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Assassin 77

 
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Para
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Joined: 08 Nov 2006
Posts: 384
Location: The Netherlands

PostPosted: Fri Nov 16, 2007 12:46 pm    Post subject: Assassin 77 Reply with quote

Hi all

This is an odd puzzle. The opening is very easy, after that i think there's very little places to progress but i think my path probably is the shortest to finish it. For me it's a rating 1.00.

Walk-through Assassin 77

1. 11(3) at R1C1 and R5C1 = {128/137/146/236/245}: no 9

2. R34C1 = {39/48/57}: no 1,2,6

3. R34C9 = {18/27/36/45}: no 9

4. 19(3) at R6C4 and R8C1 = {289/379/469/478/568}: no 1

5. R7C12 and R89C6 = {15/24}: no 3,6,7,8,9

6. R7C89 = {59/68}: no 1,2,3,4,7

7. R89C4 = {69/78}: no 1,2,3,4,5

8. R89C5 = {29/38/47/56}: no 1

9. R9C23 = {19/28/37/46}: no 5

10. R9C78 = {12} -> locked for R9 and N9
10a. Clean up: R8C5: no 9; R8C6: no 4,5; R9C23: no 8,9

11. 45 on N47: 1 outie: R3C1 = 3
11a. R4C1 = 9
11b. 11(3) at R1C1 = {128/146/245}: no 7
11c. 18(3) at R4C2 = {378/468/567}: no 1,2
11c. Clean up: R4C9: no 6

12. 45 on N9: 2 outies: R56C7 = 15 = {69/78}: no 1,2,3,4,5
12a. 45 on N9: 2 innies: R78C7 = 10 = {37/46}: no 5,8,9
12b. 25(4) at R5C7 = {3679/4678} -> 6,7 locked for C7

13. 45 on N7: 2 outies: R56C3 = 7 = {16/25/34}: no 7,8
13a. 45 on N7: 2 innies: R78C3 = 10 = {19/28/37/46}: no 5

14. 45 on C1: 4 outies: R1678C2 = 14 = {1238/1247/1256/1346/2345}: no 9
14a. 9 in N7 locked within R78C3 -> R78C3 = {19} -> locked for C3 and N7
14b. R7C12 = {24}(last combo) -> locked for R7 and N7
14c. R9C23 = {37}(last combo) -> locked for R9 and N7
14d. Clean up: R56C3: no 6; R8C4: no 8; R8C5: no 4,8; R8C7: no 6

15. 45 on R89: 2 innies: R8C37 = 8 = [17]
15a. R7C3 = 9; R7C7 = 3; R89C6 = [24]
15b. R89C4 = {69}(last combo) -> locked for C4 and N8
15c. R89C5 = [38](last combo)
15d. R7C89 = {68}(last combo) -> locked for N9
15e. R56C7 = {69}(last combo) -> locked for C7 and N6

16. 1 in N4 and 7 in C1 locked within 11(3) cage at R5C1 -> 11(3) = {17}[3]; R6C2 = 3; R56C1 = {17} -> locked for C1 and N4
16a. R9C23 = [73]
16b. R56C3 = {25}(last combo) -> locked for C3 and N4

16. 31(5) at R3C2 = {16789/25789/34789/35689/45679}: 9 locked within cage -> R3C2 = 9(only place in cage)

17. 45 on C1234: 3 innies: R167C4 = 8 = {125}/[341]: no 7,8; R1C4: no 4; 1 locked for C4

18. 45 on C6789: 3 innies: R267C6 = 22 = {89}[5]/{69}[7]: no 1,3; R26C6: no 5,7; 9 locked for C6

19. 45 on R6789: 4 outies: R5C1379 = 20 = [1298/1568/7265/7562]: R5C9: no 1,3,4,7

20. 13(3) at R5C9 = [2]{47}/[8]{14}: [5]{17} blocked by R6C1: R5C9: no 5; R6C89: no 2,5,8; 4 locked for R6 and N6
20a. Naked triple {147} in R6C189 -> locked for R6
20b. R6C6 = 8(hidden); R27C6 = [95](step 18); R7C45 = [17]
20c. R16C4 = {25}(last combo from step 17) -> locked for C4
20d. Naked Pair {25} in R6C34 -> locked for R6
20e. Clean up: R3C9: no 5

21. 31(5) at R3C2 = 9{3478}(last combo): no 6; 3 locked within R45C4 for C4 and N5
21a. R1C6 = 3(hidden)

22. 13(3) at R4C6 = {1[5]7}(last combo) -> R4C7 = 5; R45C6 = {17} -> locked for C6 and N5
22a. R3C6 = 6
22b. Naked Pair {34} in R45C4 -> locked for C4, N5 and 31(5) at R3C2
22c. Naked Pair {78} in R3C34 -> locked for R3
22d. Clean up: R3C9: no 4; R4C9: no 1,2,3

23. 20(4) at R1C4 = 9{245}(last combo) -> locked for N2
23a. R3C5 = 1; R34C9 = [27]; R3C78 = [45]; R5C9 = 8;
23b. R7C89 = [86]; R2C9 = 3(hidden); R9C7 = 2(hidden); R9C8 = 1
23d. R6C89 = [41]; R1C9 = 9; R12C8 = [76]; R8C8 = 9; R89C9 = [45]
23d. R89C4 = [69]; R9C1 = 6

24. 11(3) at R1C1 = {128/245}: no 6; 2 locked for N1
24a. R1C3 = 6(hidden)
24b. R2C234 within 22(4) at R1C3 = [547]: [1]{78} blocked by R2C7

And the rest is all naked singles.

greetings

Para


Last edited by Para on Tue Nov 27, 2007 6:14 pm; edited 3 times in total
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goooders
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PostPosted: Fri Nov 16, 2007 3:46 pm    Post subject: Reply with quote

im not sure i agree with paras rating sure the beginning is easy but then it grinds to a halt and becomes horrible is it possible that para is really rather good and cant see the difficulties others may have?
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Afmob
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PostPosted: Fri Nov 16, 2007 5:46 pm    Post subject: Reply with quote

I didn't have any problems with this one at all. Maybe I immediately saw a direct and short solving path?

A77 Walkthrough:

1. C1234
a) Innies N7 = 10(2) <> 5
b) Outies N7 = 7(2) <> 7,8,9
c) Innies N47 = 9 -> R4C1 = 9
d) 12(2) = [39] -> R3C1 = 3
e) 11(3) @ N1 = {128/146/245} -> no 7
f) Innies C1234 = 8(3) = 1{25/34} -> 1 locked for C4
g) 19(3) @ C4 must have 2,3,4 xor 5 and R6C4 = (2345) -> R6C56 <> 2,3,4,5

2. R789
a) 3(2) = {12} locked for R9+N9
b) 6(2): R8C6 <> 4,5
c) 11(2): R8C5 <> 9
d) 10(2) = {37/46}
e) Innies N9 = 10(2) = {37/46}
f) Outies N9 = 15(2) = {69/78}
g) 25(4) = 67{39/48} -> 6,7 locked for C7
h) Innies R89 = 8(2) = [17/26]
i) Innies N7 = 10(2) = [82/91]
j) Innies N9 = 10(2) = [37/46]

3. N89
a) 7 locked in 13(3) @ R7 for N8 = 7{15/24}
b) 15(2) = {69} locked for C4+N8
c) 11(2) = {38} locked for C5
d) Hidden triple (689) in R7C389 @ R7 -> no other candidates
e) 14(2) = {68} locked for R7+N9
f) 18(3) = {459} locked for N9
g) R7C3 = 9, R7C7 = 3, R8C7 = 7
h) Innies N7 = 10(2) = [91] -> R8C3 = 1
i) 6(2) = {24} locked for R7+N7
j) 10(2) = {37} locked for R9+N7
k) R9C5 = 8, R8C5 = 3, R8C6 = 2 -> R9C6 = 4

4. C6789
a) 25(4) = {3679} -> 6,9 locked for C7+N6
b) Innies C6789 = 22(3) = 9{58/67} -> 9 locked for C6
c) Innies C6789 = 22(3) must have 5 xor 7 and R7C6 = (57) -> R26C6 <> 5,7
d) Outies C9 = 27(4) = 9{378/468/567} -> 9 locked for C8

5. N14
a) Innies N4 = 7(2) = {25/34}
b) 7 locked in 11(3) @ C1 -> 11(3) = {137}, R6C2 = 3, {17} locked for C1+N4
c) 17(4) = {1259} -> {25} locked for C3+N4
d) R9C2 = 7, R9C3 = 3
e) 31(5) = 9{1678/2578/3478/3568/4567} -> R3C2 = 9

6. C456
a) 19(3) = 8{29/47/56} because {469} blocked by R6C7 = (69) -> R6C6 = 8
b) Outies C6789 = 22(3) = [985] -> R2C6 = 9, R7C6 = 5
c) R7C4 = 1, R7C5 = 7
d) 19(3) = 8[29/56]
e) Outies C1234 = 8(3) = {125} because R6C4 = (25) -> {25} locked for C4
f) 31(5) = {34789} -> 3 locked for C4+N5
g) 13(3) = {157} because R45C6 = {16/17/67} -> only {17} leads to a combination for 13(3)
-> R4C7 = 5, {17} locked for C6+N5
h) 20(4) = {2459} locked for N1 because R1C4 = (25); 4 locked for C5
i) 12(3) = 1[29/65] -> R3C5 = 1
j) Naked pair (34) locked in R45C4 for 31(5)
k) Naked pair (78) locked in R3C34 for R3
l) R3C6 = 6, R1C6 = 3

7. N3
a) Hidden Single: R1C9 = 9
b) 3 locked in 18(3) = {369} locked; {36} locked for R2
c) 19(4) = 37{18/45} -> R1C8 = 7
d) 19(4) = {1378} -> {18} locked for C7

8. N1
a) 22(4) <> 2 because {2578} impossible since (25) only possible @ R2C2
b) 2 locked in 11(3) = 2{18/45}
c) Hidden Single: R1C3 = 6 @ R1
d) 22(4) = [6547] because 6{178} blocked by R2C7 = (18)
-> R2C2 = 5, R2C3 = 4, R2C4 = 7

9. Rest is singles.

Rating: 1.0, an easy assassin, so Para's estimated rating should fit.


Last edited by Afmob on Sun Nov 25, 2007 10:51 am; edited 2 times in total
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Para
Yokozuna
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Joined: 08 Nov 2006
Posts: 384
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PostPosted: Fri Nov 16, 2007 6:42 pm    Post subject: Reply with quote

goooders wrote:
im not sure i agree with paras rating sure the beginning is easy but then it grinds to a halt and becomes horrible is it possible that para is really rather good and cant see the difficulties others may have?

Check my walk-through. I think you'll have to agree with the way i solved it, it is a 1.00. But as i said there are very few places to progress, but the way i went isn't that hard, just have to see it.

greetings

Para
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gary w
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PostPosted: Sat Nov 17, 2007 1:04 am    Post subject: 77 Reply with quote

I sympathise with goooders.I too started off well and then got stuck for quite a while.Eventually I solved it along lines very similar to Para's wt and found his step 19 to be my crucial break through.
I missed Afmob's move 4d which might have been useful (although re step 6a Afmob why couldn't the 19(3) cage be 829..must have missed something earlier on but can't see what ).
Took me over 3 hours to complete..so I too would rate this as more than 1.0.Be interesting to see what others think.

Regards

Gary
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Para
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PostPosted: Sat Nov 17, 2007 12:21 pm    Post subject: Re: 77 Reply with quote

gary w wrote:
although re step 6a Afmob why couldn't the 19(3) cage be 829..must have missed something earlier on but can't see what )

Check step 1fg
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gary w
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PostPosted: Sat Nov 17, 2007 11:44 pm    Post subject: 77 wt Reply with quote

Thanks Para..I've replied to Afmob.A rather silly oversight (as I had r167c4=8 written down myself) Embarassed
Having missed this move by Afmob which I had all the prelims for ...must stop doing these killers at 2am !!...I have to agree with you two guys that it really wasn't that hard an assassin.So,I'm going to award myself both a Embarassed but also a Smile because it should have come out much quicker for me!
Regards

Gary
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Ruud
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PostPosted: Tue Nov 20, 2007 12:11 am    Post subject: Reply with quote

A77V2



3x3::k:4608:4608:4610:3843:3843:6405:6405:6405:3592:4608:4610:4610:4610:3843:3843:6405:3592:3592:2578:4883:4883:4883:4630:4887:4887:4887:3098:2578:3356:3356:4883:4630:5408:5408:4887:3098:4132:3356:5414:4883:4630:5408:2858:4887:4140:4132:4132:5414:4400:4400:4400:2858:4140:4140:2870:2870:5414:3385:3385:3385:2858:4413:4413:3135:3135:5414:6978:1603:5188:2858:4166:4166:3135:6978:6978:6978:1603:5188:5188:5188:4166:

Without the easy starter and a lot more work.

Ruud
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Andrew
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PostPosted: Tue Nov 20, 2007 1:12 am    Post subject: Reply with quote

I finished A77 late Thursday night, well actually about 1am on Friday but felt it was getting too late to post a walkthrough then. I've only just gone through Para's and Afmob's walkthroughs.

I was going to rate A77 at 1.25 since I felt it was a typical Assassin, admittedly with a fairly easy start, but still in the range covered by 1.25. I'll stick with that rating for the way I solved it. However I missed one important step, see my comment after step 3. Don't know how I missed that, it's so obvious! Embarassed Spotting that ought to have made my solution a bit quicker.

Para wrote:
Check my walk-through. I think you'll have to agree with the way i solved it, it is a 1.00.

I've just done that. As well as spotting his key move, step 19, Para also did a reasonable amount of combination/permutation work so IMHO it's arguable that the rating should be an easier 1.25 rather than 1.0.

I think there has been a tendency recently to rate puzzles down by comparing them with the hardest ones in a rating range, overlooking that each rating value covers a range of difficulty.

gary w wrote:
Took me over 3 hours to complete..so I too would rate this as more than 1.0.Be interesting to see what others think.

Good point Gary. It took me longer, including time to re-work steps when I spotted steps that ought to have gone in earlier.

Here is my walkthrough for A77.

Prelims

a) R34C1 = {39/48/57}, no 1,2,6
b) R34C9 = {18/27/36/45}, no 9
c) R7C12 = {15/24}
d) R7C89 = {59/68}
e) R89C4 = {69/78}
f) R89C5 = {29/38/47/56}, no 1
g) R89C6 = {15/24}
h) R9C23 = {19/28/37/46}, no 5
i) R9C78 = {12}, locked for R9 and N9, clean-up: no 8,9 in R9C23, no 9 in R8C5, no 4,5 in R8C6
j) 11(3) cage in N1 = {128/137/146/236/245}, no 9
k) 11(3) cage in N4 = {128/137/146/236/245}, no 9
l) R6C456 = {289/379/469/478/568}, no 1
m) 19(3) cage in N7 = {289/379/469/478/568}, no 1
n) 31(5) cage at R3C2 must contain 9

1. 45 rule on N47 1 innie R4C1 = 9, R3C1 = 3, clean-up: no 6 in R4C9
1a. 11(3) cage in N1 = {128/146/245}, no 7

2. 45 rule on R89 2 innies R8C37 = 8 = [17/26]/{35}, no 4,8,9, no 6,7 in R8C3

3. 45 rule on C1234 3 innies R167C4 = 8 = 1{25/34}, 1 locked for C4
[At this stage I ought to have seen 45 rule on C6789 3 innies R267C6 = 22 = 9{58/67}, 9 locked for C6.]

4. 45 rule on N7 2 innies R78C3 = 10 = [73/82/91], clean-up: no 3 in R8C7 (step 2)
4a. R56C3 = 7 = {16/25/34}

5. 45 rule on N9 2 innies R78C7 = 10 = [37/46], clean-up: no 3 in R8C3 (step 2), no 7 in R7C3 (step 4)
5a. R56C7 = 15 = {69/78}
5b. R5678C7 = 67{39/48}, 6,7 locked for C7

6. Naked pair {12} in R8C36, locked for R8, clean-up: no 9 in R9C5

7. 19(3) cage in N7 = {469/568} (cannot be {379} because 3,9 only in R8C2, cannot be {478} which clashes with R9C23) = 6{49/58}, no 3,7, 6 locked for N7, clean-up: no 4 in R9C23
7a. 9 of {489} must be in R8C2 -> no 4 in R8C2

8. Naked pair {37} in R9C23, locked for R9, clean-up: no 8 in R8C4, no 4,8 in R8C5

9. 7 in C1 locked in R56C1 -> 11(3) cage in N4 = {137}, locked for N4, clean-up: no 4,6 in R56C3 (step 4a)
9a. R6C2 = 3, R56C1 = {17}, R9C23 = [73]
9b. Naked pair {17} in R56C1, locked for C1, clean-up: no 5 in R7C2

10. Naked pair {25} in R56C3, locked for C3 and N4 -> R8C3 = 1, R7C3 = 9 (step 4), R8C6 = 2, R9C6 = 4, R8C7 = 7 (step 2), R7C7 = 3 (step 5), clean-up: no 8 in R56C7 (step 5a), no 5 in R7C1, no 5 in R7C89, no 4 in R8C1 (step 7), no 8 in R9C4

11. Naked pair {68} in R7C89, locked for R7 and N9

12. R89C5 = [38] (hidden pair in N8)

13. Naked pair {69} in R56C7, locked for C7 and N6

14. Naked pair {69} in R89C4, locked for C4

15. R3C2 = 9 (only remaining cell for 9 in 31(5) cage)

16. 11(3) cage in N1 (step 1a) = {128/146/245}
16a. 1 in {128/146} must be in R1C2 -> no 6,8 in R1C2
16b. R12C1 = {24} would clash with R7C1 -> no 5 in R1C2

17. R6C456 = {289/478/568} (cannot be {469} which clashes with R6C7) = 8{29/47/56} -> R6C6 = 8
17a. R6C4 = {245} -> no 2,4,5 in R6C5
17b. Hidden killer pair 6,9 in R6C5 and R6C7 -> R6C5 = {69}, clean-up: no 4 in R6C4 (step 17)

18. Naked pair {25} in R6C34, locked for R6

19. 4 in R6 locked in R6C89, locked for N6, clean-up: no 5 in R3C9
19a. 13(3) cage in N6 = 4{18/27}, no 3,5
19b. 2,8 only in R5C9 -> R5C9 = {28}

20. 4 in C7 locked in R123C7, locked for N3, clean-up: no 5 in R4C9

21. 45 rule on C9 4 outies R2678C8 = 27 = {3789/4689/5679} = 9{378/468/567}, no 1,2, 9 locked for C8
21a. 4 of {4689} must be in R6C8 -> no 4 in R8C8
21b. 3 of {3789} must be in R2C8, 7 of {5679} must be in R6C8 -> no 7 in R2C8

22. R8C9 = 4 (hidden single in R8)

23. R6C8 = 4 (hidden single in R6)

24. R167C4 (step 3) = {125} (cannot be {134} because 3,4 only in R1C4), 2,5 locked for C4

25. 31(5) cage at R3C2 = {34789} (only remaining combination), no 6
25a. 3 locked in R45C4, locked for C4 and N5
25b. 8 locked in R3C34, locked for R3, clean-up: no 1 in R4C9

26. 13(3) cage at R4C6 = {157/256} = 5{17/26}, no 8,9
26a. CPE no 5 in R4C5

27. Naked quad {1567} in R3457C6, locked for C6

28. Naked pair {39} in R12C6, locked for N2

29. 45 rule on C789 2 outies R13C6 – 4 = 1 innie R4C7
29a. Max R4C7 = 5 -> max R13C6 = 9 -> R1C6 = 3, R2C6 = 9
29b. -> R3C6 – 1 = R4C7 -> R3C6 = 6, R4C7 = 5, clean-up: no 3 in R4C9

30. Naked pair {17} in R45C6, locked for C6 and N5 -> R7C6 = 5, R7C45 = [17]

31. Naked pair {34} in R45C4, locked for C4, N5 and 31(5) cage

32. 20(4) cage in N2 = {2459} (only remaining combination), no 1, locked for N2 -> R3C5 = 1, clean-up: no 8 in R4C9
32a. R45C5 = 11 = [29/65]

33. Naked pair {78} in R3C34, locked for R3 -> R34C9 = [27], R56C9 = [81], R45C6 = [17], R56C1 = [17], R7C89 = [86], R3C78 = [45], R19C9 = [95], R2C9 = 3, R2C8 = 6, R8C8 = 9, R9C1 = 6, R89C4 = [69]

34. Naked pair {18} in R12C7, locked for C7 and N3 -> R9C78 = [21], R1C8 = 7

35. R1C3 = 6 (hidden single in R1)
35a. 22(4) cage at R1C3 = {4567} (cannot be {1678} because R2C234 = {178} clashes with R2C7) -> R2C234 = [547]
[This step could also be done by UR -> R2C3 = 4 but why would anybody use UR when there’s a direct killer move?]

and the rest is naked singles


Last edited by Andrew on Fri Nov 23, 2007 5:46 am; edited 1 time in total
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Para
Yokozuna
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PostPosted: Tue Nov 20, 2007 4:53 pm    Post subject: Reply with quote

Hi all

Here's a walk-through for A77V2. There was so many combination work in the beginning that i wanted to see if i could avoid the 45-test till the end. And i succeeded. So this walk-through doesn't contain a single 45-test.
At least i understand the non-symmetrical cage-pattern now, didn't notice the 77 in the first run.

Walk-through A77V2.

1. R34C1 = {19/28/37/46}: no 5

2. R34C9 = {39/48/57}: no 1,2,6

3. 21(3) at R4C6 = {489/579/678}: no 1,2,3

4. R7C12 = {29/38/47/56}: no 1

5. 27(4) at R8C4 = {3789/4689/5679}: no 1,2

6. R89C5 = {15/24}: no 3,6,7,8,9

7. 11(4) at R5C7 = {1235} -> locked for C7

8. R7C89 = {89} -> locked for R7 and N9
8a. R7C12 = {47/56}: no 2,3
8b. 13(3) at R7C4 = {247/256}: {157/346} blocked by R7C12: no 1,3; 2 locked for R7 and N8
8c. R89C5 = {15}: no 4 -> locked for C5 and N8
8d. 13(3) at R7C4 = {247} -> locked for R7 and N8
8e. R7C12 = {56} -> locked for R7 and N7

9. 12(3) at R8C1 = {129/147/237} = {1|3..},{7|9..}: {138} blocked by R7C3: no 8
9a. Killer Pair {13} in R7C3 + 12(3) at R8C1 -> locked for N7

10. 16(3) at R8C8 = {367/457} = {3|4..},{4|6..}: no 1,2; 7 locked for N9
10a. Killer Pair {46} in 16(3) at R8C8 + R9C7 -> locked for N9

11. 27(4) at R8C4(R89C4-R9C23) = {39}{78}/{68}{49}/{69}{48}: {38}{79} blocked by 12(3) at R8C1; 27(4) needs either a 3 in N8 or a 4 in R9

12. 20(3) at R8C6: combination analysis
12a. {1289} blocked by R9C7
12b. {69}[41] blocked by R7C7({13}) + 16(3) at R8C8({3|4..})
12c. {1568} blocked by R9C5
12d. {2459} blocked by R89C6
12e. {38}[45] blocked by 27(4) at R8C4(has both a 3 in N8 and a 4 in R9)
12f. 20(4) at R8C6 = {39}[62]/{68}[42]: R9C8 = 2

13. 27(4) at R8C4(R89C4-R9C23) = {39}{78}/{68}{49}: {69}{48} blocked by 20(4) at R8C6: R9C23 = {49/78} = {4|7..},{7|9..}
13a. 12(3) at R8C1 = {129/237}: {147} blocked by R9C23: no 4; 2 locked for N7
13b. Killer Pair {79} in 12(3) at R8C1 + R9C23 -> locked for N7

14. 1 in N9 locked for C7
14a. 2 in C7 locked for N6

15. 2 in N3 locked within 14(3) at R1C9: 14(3) = {239/248/257}={7/8/9..}: no 1,6
15a. R123C7 needs at least 2 of {789} because of C7(only other place is R4C7)
15b. R123C7 can have a maximum of 2 of {789} because of 14(3) at R1C9, so R123C7 contains 2 of {789} -> R4C7 = {789}
15c. Killer Triple {789} in R123C7 + 14(3) at R1C9 -> locked for N3
15d. Clean up: R4C9: no 3,4,5

16. 1 in N3 locked for C8
16a. 19(5) at R3C6 = {12349/12358/12367/12457/13456}: 1 locked in R3C68 -> locked for R3
16b. 19(5) at R3C2: 1 locked within R45C4 -> locked for C4 and N5
16c. Clean up: R4C1: no 9

17. 1 in N6 locked within 16(3) cage at R5C9: 16(3) = {169}: {178} blocked by R4C79: {169} -> locked for N6
17a. Naked Pair {78} in R4C79 -> locked for R4 and N6
17b. 4 in N6 locked for C8 and 19(5) at R3C6
17c. 9 in C7 locked for N3
17d. Clean up: 14(3) at R1C9 = {248/257}: no 3; R3C1: no 2,3; R3C9: no 3

18. Killer Pair {45} in 14(3) at R1C9 + R3C9 -> locked for N3
18a. R9C7 = 4(hidden); R8C3 = 4(hidden)
18b. 16(3) at R8C8 = {367} -> locked for N9
18c. R78C7 = [15]; R89C5 = [15]; R7C3 = 3; R9C1 = 1(hidden)
18d. R8C12 = {29}(last combo) -> locked for R8 and N7
18e. R9C23 = {78} -> locked for R9 and 27(4) at R8C4
18f. R8C6 = 8(hidden); R9C6 = 6; R89C4 = [39]; R9C9 = 3
18g. R56C7 = {23} -> locked for N6
18h. R45C8 = {45} -> locked for C8 and 19(5) at R3C6
18i. Naked Quad {6789} in R123C7 + R2C8 -> locked for N3
18j. Clean up: R3C1: no 9

19. 19(5) at R3C6 = [237]{45}/{1[6]3}{45}: no 8,9; R3C6: no 7

20. 21(3) at R4C6 = {4[8]9/5[7]9}: R45C6 = {49/59}: no 7; 9 locked for C6 and N5

21. 15(3) at R1C4 = {1248/1257/1347/1356/2346}: {1239} blocked by R3C6: no 9
21a. R3C5 = 9(hidden)
21b. 18(3) at R3C5 = 9[27]/{36}: no 4,8; R5C5: no 2

22. 17(3) at R6C4 = {278/368}: {458} blocked by R45C6; {467} blocked by R45C5: no 4,5; 8 locked for R6 and N5
22a. Naked Quint {23678} in R45C5 + R6C456 -> locked for N5
22b. Killer Pair {23} in 17(3) at R6C4 + R6C7 -> locked for R6

23. 4 in R6 locked for N4
23a. 5 in R6 locked for N4
23b. 4 in R6 locked within 16(3) at R5C1: 16(3) = [3]{49}/[7]{45}: no 1,2,6,8; R5C1: no 9; R6C12: no 7

24. 21(4) at R5C3 = [95/86]34: R5C3 = {89}; R6C3 = {56}
24a. 7 in R6 locked within 17(3) at R6C4: 17(3) = {278} -> locked for R6 and N5
24b. R56C7 = [23]; R6C9 = 1(hidden)
24c. R45C5 = {36} -> locked for C5

25. 13(3) at R4C2 = {139/238}: no 6,7; 3 locked for C2 and N4
25a. R5C1 = 7
25b. R6C12 = {45}(last combo within 16(3)) -> locked for N4
25c. R6C3 = 6; R6C8 = 9; R5C9 = 6; R7C89 = [89]; R8C89 = [67]
25d. R4C79 = [78]; R45C5 = [63]; R5C3 = 8; R34C1 = [82]
25e. R3C79 = [64]; R2C8 = 7; R4C2 = 3(hidden); R8C12 = [92]; R9C23 = [87]
25f. R45C6 = {59}(last combo within 21(3)) -> locked for C6 and N5
25g. R45C4 = {14} -> locked within C4

26. 25(4) at R1C6 = {1789} -> R1C68 = [71]
26a. R3C8 = 3; R3C2 = 7(hidden); R3C6 = 1(hidden)
26b. R67C6 = [24]; R2C6 = 3; R1C1 = 3(hidden)

27. 15(4) at R1C4 = {246}3 -> R1C4 = 6; R12C5 = {24} -> locked for C5 and N2
27a. R23C4 = [85]; R3C3 = 2; R12C7 = [89]; R6C45 = [78]; R7C45 = [27]

28. 18(3) at R1C1 = 3[96]: R1C2 = 9; R2C1 = 6

And the rest is naked singles.

Solution

Code:
.---------.---------.---------.
| 3  9  5 | 6  4  7 | 8  1  2 |
| 6  4  1 | 8  2  3 | 9  7  5 |
| 8  7  2 | 5  9  1 | 6  3  4 |
:---------+---------+---------:
| 2  3  9 | 1  6  5 | 7  4  8 |
| 7  1  8 | 4  3  9 | 2  5  6 |
| 4  5  6 | 7  8  2 | 3  9  1 |
:---------+---------+---------:
| 5  6  3 | 2  7  4 | 1  8  9 |
| 9  2  4 | 3  1  8 | 5  6  7 |
| 1  8  7 | 9  5  6 | 4  2  3 |
'---------'---------'---------'


greetings

Para


Last edited by Para on Wed Nov 28, 2007 11:37 pm; edited 2 times in total
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Afmob
Expert
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Joined: 22 Sep 2007
Posts: 103
Location: MV, Germany

PostPosted: Thu Nov 22, 2007 9:42 pm    Post subject: Reply with quote

Seems like Para is the only one up til now who made a walkthrough for V2, so I'd like to join him. I used Innies and Outies to crack this one.

A77 V2 Walkthrough:

1. N9
a) 17(2) = {89} locked for R7+N9
b) 16(3) = 7{36/45} -> 7 locked
c) 11(4) = {1235} locked for C7
d) Killer pair (46) locked in 16(3) + R9C7

2. R789
a) Innies R7 = 4(2) = {13} locked for R7
b) Killer pair (25) of 6(2) blocks {256} of 13(3)
c) 13(3) = {247} locked for R7+N8
d) 11(2) = {56} locked for N7
e) 6(2) = {15} locked for C5+N8
f) Innies R89 = 9(2) = [45/72/81]
g) 12(3) <> 8 because {138} blocked by R7C3 = (13)
h) Killer pair (13) locked in 12(3) + R7C3 for N7
i) 12(3) <> 4 because {147} blocked by Killer pair (47) of 27(4)

3. C6789
a) Outies C9 = 30(4) = {6789} locked for C8
b) 14(3): R12C9 <> 8,9 because R2C8 >= 6
c) Innies C6789 = 9(3) <> 7,8,9
d) Innies C6789 = 9(3) = 2{16/34} because R7C6 = (24) -> 2 locked for C6

4. R9+N9
a) 27(4) = 89{37/46} -> R9C6 <> 8,9
b) Killer pair (36) locked in 27(4) + R9C6 for N8
c) 27(4): R9C4 <> 6 because R9C7 = 4 would block {4689}
d) 20(4) = {1469/2369/2468/3458} because R9C67 = {34/36/46}
e) 20(4): R9C8 <> 3 because there is no combo with {346}
f) 20(4) <> {3458} because it's blocked by Killer pair (34) of 27(4)
-> 6 locked for R9
-> no 5 in 20(4)

5. C6
a) Killer pair (36) locked in Innies C6789 + R9C6

6. N47 !
a) Innies = 17(1+2): R4C1 <> 7,8,9 because R9C23 >= 11
b) Innies = 17(1+2): R4C1 <> 6 because R9C23 would be {47} -> not possible in 27(4)
c) 10(2): R3C1 <> 1,2,3,4
d) Innies N4 = 16(3): R56C3 <> 1,2 because R4C1 <= 4
e) Outies N4 = 15(1+2): R3C1 <> 9 because R78C3 <> 2,5 (6(2) impossible)
f) 10(2): R4C1 <> 1
g) Innies = 17(1+2): R4C1 <> 3 because R9C23 <> 5,6 (14(2) impossible)
h) 10(2): R3C1 <> 7
i) ! Outies N4 = 15(1+2): R8C3 <> 7 because R3C1 = (68) -> R78C3 = 7/9(2) = [18/34]

7. R89
a) Innies = 9(2): R8C7 <> 2
b) Hidden Single: R9C8 = 2 @ N9
c) 1 locked R78C7 for C7

8. C789
a) 2 locked in 14(3) for C9 -> 14(3) = 2{39/48/57}
b) 19(5) = {13456} -> R3C7 = 6
c) R3C1 = 8 -> R4C1 = 2
d) 1 locked in 16(3) @ C9(N6) = 1{69/78}
e) 20(4) = {2468} -> R9C7 = 4, R9C6 = 6, R8C6 = 8
f) 16(3) @ N9 = {367}, 3 locked for C9+N9
g) 12(2),14(3) <> 9, R4C9 <> 4

9. N47
a) Innies = 17(1+2): R9C23 = 15(2) = {78} locked for N7+R9 because R4C1 = 2
b) 12(3) = {129} -> R8C2 = 2, {19} locked for C1+N7
c) R7C3 = 3, R8C3 = 4, R7C7 = 1, R8C7 = 5
d) 27(4) = {3789} -> {39} locked for C4

10. C789
a) Naked triple (789) locked in R12C7+R2C8 for N3
b) Killer pair (45) locked in 14(3) + R3C9 for N3
c) 25(4) = 89{17/35} because R1C8 = (13) -> R1C6 <> 1,4; 8 locked for C7
d) 12(2): R4C9 <> 5
e) 16(3) @ N6 = {169} locked for N6 because R4C9 = (78) blocks {178}
f) 21(3) = {579} -> R4C7 = 7, {59} locked for C6+N5
g) 25(4) = {1789} -> R1C6 = 7, R1C8 = 1
h) 19(5) = {13456} -> R3C6 = 1

11. R123
a) 15(4) = {2346} locked for N2
b) R3C4 = 5, R2C4 = 8
c) 18(4) = 8{...} -> no 9
d) 19(5) = 5{...} -> no 9
e) 19(5) = {12457} because R3C3 = (27)
f) Hidden Single: R1C2 = 9 @ N1
g) R2C8 = 7
h) 1 locked in 18(4) @ N1 -> no 2
i) 18(4) must have 3 xor 4 and it's only possible @ R2C2 -> R2C2 = (34)
j) 18(4) must have 5 xor 6 and R1C3 = (56) -> R2C3 <> 5,6

12. C123
a) Killer pair (56) locked in 18(3) + R7C1 for C1
b) 7 locked in 16(3) @ C1 for N4 = 7{36/45}
c) Killer pair (56) locked in 16(3) + 21(4) for N4

13. C5
a) Hidden Single: R4C5 = 6 @ R4
b) 18(3) = {369} locked for C5 because R3C5 = (39)
c) 17(3) = {278} locked for R6+N5

14. Rest is singles.

Rating: It was a bit more difficult than V1 so I estimate rating about 1.25.


Last edited by Afmob on Mon Nov 26, 2007 6:01 am; edited 2 times in total
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Andrew
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Joined: 11 Aug 2006
Posts: 300
Location: Lethbridge, Alberta

PostPosted: Sun Nov 25, 2007 12:17 am    Post subject: Reply with quote

I finished this yesterday but have only just worked through Para's and Afmob's walkthroughs.

We all started pretty much the same way although sometimes finding different reasons for our steps; I think there must be one narrow part of the solving path using the 20(4) and 27(4) cages in R89 to make the first placement. Later innies of N47 seems to be another narrow part although Para must have found a different way that didn't specifically use that. Otherwise there was plenty of scope for different solving paths.

I'm impressed that Para managed to solve this puzzle by deliberately avoiding the 45 rule. However it did mean that he had to work a lot harder after the first placement than those of us who used the 45 rule.

I agree with Afmob's rating of 1.25. Para's route avoiding the 45 rule was probably an easy 1.5.

Here is my walkthrough for A77V2.

Prelims

a) R34C1 = {19/28/37/46}, no 5
b) R34C9 = {39/48/57}, no 1,2,6
c) R7C12 = {29/38/47/56}, no 1
d) R7C89 = {89}, locked for R7 and N9, clean-up: no 2,3 in R7C12
e) R89C5 = {15/24}
f) 21(3) cage at R4C6 = {489/579/678}, no 1,2,3
g) 11(4) cage at R5C7 = {1235}, locked for C7
h) 27(4) cage at R8C4 = 9{378/468/567}, no 1,2, CPE no 9 in R9C6
i) 19(5) cage at R3C2 must contain 1
j) 19(5) cage at R3C6 must contain 1

1. 45 rule on R89 2 innies R8C37 = 9 = [45/63/72/81]

2. 45 rule on R7 2 innies R7C37 = 4 = {13}, locked for R7
2a. 45 rule on R789 4 outies R56C37 = 19, max R56C7 = 8 -> min R56C3 = 11, no 1

3. 2 in R7 locked in R7C456, locked for N8, clean-up: no 4 in R89C5
3a. R7C456 = 2{47/56}

4. Naked pair {15} in R89C5, locked for C5 and N8, clean-up: no 6 in R7C456 (step 3a)

5. Naked triple {247} in R7C456, locked for R7 and N8

6. Naked pair {56} in R7C12, locked for N7, clean-up: no 3 in R8C7 (step 1)

7. 27(4) cage at R8C4 = 89{37/46}, CPE no 8 in R9C6

8. 2 in N7 locked in 12(3) cage = 2{19/37}, no 4,8
8a. Killer pair 1,3 in 12(3) cage and R7C3, locked for N7
8b. 8 in R9 locked in R9C234 -> no 8 in R8C4

9. 16(3) cage in N9 = {367/457} = 7{36/45}, no 1,2, 7 locked for N9
9a. Killer pair 4,6 in 16(3) cage and R9C7, locked for N9

10. 20(4) cage at R8C6 = {1469/2369/2468/3458} (cannot be {1289} because 8,9 only in R8C6, cannot be {1568/2459} because 1,2,5 only in R9C8)
10a. 8,9 only in R8C6 -> R8C6 = {89}
10b. 3 of {2369/3458} must be in R9C6 -> no 3 in R9C8
10c. R45C6 = {89} clashes with R8C6 -> no 4 in R4C7

11. 27(4) cage at R8C4 (step 7) = 89{37/46}
11a. 6 in {4689} must be in R8C4 (R9C24 or R9C34 = [46] clash with R9C7) -> no 6 in R9C4

12. 45 rule on C9 4 outies R2678C8 = 30 = {6789}, locked for C8
12a. Min R2C8 = 6 -> max R12C9 = 8, no 8,9

13. 45 rule on C6789 3 innies R267C6 = 9 = {126/234} (cannot be {135} because R7C6 only contains 2,4) = 2{16/34}, no 5,7,8,9, 2 locked for C6
13a. Killer pair 3,6 in R26C6 and R9C6, locked for C6
13b. Max R6C6 = 6 -> min R6C45 = 11, no 1 in R6C4

14. 25(4) cage at R1C6 = {1789/2689/3589/3679/4579/4678}
14a. 1 of {1789} must be in R1C8 -> no 1 in R1C6

15. 19(5) cage at R3C6 = {12349/12358/12367/12457/13456}
15a. 8 of {12358} must be in R3C7 -> no 8 in R3C6

16. 45 rule on N47 3 innies R4C1 + R9C23 = 17
16a. R9C23 = {4789} = 13, 15 or 16 (cannot be 11 because {47} cannot be in 27(4) cage (step 11), cannot be 12 because no 5 in R4C1) -> R4C1 = {124}, R3C1 = {689}
16b. R9C23 = {49/78/79}, R89C4 = [38/39/68/93] (step 11)
16c. R89C6 cannot be [83] -> 20(4) cage at R8C6 cannot be {3458}, no 5 in R9C8

17. 45 rule on N7 4 innies R78C3 + R9C23 = 22
17a. R9C23 = 13, 15 or 16 (step 16a) -> R78C3 = 6, 7 or 9
17b. R78C3 = [18/34] (cannot total 6), clean-up: no 2 in R8C7 (step 1)
17c. R9C23 = {49/78}, R89C4 = [39/68/93]

18. R9C8 = 2 (hidden single in N9)
18a. 1 in N9 locked in R78C7, locked for C7
18b. 2 in C7 locked in R56C7, locked for N6

19. 45 rule on C1234 3 innies R167C4 = 15 = {249/258/267/348/357/456} (cannot be {159/168} because R7C4 only contains 2,4,7), no 1

20. 19(5) cage at R3C6 (step 15) = {13456} (only remaining combination) -> R3C7 = 6, R9C7 = 4, clean-up: no 4 in R4C1, no 9 in R9C23 (step 17c), no 5 in R89C9 (step 9)
20a. 3 in 19(5) cage locked in R345C8, locked for C8
20b. 20(4) cage at R8C6 (step 10) = {2468} -> R89C6 = [86], clean-up: no 1 in R26C6 (step 13)

21. R8C7 = 5 (hidden single in N9) -> R89C5 = [15], R8C3 = 4
21a. R7C7 = 1 (hidden single in N9), R7C3 = 3, clean-up: no 7 in 12(3) cage (step 8)

22. R9C1 = 1 (hidden single in R9) -> R4C1 = 2, R3C1 = 8, R8C12 = [92], R89C4 = [39], clean-up: no 4 in R4C9

23. R9C9 = 3 (hidden single in R9), clean-up: no 9 in R34C9

24. R78C3 = 7 -> R56C3 = 14 = {59/68}, no 7

25. R3C6 = 1 (hidden single in C6)
25a. R1C8 = 1 (hidden single in C8), R3C8 = 3 (hidden single in N3)
25b. 25(4) cage at R1C6 (step 14) = {1789} (only remaining combination), no 4,5
25c. 8 locked in R12C7, locked for C7 and N3

26. Naked triple {789} in R12C7 and R2C8, locked for N3, clean-up: no 5 in R4C9

27. Naked triple {245} in R123C9, locked for C9

28. 2 in N3 locked in 14(3) cage = {257} (only remaining combination) -> R2C8 = 7, R8C89 = [67], R4C9 = 8, R3C9 = 4, R7C89 = [89], R6C8 = 9, R4C7 = 7, clean-up: no 5 in R5C3 (step 24)

29. R1C6 = 7 (hidden single in C6)

30. Naked triple {234} in R267C6, locked for C6
30a. Naked pair {59}, locked for N5

31. 5 in R6 locked in R6C123, locked for N4

32. 5,7 in R3 locked in R3C234 for 19(5) cage = {12457} (only remaining combination), no 7 in R5C4

33. Naked triple {257} in R3C234, locked for R3 and 19(5) cage -> R3C5 = 9

34. Naked pair {14} in R45C4, locked for C4 and N5

35. Naked pair {23} in R6C67, locked for R6

36. 4 in R6 locked in R6C12, locked for N4
36a. 16(3) cage = {457} (only remaining combination) -> R5C1 = 7
36b. Naked pair {45} in R6C12, locked for R6, clean-up: no 9 in R5C3 (step 24)

37. Naked pair {68} in R56C3, locked for C3 and N4 -> R9C23 = [87]

38. R3C2 = 7 (hidden single in R3)

39. R3C5 = 9 -> R45C5 = 9 = {36}
39a. Naked pair {36} in R45C5, locked for C5 and N5 -> R6C6 = 2, R27C6 = [34], R56C7 = [23]

40. 4 in C5 locked in R12C5, 15(4) cage at R1C4 = {2346} (only remaining combination) -> R1C4 = 6
40a. Naked pair {24} in R12C5, locked for C5 and N2 -> R7C45 = [27], R6C45 = [78], R56C3 = [86], R56C9 = [61], R45C5 = [63], R3C34 = [25], R2C4 = 8, R12C7 = [89]

41. R4C2 = 3 (hidden single in R4), R1C1 = 3 (hidden single in R1)
41a. R1C2 + R2C1 = 15 = [96]

and the rest is naked singles
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