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 Post subject: Assassin 122
PostPosted: Thu Sep 25, 2008 9:36 pm 
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Grand Master
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Apart from the remote cage that I had to put in for reasons of difficulty, this Killer came out just right. Like A116 this is also a concept Killer though there is no symbol used here but if you want you can look for hidden signs. :lol:

And don't listen to the software rating (JSudoku has problems with A122, too)! This one can be solved in a matter of seconds (though minutes is more realistic).

Assassin 122

Image
Note the remote cage R2378C5 = 13(4)

3x3:d:k:5120:5120:5120:4355:4355:4355:7942:7942:7942:5120:4106:5131:5131:3341:5134:5134:2320:7942:5120:3859:4106:5131:3341:5134:2320:2329:7942:5659:3859:3859:4106:6175:2320:2329:2329:5155:5659:1829:1829:6175:6175:6175:3882:3882:5155:5659:2094:2094:5424:6175:4658:3123:3123:5155:6966:2094:5424:4409:3341:2875:4658:3123:4670:6966:5424:4409:4409:3341:2875:2875:4658:4670:6966:6966:6966:3915:3915:3915:4670:4670:4670:

Solution:

1 2 9 4 6 7 8 5 3
3 4 8 9 1 5 7 2 6
5 6 7 3 2 8 1 4 9
9 8 1 5 4 6 2 3 7
7 3 4 2 8 1 6 9 5
6 5 2 7 9 3 4 1 8
8 1 5 6 3 2 9 7 4
2 9 3 8 7 4 5 6 1
4 7 6 1 5 9 3 8 2


SS Score: 1.63
Estimated rating: 1.0

A tougher version with perfect symmetry will be posted on Sunday.


Last edited by Afmob on Sun Sep 28, 2008 12:05 am, edited 2 times in total.

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 Post subject: Re: Assassin 122
PostPosted: Fri Sep 26, 2008 2:30 am 
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Grand Master
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Posts: 302
Location: Sydney, Australia
It seems these days the common goal is to attack the weakness of JSudoku... :ugeek:

No time to write a complete walkthrough, but here is the most critical step right at the start:


Critical step:
Overlaps @ r19c19: r19c19=10={1234}
(r19c19=r1+r9+c1+c9-(20+17+31+22+20+27+15+18)=45*4-170=10)
Innies @ d\: \159=11
Innies @ d/: /159=15
Overlaps @ d\/: r5c5=8 (NE @ d\/)
(\159+/159=r19c19+r5c5*2, r5c5=(11+15-10)/2=8)
=> \19=11-8=3={12} (NP @ d\)
=> /19=15-8=7={34} (NP @ d/)
Innie-outies @ n7: r6c6=r7c2+r8c3+3
=> Min r6c6=1+2+3=6

Afterwards the puzzle is dead easy.
Next week you'll get an assassin with a similar cage layout, but I'm sure it's just a pure coincidence! :alien:

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 Post subject: Re: Assassin 122
PostPosted: Fri Sep 26, 2008 5:56 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Afmob wrote:
... but if you want you can look for hidden signs
When I coloured the cages, the pattern looked like a flower.

Afmob wrote:
This one can be solved in a matter of seconds (though minutes is more realistic).
I assume you mean that the breakthrough can be achieved in that time. Congratulations to everyone who does that! Unfortunately I didn't. It took me about 2 hours until I eventually spotted the breakthrough and then about another hour to complete my walkthrough. Still I'm not a quick solver.

I'm surprised at the SS rating. I'll rate A122 at 1.25 the way I solved it. If one gets the breakthrough move early then it's probably Hard 1.0.

Here is my walkthrough. I've left the breakthrough move where I found it. Some of my earlier moves were interesting and might possibly be useful for Afmob's harder version.

Prelims

a) R5C23 = {16/25/34}, no 7,8,9
b) R5C78 = {69/78}
c) 20(3) cage at R2C3 = {389/479/569/578}, no 1,2
d) 20(3) cage at R2C6 = {389/479/569/578}, no 1,2
e) 9(3) diagonal cage at R2C8 = {126/135/234}, no 7,8,9
f) 9(3) cage at R3C8 = {126/135/234}, no 7,8,9
g) R456C1 = {589/679}, 9 locked for C1 and N4
h) R456C9 = {569/578} (cannot be {389/479} which clash with R5C78), 5 locked for C9 and N6
i) 8(3) cage at R6C2 = {125/134}, CPE no 1 in R45C2, clean-up: no 6 in R5C3
j) 21(3) diagonal cage at R6C4 = {489/579/678}, no 1,2,3
k) 11(3) cage at R7C6 = {128/137/146/236/245}, no 9
l) 13(4) remote cage at R2C5 = {1237/1246/1345}, no 8,9, 1 locked for C5
m) 31(5) cage in N3 = {16789/25789/34789/35689/45679}, 9 locked for N3
n) 18(5) cage in N9 = {12348/12357/12456}, 1,2 locked for N9

1. Naked quint {56789} in R5C78 and R456C9, locked for N6

2. 45 rule on C1234 3 innies R159C4 = 7 = {124}, locked for C4
2a. Max R1C4 = 4 -> min R1C56 = 13, no 1,2,3,4 (because R1C456 cannot be 4{49})
2b. Max R9C4 = 4 -> min R9C56 = 11, no 1 in R9C6

3. 45 rule on N4 2 outies R37C2 = 7 = {25/34}/[61], no 1,7,8,9 in R3C2

4. 45 rule on N6 2 outies R37C8 = 11 = [29/38/47/56/65], no 1 in R3C8, no 3,4 in R7C8

5. 45 rule on D\ 3 innies R1C1 + R5C5 + R9C9 = 11 = {128/137/146/236/245}, no 9

6. 45 rule on N2 2 outies R2C37 = 2 innies R23C5 + 12
6a. Min R23C5 = 3 -> min R2C37 = 15, no 3,4,5, no 6 in R2C7
6b. Max R2C37 = 17 -> max R23C5 = 5, no 5,6,7

7. 45 rule on N3 4 innies R23C78 = 14 = {1238/1247/1256/1346} (cannot be {2345} because R2C7 only contains 6,7,8), 1 locked in R2C8 + R3C7, locked for N3 and D/
7a. 6 of {1256/1346} must be in R2C7 -> no 6 in R2C8 + R3C78, clean-up: no 5 in R7C8 (step 4)
7b. 1 in C9 locked in R789C9, locked for N9
7c. 9(3) cage at R3C8 = {135/234}, CPE no 3 in R6C8

8. 9(3) diagonal cage at R2C8 = {126/135}, no 4
8a. 6 of {126} must be in R4C6 -> no 2 in R4C6

9. 45 rule on N8 4 outies R23C5 + R8C37 = 11
9a. Min R23C5 = 3 -> max R8C37 = 8, no 6,7,8,9 in R8C3, no 8 in R8C7

10. 45 rule on N7 1 outie R6C4 = 2 innies R7C2 + R8C3 + 3
10a. Min R7C2 + R8C3 = 3 -> min R6C4 = 6

11. 11(3) cage at R7C6 = {137/146/236/245} (cannot be {128} because no 1,2,8) in R8C7), no 8

12. Hidden killer pair 8,9 in R78C4 and R9C56 for N8, neither can have both of 8,9 -> each must contain one of 8,9
12a. R9C456 = {159/168/249/258/348} (cannot be {267/357/456} which don’t contain 8 or 9), no 7

13. 45 rule on N1 2 innies R2C3 + R3C2 = 1 outie R4C4 + 9
13a. Min R4C4 = 3 -> min R2C3 + R3C2 = 12, no 2 in R3C2, clean-up: no 5 in R7C2 (step 3)
13b. Max R2C3 + R3C2 = 15 -> max R4C4 = 6

14. Hidden killer pair 7,8 in R456C1 and R4C23 for N4 -> R4C23 must contain one of 7,8
14a. 15(3) cage at R3C2 = {168/258/267/348/357} (cannot be {456} which doesn’t contain 7 or 8)
14b. 6 of {168/267} must be in R3C2 -> no 6 in R4C23

15. 45 rule on N5 4 innies R46C46 = 21 = {1569/2568/3459/3468/3567} (other combinations don’t contain at least two of 3,5,6)
15a. 1,2 of {1569/2568} must be in R6C6, 8,9 of {3459/3468} must be in R6C4 -> no 8,9 in R6C6

16. Hidden killer quad 1,2,3,4 in R1C4 + R23C5 + R23C46 for N2 -> R23C46 must contain 3 or 4 -> one of 20(3) cage at R2C3 + 20(3) cage at R2C6 must contain {389/479} and the other must contain {569/578} -> 5 locked in R23C46, locked for N2

17. 45 rule on N3 3 outies R4C678 = 1 innie R2C7 + 4
17a. Min R2C7 = 6 -> min R4C678 = 10, max R4C78 = 7 -> no 3 in R4C6 (because R4C678 cannot be 3{34})
17b. 9(3) diagonal cage at R2C8 (step 8) = {126/135}
17c. 5 of {135} must be in R4C6 -> no 5 in R2C8 + R3C7

18. 45 rule on N1 4 innies R23C23 = 25 = {2689/3589/3679/4579/4678} (cannot be {1789} because no 7,8,9 in R3C2), no 1

Only just spotted an important step!
19. 45 rule on R1 + R9 + C1 + C9 4 innies R19C19 = 10 = {1234} (because total of the outside cages = 170 and is the only combination because R19C19 are common peers)

20. 45 rule on D/ 3 innies R1C9 + R5C5 + R9C1 = 15 = {348} (only remaining combination, cannot be {258/267/357/456} which only contain one of 2,3,4) -> R5C5 = 8, locked for D/ and D\, R1C9 + R9C1 = {34}, locked for D/, CPE no 3,4 in R1C1 + R9C9, clean-up: no 5 in R4C6 (step 8), no 7 in R5C78
20a. Naked pair {12} in R1C1 + R9C9, locked for D\
20b. R4C6 = 6, locked for D/
20c. Naked pair {69} in R5C78, locked for R5 and N6, clean-up: no 1 in R5C3
20d. Naked triple {578} in R456C9, locked for C9
20e. Naked triple {579} in 21(3) diagonal cage at R6C4, 5 locked for N7
20f. Naked pair {12} in R2C8 + R3C7, locked for N3, clean-up: no 9 in R7C8 (step 4)

21. Naked pair {57} in R5C19, locked for R5, clean-up: no 2 in R5C23
21a. Naked pair {34} in R5C23, locked for R5 and N4

22. R5C456 = {128} = 11 -> R46C5 = 13 = {49} (only remaining combination), locked for C5 and N5 -> R6C4 = 7
22a. Naked pair {59} in R7C3 + R8C2, locked for N7
22b. Naked pair {35} in R4C4 + R6C6, locked for D\

23. 13(4) remote cage at R2C5 (prelim l) = {1237} (only remaining combination), locked for C5, 7 locked in R78C5 for N8
23a. R1C5 = 6 -> R1C46 = 11 = [29/47], no 1 in R1C4, no 8 in R1C6
23b. R9C5 = 5 -> R9C46 = 10 = [19/28], no 4 in R9C4, no 2,3,4 in R9C6
23c. R1C4 = 4 (hidden single in C4), R1C6 = 7 (step 23a), R1C9 = 3, locked for D/ -> R9C1 = 4, clean-up: no 8 in R2C7 (step 7), no 3 in R3C2 (step 3), no 8 in R7C8 (step 4)

24. R6C1 = 6 (hidden single in N4), R45C1 = [97] (prelim g), R5C9 = 5, R46C9, = [78], R46C5 = [49]
24a. 8 in R4 locked in R4C23 -> 15(3) cage at R3C2 = {168/258}, no 4, clean-up: no 3 in R7C2 (step 3)
24b. 5 of {258} must be in R3C2 -> no 5 in R4C23
24c. 5 in N4 locked in R6C23, locked for R6 -> R6C6 = 3, R4C4 = 5

25. 20(3) cage at R2C3 = {389} (step 16), 3 locked in R23C4, locked for C4 and N2
25a. Naked pair {12} in R23C5, locked for C5

26. R2C7 = 7 (hidden single in N3), clean-up: no 9 in R23C6 (prelim d)
26a. Naked pair {58} in R23C6, locked for C6 and N2 -> R9C6 = 9, R9C4 = 1 (step 23b), R9C9 = 2, locked for D\, R1C1 = 1, R5C46 = [21]
26b. Naked pair {39} in R23C4, locked for C4 and 20(3) cage -> R2C3 = 8, R23C6 = [58]

27. Naked quad {2359} in R1C23 + R23C1, locked for N1 -> R3C2 = 6, R2C2 = 4, R3C3 = 7, both locked for D\, R5C23 = [34]

28. 2 in R1 locked in R1C23, locked for N1 -> R23C1 = [35], R23C4 = [93], R2C9 = 6, R3C89 = [49], R7C8 = 7 (step 4), R78C5 = [37]

29. Naked triple {124} in R7C269, locked for R7 -> R78C1 = [82]

and the rest is naked singles.


Last edited by Andrew on Fri Oct 03, 2008 9:37 pm, edited 1 time in total.

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 Post subject: Re: Assassin 122
PostPosted: Fri Sep 26, 2008 8:58 pm 
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Joined: Fri Aug 08, 2008 5:35 pm
Posts: 61
Location: UK
Thank you Afmob! A new first for me:
Hidden Text:
the first time I've found for myself one of these perimeter-sum tricks and got it to work[[hide]

Indeed it's such a pure example of this, it should be archived as a demo for learners.
Though fond of sashimi in real life, I've found it hard to get the hang of these various fishy techniques in samunamu. Since different techniques suit different players, 'objective' measures of difficulty are likely to seem counter-intuitive to some players. I suspect there are too many dimensions of difficulty for a single linear scale.

cheers

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 Post subject:
PostPosted: Sun Sep 28, 2008 12:05 am 
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Grand Master
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
This Killer has an easy start but it gets tougher as you progress. Have fun with it and don't think that (only) the cracking move from V1 will solve it for you!

Assassin 122 V1.5

Image
Note that there is no remote cage. :mrgreen:

3x3:d:k:6912:6912:6912:3843:3843:3843:6918:6918:6918:6912:2314:3083:3083:3085:4878:4878:3088:6918:6912:5395:2314:3083:3085:4878:3088:2841:6918:2587:5395:5395:2314:5919:3088:2841:2841:2851:2587:3365:3365:5919:5919:5919:4138:4138:2851:2587:3118:3118:5168:5919:4658:3635:3635:2851:5430:3118:5168:4409:2618:3387:4658:3635:6974:5430:5168:4409:4409:2618:3387:3387:4658:6974:5430:5430:5430:3915:3915:3915:6974:6974:6974:

Solution:

7 2 4 8 1 6 5 9 3
9 1 6 2 5 3 7 4 8
5 8 3 4 7 9 1 6 2
1 4 9 5 8 7 2 3 6
6 5 8 3 2 1 9 7 4
3 7 2 6 9 4 8 5 1
2 3 5 9 4 8 6 1 7
4 9 7 1 6 2 3 8 5
8 6 1 7 3 5 4 2 9


SS Score: 1.84
Estimated rating: 1.25 - (Hard) 1.25


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 Post subject: Re: Assassin 122
PostPosted: Sun Sep 28, 2008 2:19 am 
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Funny fact about V2. Remove the diagonals and it scores lower in SudokuSolver.


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 Post subject: Re: Assassin 122
PostPosted: Mon Sep 29, 2008 10:45 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
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Thanks Afmob for a nice variant. As you say there is more work after the cracking move for V1 and its logical extension which gives the first placement.

I'll rate A122 V1.5 at 1.25. Maybe that's a bit high but I'll stick with it because of the I-O work on the four corner nonets.

Here is my walkthrough. I've given eliminations on the diagonals; it's so easy for those of us doing manual eliminations to overlook them.

Prelims

a) R23C5 = {39/48/57}, no 1,2,6
b) R5C78 = {79}, locked for R5 and N6
c) R5C23 = {58} (only remaining combination), locked for R5 and N4
d) R78C5 = {19/28/37/46}, no 5
e) 9(3) diagonal cage at R2C2 = {126/135/234}, no 7,8,9
f) 19(3) cage at R2C6 = {289/379/469/478/568}, no 1
g) 21(3) cage at R3C2 = {489/579/678}, no 1,2,3
h) 11(3) cage at R3C8 = {128/137/146/236/245}, no 9
i) R456C1 = {127/136}, no 4,9, 1 locked for C1 and N4
j) 20(3) diagonal cage at R6C4 = {389/479/569/578}, no 1,2

1. 45 rule on R1 + R9 + C1 + C9 4 innies R19C19 = 27 = {3789/4689/5679} (because total of the outside cages = 153 and the combinations apply because R19C19 are common peers), no 1,2

2. 45 rule on D/ and D\, (90-86)/2 (because the centre cell is on both diagonals) -> R5C5 = 2, locked for D/ and D\, clean-up: no 4,6 in 9(3) diagonal cage at R2C2 (prelim e), no 8 in R78C5
2a. Naked triple {135} in 9(3) diagonal cage at R2C2, locked for D\

3. 45 rule on D\, 2 remaining innies R1C1 + R9C9 = 16 = {79}, locked for D\, CPE no 7,9 in R1C9 + R9C1
3a. R1C9 + R9C1 = 27-16 = 11 = {38/56}, no 4
3b. 1 on D/ locked in 12(3) diagonal cage at R2C8 = {138/147/156}, no 9

4. 21(3) cage at R3C2 = {489/579} (cannot be {678} which clashes with R456C1), no 6
4a. 5,8 only in R3C2 -> R3C2 = {58}
4b. 9 locked in R4C23, locked for R4 and N4
4c. Naked pair {58} in R35C2, locked for C2

5. 45 rule on N4 2 outies R37C2 = 11 = [56/83]
5a. 12(3) cage at R6C2 = {237/246}, 2 locked in R6C23, locked for R6 and N4, clean-up: no 7 in R46C1 (prelim i)
5b. Naked triple {136} in R456C1, locked for C1 and N4, clean-up: no 5,8 in R1C9 (step 3a)

6. 45 rule on N2 2 outies R2C37 = 13 = {49/58/67}, no 1,2,3

7. 45 rule on N6 2 outies R37C8 = 7 = {16/25/34}

8. 45 rule on N8 2 outies R8C37 = 10 = {19/28/37/46}, no 5

9. R456C9 = {128/146/245}, (cannot be {236} which clashes with R1C9), no 3
9a. 2 of {128/245} must be in R4C9 -> no 5,8 in R4C9

10. 14(3) cage at R6C7 = {158/248/356}
10a. 2 of {248} must be in R7C8 -> no 4 in R7C8, clean-up: no 3 in R3C8 (step 7)

11. 45 rule on N9 1 outie R6C6 = 2 innies R7C8 + R8C7
11a. Max R6C6 = 8 -> Max R7C8 + R8C7 = 8, no 8,9 in R8C7, clean-up: no 1,2 in R8C3 (step 8)

12. 45 rule on N1 2 innies R2C3 + R3C2 = 1 outie R4C4 + 9
12a. R2C3 + R3C2 cannot total 10 -> no 1 in R4C4
12b. 1 on D\ locked in R2C2 + R3C3, locked for N1
12c. R4C4 = {35} -> R2C3 + R3C2 = 12,14 = [48/75/68/95], no 5,8 in R2C3, clean-up: no 5,8 in R2C7 (step 6)

13. 45 rule on R1234 3 innies R4C159 = 15 = {168/267/348/456} (cannot be {258} because R4C1 only contains 1,3,6, cannot be {357} because no 3,5,7 in R4C9)
13a. 5,7,8 only in R4C5 -> R4C5 = {578}

14. 45 rule on R6789 3 innies R6C159 = 13 = {139/148/157/346}
14a. 9 of {139} must be in R6C5, 1 of {148/157} must be in R6C1 -> no 1 in R6C5
14b. 7 of {157} must be in R6C5 -> no 5 in R6C5

15. 45 rule on C1234 3 innies R159C4 = 18 = {189/369/378/459/468/567} (cannot be {279} because R5C4 doesn’t contain 2,7,9), no 2
15a. 1 of {189} must be in R5C4 -> no 1 in R19C4

16. 2 in N1 locked in 27(5) cage = {24579/24678} (cannot be {23589} which clashes with R3C2, cannot be {23679} which clashes with R1C9), no 3, 4,7 locked for N1, clean-up: no 6,9 in R2C7 (step 6)

17. Hidden pair {13} in N1 -> R4C4 = 5 (step 2a)

18. 12(3) cage at R2C3 = {129/246} (cannot be {138/147/237} because R2C3 only contains 6,9), no 3,7,8, 2 locked in R23C4, locked for C4 and N2
18a. R2C3 = {69} -> no 6,9 in R23C4

19. 19(3) cage at R2C6 = {379/469/478} (cannot be {568} because R2C7 only contains 4,7), no 5

20. 45 rule on N3 2 innies R2C7 + R3C8 = 1 outie R4C6 + 6
20a. Max R2C7 + R3C8 = 13 -> max R4C6 = 7
20b. R2C7 + R3C8 cannot total 7 -> no 1 in R4C6
20c. Min R4C6 = 3 -> min R2C7 + R3C8 = 9, no 1 in R3C8, clean-up: no 6 in R7C8 (step 7)
20d. No 5 in R4C6 -> R2C7 + R3C8 cannot total 11 -> no 4 in R3C8, clean-up: no 3 in R7C8 (step 7)

21. 12(3) diagonal cage at R2C8 (step 3b) = {138/147/156}, 1 locked in R2C8 + R3C7, locked for N3
21a. 3,6 of {138/156} must be in R4C6 -> no 3,6 in R2C8 + R3C7

22. 1 in R1 locked in R1C456, locked for N2
22a. Naked pair {24} in R23C4, locked for C4 and N2, R2C3 = 6 (step 18), R2C7 = 7 (step 6), R5C78 = [97], R3C2 = 8 (step 12c), R5C23 = [58], R7C2 = 3 (step 5), R2C2 = 1, R3C3 = 3, clean-up: no 8,9 in R2C5, no 5 in R3C5, no 8,9 in R2C6, no 6 in R3C6 (both step 19), no 7 in R4C23 (step 4), no 4 in R6C23 (step 5a), no 7 in R8C5, no 2,4 in R8C7 (step 8)
22b. R23C6 = [39], R23C5 = [57], R4C5 = 8, clean-up: no 8 in R2C8 (step 3b), no 3 in R8C5
22c. R2C8 = 4, R3C7 + R4C6 = [17] (step 3b), 4,7 locked for D/, R23C4 = [24], R2C19 = [98], R1C1 = 7, locked for D\, R9C9 = 9, clean-up: no 9 in R8C3 (step 8)
22d. Naked triple {168} in R1C456, locked for R1 -> R1C9 = 3, locked for D/, R9C1 = 8 (step 3a)

23. 9 in N7 locked in R7C3 + R8C2, locked for D/ -> R6C3 = 6, R8C2 = 9, R7C3 = 5, R56C6 = [14], R5C4 = 3, R6C5 = 9

24. 45 rule on N3 1 remaining innie R3C8 = 6, R7C8 = 1 (step 7), R8C8 = 8, R78C7 = [63]

and the rest is naked singles.

Para wrote:
Funny fact about V2. Remove the diagonals and it scores lower in SudokuSolver.
That surprises me. It must be something about the order of doing moves. It looks to me as if it would make this puzzle much harder because it takes away the second part of step 1 and also takes away steps 2 and 3.


Last edited by Andrew on Fri Oct 03, 2008 9:42 pm, edited 1 time in total.

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 Post subject: Re: Assassin 122
PostPosted: Thu Oct 02, 2008 7:31 am 
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Para wrote:
Funny fact about V2. Remove the diagonals and it scores lower in SudokuSolver.

I suspect if you put the priority of the "overlaps" techniques (provided they're there) higher it would score much lower with diagonals.

Meanwhile, here is my walkthrough for the "non-diagonal" version. I don't think it's that much harder than the one using diagonals (see Andrew's walkthrough above) but you need to think "instinctively/intuitively" and think outside of the way a computer thinks to appreciate my tricks.

My walkthrough for Assassin 122 v1.5 without diagonals:
1.
16/2 @ r5c7={79} (NP @ r5,n6)
13/2 @ r5c2 from {4568}={58} (NP @ r5,n4)
21/3 @ r3c2={489|579|678} must have 5|8
=> r3c2 must be from {58} (only cell for 21/3)
=> r35c2={58} (NP @ c2)
Outies @ n4: r37c2=11=[56|83]
12/3 @ r6c2 can't have both of {36}
=> r6c23 can't have {36}
=> 3 @ c1,n4 locked @ 10/3 @ r4c1={136} (NT @ c1,n4)
=> 21/3 @ r3c2=[5{79}|8{49}] (9 @ r4,n4 locked @ r4c23)

2.
Outies @ n8: r8c37=10={19|28|37|46} can't have 5
Innie-outies @ n9: r7c8+r8c7=r6c6 (max value=9)
=> r7c8+r8c7 can't have 9
=> r8c3=10-r8c7 can't be 1
20/3 @ r6c4 can't have 1|2
Innie-outies @ n7: r6c234=r8c3+8 can't be 13={247}
=> r6c4 can't be 4|7, must be from {35689}
Innie-outies @ n7: r7c2+r8c3=r6c4+4=7|9|10|12|13
=> r7c2+r8c3 can't be [32|62|38|68]
=> r8c3 can't be 2|8, must be from {34679}
Innies @ n7: r78c23=24 from {3456789} must have 5|8
(subtraction combo: {34679} can't make 24/4)
=> r7c3 must be from {58} (only cell for r78c23)
=> r57c3={58} (NP @ c3)

3.
Cell cloning: r5c23 & r57c3 both are {58}
=> r5c2=r7c3
Now r357c2=[586|853]
=> r7c23=[35|68]
But r8c37=10
=> r8c23 can't sum to 10
=> r7c23=24-r8c23 can't be [68]=14, must be [35]
=> 12/3 @ r6c2: r6c23=12-3=9={27} (NP @ r6,n4)
=> r8c23=24-3-5=16={79} (NP @ r8,n7)
=> r789c1={248} (NT @ c1,n7)
=> r123c1={579} (NT @ n1)
=> 27/5 @ r1c1: r1c23=27-5-7-9=6={24} (NP @ r1,n1)

4.
Outies @ n2: r2c37=13=[67]
=> 9/3 @ r2c2=[135]
=> 12/3 @ r2c3: r23c4=12-6=6={24} (NP @ c4,n2)
=> 19/3 @ r2c6: r23c6=19-7=12=[39]
=> 12/2 @ r2c5 from {15678}=[57]
HS @ n5: r4c6=7
=> 12/3 @ r2c8: r2c8+r3c7=12-7=5 from {1245689}=[41]
Innies @ n3: r3c8=6
Outies @ n6: r7c8=1
Outies @ n8: r8c37=10=[73]
=> 17/3 @ r7c4: r78c4=17-7=10=[91]
Innies @ n5: r6c46=10 from {13468}=[64]
=> 18/3 @ r6c6: r7c7+r8c8=18-4=14=[68]
=> 13/3 @ r7c6: r78c6=13-3=10=[82]

All naked singles from here.

Maurice will be familiar with my "cell cloning" trick, which I don't think is that easy to be composed into programs. Also, I wonder how many programs can see an innie-outies move in 2 or more different ways. I know JSudoku can't. :ugeek:

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Last edited by udosuk on Thu Oct 02, 2008 5:19 pm, edited 1 time in total.

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 Post subject: Re: Assassin 122
PostPosted: Thu Oct 02, 2008 10:57 am 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
Thanks for these very enjoyable puzzles Afmob. Feel very happy to have found the break-through tricks relatively easily for both these, though not as elegantly as Andrew for V1.5.

To celebrate, here's a full walkthrough for the V1 using Andrew's V1.5 beginning. 8-) I see now that udosuk started the V1 this way too :applause: . Sounds like Joe-Casey got the step 1 part. Great! Any chance of a walkthrough next time? :D

I'll rate the V1 as a Hard 1.0 based mostly on the first 2 steps. Also, it kept me thinking throughout and ended up with over 30 steps before getting it to singles.

The new Aweek is about to begin, so no hiding this time. Please let me know of any errors or things that are unclear.

Walkthrough for Assassin 122

Prelims
i. 20(3)n1: no 1 or 2
ii. 13(4)n2 (remote cage r2378c5): no 8 or 9
iii. 20(3)n2: no 1 or 2
iv. 2 X 9(3)n3: no 7, 8 or 9
v. 22(3)n4: no 1...4
vi. 7(2)n4: no 7, 8 or 9
vii. 8(3)n4: no 6..9
viii. 21(3)n5: no 1, 2 or 3
ix. 20(3)n6: no 1 or 2
x. 15(2)n6 = {69/78}
xi. 11(3)n8: no 9
xii. 18(5)n9: no 9

1. "45" r1 + r9 + c1 + c9 -> 4 corners = 180 - (cage sums: 170) = 10
1a. because of diagonals, all 4 corners see each other -> they cannot have repeats = h10(4) = {1234}
1b. Common Peer Elimination (CPE): no 1, 2, 3 or 4 in r5c5 because it sees all 4 corners = h10(4)

2. "45" D\ and D/ (incuding the hidden 10(4) in step 1a)
2a. 1 innie r5c5 = (90 - cage sums )/2 (/2 because r5c5 is counted twice on both diagonals) = 16/2
2b. -> r5c5 = 8 (including placed for diagonals)

3. 15(2)n6 = {69}: both locked for r5 & n6
3a. no 1 in r5c23

4. 20(3)n6 = {578}: all locked for n6 & c9

5. naked pair (57) in r5c19: both locked for r5

6. 7(2)n4 = {34}: both locked for r5 & n4

7. naked pair (12) in r5c46: both locked for n5

8. 21(3)n5 diagonal cage = {579}: locked for D/

9. 6 in D/ only in 9(3) = {126}: 1 & 2 locked for D/ and n3
9a. r4c6 = 6

10. r6c1 = 6 (h single n4)
10a. r45c1 = [97] (last permutation)
10b. r5c9 = 5

11. naked pair {34} in r1c9 + r9c1: CPE, no 3 or 4 in r1c1 or r9c9

12. naked pair {12} in r1c1 & r9c9: both locked for D\

13. 9 in c9 only in n3: locked for n3

14. 8(3)n4 = {125}: last valid combination
14a. CPE -> no 1, 2 or 5 in r4c2
14b. r4c2 = 8
14c. r46c9 = [78]

15. 15(3)n1 = [8][61/52/25], r3c2 = (256)

16. "45" n7: r6c4 - 3 = r7c2 + r8c3
16a. -> r6c4 = 7 or 9, 2 innies = 4 or 6
16b. 5 in D/ only in n7: 5 locked for n7
16c. 2 innies = 4 or 6 = [13/24]: r8c3 = (34)

17. naked pair (34) in r7c3 with both r9c1 & r5c3: 3 & 4 both locked for n7 & c3

18. 5 required in 8(3)n4 only in r6 & n4: 5 locked for r6 & n4
18a. max r4c3 = 2 -> min r3c2 = 5 (cage sum)

19. 24(5)n5 = 12489 (no 357)
19a. r46c5 = [49]
19b. r4c4 = 5 (hsingle n5) (5 placed for D\)

20. r2c2 + r3c3 = 11 = [47] (only permution) (both placed for D\)

21. r6c46 = [73]: placed for Ds

22. naked pair (59) in n7: 9 locked for n7

23. naked pair (69) in n9: both locked for n9

24. r6c4 = 7 -> 2 innies n7 = 4 (step 16) = [13]

25. naked pair (28) in n7: locked for n7 & c1

26. r9c123 = [476]

27. naked pair (25) in n4: 2 locked for n4 & r6

28. naked pair (14) in n6: 1 locked for n6
28a. r7c8 = 7 (cage sum)

29. r4c78 = (23) -> r3c8 = 4 (cage sum)

30. r4c3 = 1 -> r3c2 = 6 (cage sum)
30a. 1 innie n1 = 8

31. r123c9 = [369]

32. 2 innies c5 = 11 = [65]

33. r23c4 = [93]
33a. r1c46 = 11 = [47]

Rest is naked.

Cheers
Ed


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