)n4 = {136/145/235}
58b. -> 21(4)n1 can only 1 of {789} = {1569/2469/2468/3459/3468/3567}
59. h7(2)r19c3 = {25/34} = [2/3,3/5,4/5..]
59a. -> 10(3)n4 = {136/235}(no 4) = {36}[1]/{25}[3] ({145} blocked by h7(2))
59b. r6c4 = {13}
60. 6 in c4 only in r45c4 in 21(4)n1
60a. no 6 r34c3
61. 6 in c3 only in r56c3 -> 10(3) = {36}[1]
61a. {36} locked for n4 & c3
62. h7(2)r19c3 = {25} locked for c3
63. 18(3)n4 = {189/279/459} = 9{..}
63a. 9 locked for n4
63b. no 3 r7c4
63c. no 9 r8c3
64. from 51j. r7c456 = [496/586] -> h16(3)r6c159 = [835/745]
64a. r6c9 = 5, r7c6 = 6, r9c5 = 7
64b. r45c5 = {59}: both locked for c5 & n5
64c. 9(2)n2 = {36}: both locked for n2, c5
things feel easy from here!
So mine is more combination pecking. Hopefully easy enough to follow. Still no-where near A60 RP Lite in difficulty. But a very nice 1.75! Sadly, my way doesn't help much with the V3.
Assassin 68 V2
Preliminaries
i. 24(3)n2 = {789}
ii. 9(2)n2: no 9
iii. 22(3)n2 = {589/679}
iv. 19(5)n3 must have 1: 1 locked for n3
v. 14(4)n1: no 9
vi. 10(3)n4: no 8 or 9
vii. 12(2)n5: no 1,2 or 6
viii. 14(2)n7 = {59/68}
ix. 11(3)n9: no 9
x. 15(2)n9 = {69/78}
1. 24(3)n2 = {789} -> no 7,8,9 in r2c56
1a. no 1 or 2 in r1c5
2. 22(3)n2 = 9{58/67} = [5/6..]
2a. r2c6 = {56} -> no 5/6 elsewhere in 22(3)n2 (step 2)
2b. 22(3) must have 9 -> no 9 r2c4
2b. Common Peer Elimination (CPE): r1c3 sees both 9's which must be in 24(3)n2 -> no 9 r1c3
2c. Generalized X-Wing 9 in 24(3) & 22(3)-> 9 locked for r12
3. naked triple {789} in r12c4 + r1c6: all locked for n2
3a. no 1 or 2 in r2c5
4. 9(2)n2 = {36/45} = [4/6,5/6..]
4a. Killer pair 5/6 with r2c6: both locked for n2
5. 1 & 2 in n2 only in r3: both locked for r3 and no 1 or 2 in r45c5
5a. 21(5) must have 3 of {1234} in r3c456 = 12{369/378/459} ({12468} blocked: clashes with [4/6] needed in 9(2)n2 which 'sees' each cell in 21(4))
5b. r45c5 = {69/78/59}(no 3,4) = [8/9..]
6. Naked Triple {789} r2c347: all locked for r2
7. deleted
8. {57} combo. in 12(2)n5 is blocked: forces r45c5 to {69} (step 5b) but {56} clashes with 5/6 needed in 9(2)n2
8a. 12(2)n5 = {39/48} = [8/9..]
8b. Killer pair {89} in r4567c5: locked for c5
8c. Killer pair {34} in 9(2) & 12(2): both locked for c5
9. "45" c12: r19c3 = h7(2): no 789
10. "45" c1234: r389c4 = h15(3)
10. max. r3c4 = 4 -> min. r89c4 = 11 (no 1)
11. "45" c89: r19c7 = h5(2) = {14/23}
12. "45" c6789: r389c6 = h8(3) = 1{25/34}
12a. 1 locked for c6
13. 1 in n5 only in c4: 1 locked for c4
13a. h15(3)r389c4 = {249/258/267/348/357/456}
14. "45" r9: r8c1289 = h19(4)
14a. min r8c19 = 11 -> max r8c28 = 8 (no 8,9)
15. "45" r89: r8c47 = h12(2) = {39/48/57} (no 1,2 or 6)
16. "45" r89: r7c3467 = h16(4)
17. "45" n8: r7c456 = h19(3) -> r7c5 = r7c37 + 3 (step 16)
17a. min r7c37 = {12} = 3 -> min r7c5 = 6
17b. r67c5 = [39/48]
17c. r7c5 = 8/9 -> r7c37 = 5/6 = {14/23/15/24}(no 6789}
17d. r7c37+r7c5 = {14/23}[8]/{15/24}[9]
18. 14(3)n8 = {149/158/167/239/248/257/356} ({347} clashes with h12(2)r8c37)
19. "45" r789: r6c159 = h16(3)
19a. max r6c5 = 4 -> min r6c19 = 12 (no 1,2)
20. "45" n78: 2 outies r6c15 - 5 = r7c6
20a. max r6c15 = [94] = 13 -> max r7c6 = 8. However this means 2 8's in r7c56
20b. -> r6c15 max = [93] = 12 -> max r7c6 = 7
20c. min. r6c9 = 4 (step 19)
20d. max r7c56 = [97] = 16 -> min r7c4 = 3 (step 17)
21. "45" n9: 2 outies = 11
Should have done this next one after 17b.
23. "45" r1234: r5c456 = h16(3) & remembering r45c5 = {59/68/78} (step 5b)
23a. r5c456 = {169/178/268/358/367/457} ({259} blocked by clash with r4c5;{349} blocked by r6c5)
23b. 1 only in r5c4 -> no 9 r5c4
24. "45" n1:r4c12 + 10 = r23c3
24a. min r4c12 = 3 -> min r23c3 = 13
24b. no 3 r3c3
24c. max r23c3 = 17 -> max r4c12 = 7
24d. r4c12, no 7,8
25. 12(3)n7 = {129/138/147/237/246/345}({156} blocked by 14(2))
26. A nice straight chain shows a complex hidden single 5 in r1234567C5. Here's how.
26a. r45c5 = {59/69/78} (step 5b) & 9(2) = [5/6..]
26b. -> r1245c5 = Killer pair 5/6 or r45c5 = {78} -> 12(2) = {39} -> 9(2) = {45}
26c. ->5 locked for c5
27. 12(3)n8 = {129/138/147/156/237/246} = [1/6/7..]({345} blocked by r9c5)
28. 14(3)n8 = {149/158/239/248/257/356} ({167} blocked by 12(3) step 27)
28a. 1 must be in r8c5 for {149/158} -> no 1 r8c6
28b. 4 must be in r8c6 for {149/248} -> no 4 r8c4
28c. 6 must be in r8c5 for {356} -> no 6 r8c4
29. deleted
30. deleted
31. deleted
32. OK - much more creative. Maybe this is a Killer AIC.
32a. when r3c4 = 4 -> 9(2)n2 = {36} -> r2c6 = 5 -> h8(3)r389c6 = [1]{34}
32b. this is useful for next step
33. h15(3)r389c4 = {249/258/267/348/357/456}
33a. = [294/4{29}/2{58}/276/384/357] ([4]{38} blocked by 3 in r89c6 step 32a; [456] blocked by {34} in r89c6 (step 32a- forces r8c5 = 6: 2 6's n8;[375] blocked by 14(3) must be [725] but 2 5s n8)
33b. no 3 r89c6;
34. h15(3)r389c4 = {249/258/267/348/357) = [7/8/9..]
34a. hidden killer triple 7/8/9 with r12c4: all locked for c4
35. h19(3)r7c456 = {379/469/478/568}(no 2)
35a. 3 in {379} only in r7c4 -> no 3 r7c6
36. 13(3)n7 = {139/148/157/238/247/256/346}
36a. 1 and 2 only in r7c3 -> no 5 r7c3
36b. r7c34 = [13/14/15/23/24/26/36/46]
37. "45" n9: 2 outies = 11
37a. min r7c6 = 4 -> max r6c9 = 7
38. "45" n7: 2 outies = 12
38a. max r7c4 = 6 -> min r6c1 = 6
39. h16(3)r6c159 = [934/835/637/745] = [3/5..] ([736] blocked by [55] forced into r7c46 steps 37, 38)
39a. no 6 r6c9 -> no 5 r7c6 (step 37)
39b. & following up on step 37, 38: h19(3)r7c456 = [397/496/694/586] = {379/469/568} = [3/6..]
39c. -> from step 36b.r7c34 = [13/14/15/23/24/26/36]([46] blocked by [694] in h19(3))
39d. no 4 r7c3
39e. max r7c34 = 9 -> min r8c3 = 4
39f. no 9 r8c7 (h12(2)r8c47)
40. 14(3)n8 = {149/158/239/248/257}(no 6) = [1/2..]({356} blocked by h19(3) step 39b)
41. 12(3)n8 = {138/147/156/237/246}(no 9) ({129} blocked by 14(3) step 40)
42. R89c5 must have 1/2 for c5 (but cannot have both)
42a. When 14(3)n8 = {257} -> 12(3)n8 can only be {138} = [813] -> r8c5 !=2 (step 42) -> 14(3) = [572]
42b. -> 7 must be in r8c5 when 14(3) = {257} -> no 7 r8c4
42c. no other combo with 7, & {257} cannot combine with any other combo's in 12(3)
42d. -> no 7 r8c4
43. from step 33. h15(3)r389c4 = [294/492/258/285/384/357](no 6 r9c4) ([276] blocked by r8c4)
44. 12(3)n8 = {138/147/156/237/246}
44a. 5 in {156} must be in r6c4 -> no 5 r9c6
45. h8(3)r389c6 = 1{25/34}.
45a. 5 in {125} only in r8c6 -> no 2 r8c6
46. 14(3)n8 = {149/158/239/248/257}
46a. 5 in {158/257} must be in r8c6
46b. no 5 r8c4
47. from step 43. h15(3)r389c4 = [294/492/285/384]
47a. no 2 r8c4; no 7,8 r9c4
48. 7 in c4 only in r12c4: 7 locked for n2 and not in r2c3
48. 14(3)n7 = {149/158/239/248}(no 7)
49. naked pair {12} r38c5: locked for c5
50. from 39c.r7c34 = [13/14/15/23/24/26/36]
50a. 13(3) = [139/148/157/247/265/364] ([238] combined with h12(2)r8c37 clashes with [3/4/8] needed in 14(3)n8;
50b. r7c34 = [13/14/15/24/26/36]
51. from 39b h19(3)r7c456 = [397/496/694/586]
51a. combining with 50b -> h16(4)r7c3467+r7c5 = [1375][9]/[1465][9]/[1564][8] ([2464][9]/[2644][9]/[3643][9] clash)
51b. -> r7c3 = 1 finally!
51c. r7c4 = {345}, r7c6 = {67}, r7c7 = {45}
51d. 13(3)n7 = [1][39/48/57]
51e. r8c3 = {789}
51f. r8c7 = {345}
51g. 15(3) = {357/456} = [753/654/645]
51h. r6c1: no 6 ("45"n7)
51i. r6c9: no 7 ("45"n9)
51j. r7c456 = [397/496/586] -> h16(3)r6c159 = [934/835/745]
52. 6 in c4 only in n5: 6 locked for n5
52a. r45c5 = {78/59}
53. from step 51g. r78c7 = [53/54/45]: 5 locked for n9 & c7
53a. = 8/9
54. "45"n9: 4 innies = 19 = 5{239/248/347}(no 6)
54a. from step 53, r7c89 = {29/28/37} (no 4)
54b. 15(3)n6 = {249/258/357}
55. 11(3)n9 must have 1 for n9 = 1{28/37/46}
56. 12(3)n7 = {237/246/345}
56. from 51d. r7c4 + r8c3 = [39/48/57]
57. deleted
58. c34: generalized swordfish (or is triple X-wing?) {789} in 24(3)n2(X3), r8c34(X2), 21(4)n1(X1)
58a. -> no 7 in 10(3)n4 = {136/145/235}
58b. -> 21(4)n1 can only 1 of {789} = {1569/2469/2468/3459/3468/3567}
59. h7(2)r19c3 = {25/34} = [2/3,3/5,4/5..]
59a. -> 10(3)n4 = {136/235}(no 4) = {36}[1]/{25}[3] ({145} blocked by h7(2))
59b. r6c4 = {13}
60. 6 in c4 only in r45c4 in 21(4)n1
60a. no 6 r34c3
61. 6 in c3 only in r56c3 -> 10(3) = {36}[1]
61a. {36} locked for n4 & c3
62. h7(2)r19c3 = {25} locked for c3
63. 18(3)n4 = {189/279/459} = 9{..}
63a. 9 locked for n4
63b. no 3 r7c4
63c. no 9 r8c3
64. from 51j. r7c456 = [496/586] -> h16(3)r6c159 = [835/745]
64a. r6c9 = 5, r7c6 = 6, r9c5 = 7
64b. r45c5 = {59}: both locked for c5 & n5
64c. 9(2)n2 = {36}: both locked for n2, c5
things feel easy from here!