Assassin 73

[Andrew]

Thank goodness for another fairly easy one. I needed a break from A72V2 where I seem to have ground to a halt and although I haven't yet given up.

I liked the way that one theme kept repeating itself in the way that I solved it.

Probably about the same level as A72 so I'll rate this as 1.0.

Here is my walkthrough for A73, posted in the "wee sma' hours" again so I'll check it as soon as I can and tidy it up then; I know that I've missed so clean-ups in the later stages so may be able to make it a bit shorter. I look forward to the clocks going back so that will give Frank and I an extra hour to try to solve Assassins on Thursdays.

Edit. I've now checked my walkthrough and added the final steps that it was too late for last night. I found that I'd been getting careless and missing some clean-ups as early as step 23, which meant that I could insert an extra step shortly after that, so I've just replaced the whole walkthrough rather than editing specific steps.

1. R5C89 = {13}, locked for R5 and N6

2. R5C12 = {27/45}

3. R89C5 = {18/27/36/45}, no 9

4. 10(3) cage in N1 = {127/136/145/235}, no 8,9

5. 21(3) cage in N1 = {489/579/678}, no 1,2,3

6. R123C5 = {127/136/145/235}, no 8,9

7. 22(3) cage at R3C3 = 9{58/67}

8. 6(3) cage at R6C3 = {123}

9. 19(3) cage at R6C8 = {289/379/469/478/568}, no 1

10. 19(3) cage in N7 = {289/379/469/47/568}, no 1

11. 29(4) cage at R6C4 = {5789}
11a. CPE no 5,7,8,9 in R45C5

12. 45 rule on R5 3 outies R4C456 = 8 = 1{25/34}, 1 locked for R4

13. 45 rule on R89 2 outies R7C28 = 9 = {18/27/36/45}, no 9

14. 45 rule on C12 2 outies R28C3 = 9 = [45/54/63/72/81]

15. 45 rule on C89 2 outies R28C7 = 7 = {16/25/34}, no 7,8,9

16. 45 rule on C6789 1 innie R6C9 – 2 = 1 outie R4C5 -> R4C5 = 3, R6C9 = 5, clean-up: no 2 in R4C46 (step 12), no 6 in R89C5

17. Naked pair {14} in R4C46, locked for R4 and N5

18. R123C5 = {127/145} = 1{27/45}, no 6, 1 locked for C5 and N2, clean-up: no 8 in R89C5

19. R5C5 = 6 (hidden single in C5)

20. R67C5 = {89} (hidden pair in C5) -> R6C4 = 7

21. 20(4) cage at R4C5 = {1379/3458} (cannot be {2378} because R4C6 only contains 1,4), no 2
21a. 7 of {1379} must be in R5C7 -> no 9 in R5C7
21b. 4 of {3458} must be in R4C6 -> no 4 in R5C7
21c. 5 of {3458} must be in R5C7 -> no 8 in R5C7

22. R5C4 = 2 (hidden single in N5), clean-up: no 7 in R5C12

23. Naked pair {45} in R5C12, locked for R5 and N4 -> R5C7 = 7 -> R45C6 = [19] (step 21), R4C4 = 4, R5C3 = 8, R67C5 = [89] , clean-up: no 5 in R3C4 (step 7), no 1 in R8C3 (step 14)

24. 2 in 6(3) cage at R6C3 locked in R67C3, locked for C3, clean-up: no 7 in R2C3 (step 14)

25. 21(3) cage in N1 = {489/579/678}
25a. R2C3 only contains 4,5,6 -> no 4,5,6 in R23C2

26. 45 rule on N1 3 innies R1C3 + R3C13 = 14, min R3C3 = 5 -> max R1C3 + R3C1 = 9, no 9

27. 14(3) cage at R3C1 = {167/239/257} (cannot be {149/158/248/347/356} because R4C12 need two of 2,6,7,9), no 4,8
27a. 1,3,5 only in R3C1 -> R3C1 = {135}
27b. R4C12 = {27/29/67}

28. 2 in N1 locked in 10(3) cage = 2{17/35}, no 4,6

29. R1C3 + R3C13 (step 26) = {149/167/356} (cannot be {347} which clashes with 10(3) cage)
29a. 1 of {149/167} must be in R3C1 -> no 1 in R1C3

30. 8 in N1 locked in 21(3) cage = {489/678}, no 5, clean-up: no 4 in R8C3 (step 14)
30a. 8 locked in R23C2, locked for C2, clean-up: no 1 in R7C8 (step 13)
30b. 4 of N1 locked in R12C3, locked for C3

31. 14(3) cage at R8C4 = {158/167/356}, no 9

32. 9 in C3 locked in R34C3 -> no 9 in R3C4, clean-up: no 6 in R34C3 (step 7)

33. 9 in C4 locked in R12C4, 18(3) cage at R1C3 = 9{36/45}, no 7,8
33a. 4 of {459} must be in R1C3 -> no 5 in R1C3

34. R1C3 + R3C13 (step 29) = {149/167/356}
34a. 5 of {356} must be in R3C3 -> no 5 in R3C1
34b. 3 of {356} must be in R3C1 -> no 3 in R1C3

35. 18(3) cage at R1C3 = 9{36/45} (step 33)
35a. 6 of {369} must be in R1C3 -> no 6 in R12C4

36. Hidden killer pair 6,8 in R3C4 and R89C4 -> R89C4 must contain 6/8

37. 14(3) cage at R8C4 (step 31) = {158/167/356}
37a. R89C4 contains 6/8 (step 36) = {16/18/36/56/58}
37b. -> R9C3 = {1357}, no 6
[Alternatively naked pair {46} in R12C3, locked for C3.]

38. 19(3) cage at R6C8 = 19(3) cage at R6C8 = {289/469} (cannot be {379/478/568} because R6C89 needs two of 2,4,6,9) = 9{28/46}, no 3,5,7, 9 locked in R6C89 for R6 and N6
38a. 8 of {289} must be in R7C9 -> no 2 in R7C9

39. 16(3) cage at R3C9 = {259/268/358} (cannot be {169/178/349/367/457} because R4C89 needs two of 2,5,6,8}, no 1,4,7
39a. 9 of {259} and 3 of {358}must be in R3C9 -> no 5 in R3C9
39b. R4C89 cannot be {26} which clashes with R4C12 (step 27b) -> no 8 in R3C9

40. 12(3) cage at R6C1 = {138/156/237} {cannot be {147/345} because R6C12 needs two of 1,2,3,6, cannot be {246} because R6C12 = {26} clashes with R6C789), no 4
40a. 5,7,8 only in R7C1 -> R7C1 = {578}

41. 45 rule on N7 3 innies R7C13 + R9C3 = 12 = {138/237} (only remaining combinations) = 3{18/27}, no 5, 3 locked for N7, clean-up: no 6 in R7C8 (step 13)
41a. 7 of {237} must be in R7C1 -> no 7 in R9C3
41b. 3 locked in R79C3, locked for C3

42. R8C3 = 5 (naked single), R2C3 = 4 (step 14), R1C3 = 6, clean-up: no 2 in R2C7 (step 15), no 4 in R7C8 (step 13), no 3 in R8C7 (step 15), no 4 in R9C5, no 8 in R3C4 (step 7) -> R3C4 = 6
42a. R78C2 = 9 = {27} (only remaining combination), clean-up: R7C8 = {27} (step 13)
42b. Naked pair {27} in R78C2, locked for C2 and N7
42c. Naked pair {27} in R7C28, locked for R7

43. R7C1 = 8 (naked single) -> R6C12 = {13} -> R6C3 = 2

44. Naked pair {89} in R23C2, locked for C2 and N1 -> R4C2 = 6, R3C3 = 7, R4C3 = 9, R4C1 = 7, R3C1 = 1, R6C12 = [31], R9C2 = 4, R5C12 = [45], R1C2 = 3

45. R1C3 = 6 -> R12C4 = 12 = [93], R7C34 = [31], R9C3 = 1, R89C4 = [85], clean-up: no 4 in R8C5, no 4 in R8C7 (step 15)

46. Naked pair {27} in R89C5, locked for C5 and N8
46a. Naked triple {346} in R789C6, locked for C6
46b. Naked pair {27} in R8C25, locked for R8, clean-up: no 5 in R2C7 (step 15)

47. 7 in N2 locked in R12C6 -> 17(3) cage = {278} (only remaining permutation), no 1,4,5 in R1C7

48. Naked pair {16} in R28C7, locked for C7 -> R6C7 = 4, R7C67 = [65], R7C9 = 4, R89C6 = [43], R9C7 = 9, R89C1 = [96]

49. R3C7 = 3 (hidden single in C7)

50. 16(3) cage at R3C9 (step 39) = {259} (only remaining combination) -> R3C9 = 9, R23C2 = [98] , R3C6 = 2, R4C7 = 8, R1C7 = 2, R12C1 = [52], R6C89 = [96]

51. Naked pair {13} in R58C9, locked for C9

52. 14(3) cage at R7C8 = {167} (only remaining combination) -> R7C8 = 7, R78C2 = [27], R89C5 = [27]
51a. Naked pair {16} in R8C78 -> R8C9 = 3, R5C89 = [31]

52. 7 in N3 locked in R12C9, 13(3) cage = 7{15} -> R1C89 = [17], R2C9 = 5

and the rest is naked singles

[CathyW]

No time for a full WT this week as heading to Cornwall for a few days tomorrow, but outies of r5, outies of N5 and outies of c1234 helped to complete N5 early on. Mainly straightforward combo crunching and a couple of killer pairs after that.

[gary w]

Yes,a pretty straightforward one and no combo crunching required.Here's an outline of how I solved it.



1. I-O c1-4 -> r2c4=r5c5+1
2. I-O c6-9 -> r6c6=r4c5+2
3. r4c456=8={134}

Together with 29(4) cage N5 can easily complete N5 as

431
269
785

4. Also r5c3=8 and r7c5=9 r5c12={45}
5. r9c3<>9
6. I N7=12
7. I c12-> r2378=26 <> 1... and r28c3=9 <> {18}
8. Thus 1 in N7 is at r7c13,r9c3.
9. But cannot be 1 at r7c1 as both options {129} and {138} blocked.
The clincher... both remaining options for the 1 in N7 -> R7C1=8.
as the [129} option is blocked and 1 at r7c3->2 at r6c3 and {13} r6c12
10. r7c1=8 -> r6c12={13} and r6c3=2
11. r3c1 now must=1 no other option so 10(3) cage N1={235} -> r4c12={67}
12.8 In n1 is at r23c2
13. The second clincher... the 58 pairs in both N1 and N4 (and not at r34c3)
-> the 22(3) cage N124 <> 9{58} therefore = {967}
14. From 11. above -> r4c3=9 r3c4=6 r3c3=7 r1c3=6

Now just a mop up.

Another very nice killer..thanks Ruud

Regards

Gary

(final version)

[Afmob]

Although this Assassin was "just" of rating 1.0 it kept me busy all day long but it was more my fault since I messed up my walkthrough couple a times so that I hit a dead end.
I used pretty much the same trick as Cathy though without the outies of N5. And Ruud was right about the length of the walkthrough. After the first steps I thought the Assassin was finished but guess I was wrong or maybe my mop-up is not the shortest way.

Assassin 73 Walkthrough:

1. C1234 !
a) Outies C1 = 19(5) = 1{2349/2358/2367/2457/3456} -> 1 locked for C2
b) Outies C12 = 9(2) = [45/54/63/72/81]
c) 29(4) = {5789} -> locked for (N5+C2) -> R45C5 <> 5,7,8,9
d) ! Outies C1234 = 28(1+3) -> 3 of those 4 cells are in 29(4) = {5789}
-> 28(1+3) = R5C5 + R67C5+R6C6 = 28(4) = 89{47/56} (because every cell is related to the other 3 cells)
-> R5C5 = (46)
-> R6C4 <> 8,9 since it must be in R67C5+R6C6

2. C5
a) Innies = 26(4) = {3689/4589/4679/5678} because R5C5 = (46)
-> 26(4) <> {4589} since R45C5 <> 5,8,9
-> 6 locked in Innies = 6{389/479/578} for C5+N5
b) 9(2) <> 3
c) 10(3) = {127/145/235} -> Killer pair (57) blocks {5678} of Innies -> R67C5 <> 5
d) Innies = 26(4) = 69{38/47} -> 9 locked for C5 @ 29(4) -> R6C6 <> 9

3. C6789 !
a) Outies C89 = 7(2) = {16/25/34}
b) ! Outies C6789 = 27(1+3) -> 3 of those cells are in 29(4) = {5789}; R4C5 = (346)
-> 27(1+3) = R4C5 + R67C5+R6C6 = 27(4) = {3789/4689/5679} (every cell relates to the other 3 cells)
-> {4689} impossible because 29(4) <> 4,6 -> 27(4) = 79{38/56}
-> R4C5 = (36)
-> 7 locked @ 29(4) in Outies C6789 -> R6C6 <> 7

4. R456
a) 4(2) = {13} locked for R5+N6
b) 9(2) = {27/45}
c) 5 locked in R6C46 @ 29(4) for R6+N5
d) Outies R5 = 8(3) = {134} since R4C5 = (36)
-> {134} locked for R4+N5
-> R4C5 = 3, R5C5 = 6

5. C6789
a) Outies = 27(4) = {3789} -> R6C4 = 7, R6C6 = 5
b) 20(4) = 3{179/278/458} -> 3{278} impossible because R4C6 = (14)
-> 20(4) = 3{179/458}
-> R5C6 = (57) since it's the only position where they are possible
c) Hidden Single: R5C4 = 2 @ N5

6. N4
a) 20(4) N4 = {2468} -> R4C4 = 4, R5C3 = 8
b) R4C6 = 1, R5C6 = 9, R6C5 = 8, R7C5 = 9
c) 9(2) = {45} locked for R5+N4
d) R5C7 = 7
e) 6(3) = {123} -> 2 locked for C3
f) 14(3): R4C12 = {26/27/29/67} -> R3C1 = (1356)
-> R4C12 = {26} impossible because R3C1 would be 6
-> R3C1 <> 6

7. C245
a) 8 locked in R23C2 for C2 @ 21(3) = 8{49/67}
b) 9(2) @ C5 = {27/45}

8. C123
a) Outies = 9(2) = [45/63]
b) 21(3) must have 4 xor 6 and R2C3 = (46) -> R23C2 <> 4,6
c) 2 locked in 10(3) = 2{17/35}
d) 4,6 locked in R123C3 for C3

9. N6
a) 19(3): R6C89 = {29/46/49/69} -> R7C9 = (469) but R7C9 <> 9 since R7C5 = 9
-> 19(3) = {469}
-> 9 locked for R6+N6; 6 locked for R45C6

10. N47
a) 12(3): R6C12 = {12/13/16/23/26/36}
-> {12} impossible because R7C1 <> 9
-> {36} impossible because R7C1 would be 3
-> R7C1 = (4578)

11. R789
a) Outies R89 = 9(2) = {27/36/45}
b) 1 locked R79C3 for C3
c) 1 locked in 6(3) for R7

12. N4
a) 1 locked in 12(3) = 1{38/56} -> R7C1 = (58)
b) 19(3) <> 5 since {568} blocked by R7C1 = (58)

13. N7 !
a) ! Innies = 12(3) = {138} since they have no 4,6 and R7C1 = (58)
-> R7C1 = 8
-> R79C3 = {13} locked for C3+N7
b) R8C3 = 5, R6C3 = 2
c) 14(3) @ R7C2 = {257} -> {27} locked for C2+N7
d) 14(3) @ R8C4 = 5{18/36} -> R9C4 = 5
-> 14(3) must have 1 xor 3 and R9C3 = (13) -> R8C4 <> 1,3

14. N8
a) Hidden Single: R7C4 = 1
b) R7C3 = 3, R9C3 = 1
c) 14(3) = {158} -> R8C4 = 8

15. N1
a) 21(3) = {489} -> R2C3 = 4
b) 14(3) = {167} since R4C12 <> 3,5 -> R3C1 = 1, R4C1 = 7, R4C2 = 6
c) R6C1 = 3, R6C2 = 1, R4C3 = 9, R3C4 = 6, R3C3 = 7, R1C3 = 6
d) Hidden Single: R1C2 = 3
e) R1C4 = 9, R2C4 = 3
f) Hidden Single: R5C2 = 5 @ C2 -> R5C1 = 4, R9C2 = 4 @ C2

16. R789
a) 9(2) = {27} locked for C5+N8
b) 15(3) = {456} -> R7C7 = 5
c) 16(3) = {349} because R9C = (36) -> R9C7 = 9, R8C6 = 4, R9C6 = 3
d) R9C1 = 6, R8C1 = 9, R7C6 = 6, R6C7 = 4, R7C9 = 4
e) 14(3) @ R7C8 = {167} locked for N9 -> R7C8 = 7
f) R7C2 = 2, R8C2 = 7, R8C5 = 2, R9C5 = 7, R8C9 = 3, R5C9 = 1, R5C8 = 3

17. N3
a) Hidden Single: R3C7 = 3
b) 16(3) = {259} -> R3C9 = 9
c) 18(3) = {468} locked

18. Rest is clean-up and singles.

[gary w]

Hi all,

Let me apologise once again for the awful mess my postings represent this time.Please don't be put off ..I've checked my wt and that seems sound altho' could have worded 1/2 points a little better.

Regards

Gary but also just a hint of