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 Post subject: Assassin 314 X
PostPosted: Fri Mar 27, 2015 1:10 pm 
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Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Assassin 314 X

One from my serendipity store - SS gives it 1.4.

Image

JS code:
3x3:d:k:5889:5889:5634:1539:1539:2308:5893:5893:5893:5889:5889:5634:6918:3335:2308:2308:5893:3080:5634:5634:5634:6918:3335:4105:4105:4105:3080:4362:6918:6918:6918:5899:5899:4105:4108:4108:4362:781:781:5899:5899:7950:5903:5903:5903:4112:4112:6673:5899:7950:7950:7950:5903:5903:4114:4112:6673:6673:7699:7950:2068:2068:5903:4114:4114:6673:2581:7699:7699:2068:6934:6934:4114:2071:2071:2581:7699:7699:7699:6934:6934:

Solution:
781243965
629875134
534961728
845132679
912687543
367459281
476598312
298316457
153724896


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PostPosted: Fri Mar 27, 2015 9:35 pm 
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Grand Master
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for the new Killer, HATMAN! I'm quite shocked that JSudoku as well as SudokuSolver missed my simple step 1g and rather chose more difficult moves. The following walkthrough uses no Killer subsets whatsoever which is quite rare by my standards.

A314X Walkthrough:
1. C789 !
a) 16(2) = {79} locked for R4+N6
b) 8(3) = 1{25/34} -> 1 locked for N9
c) Innies N9 = 10(2) <> 5,9
d) Innies N3 = 10(3) <> 8,9
e) Hidden Single: R1C7 = 9 @ C7
f) ! Innies+Outies C89: 2 = R5C7 - R37C8 -> R5C7 = (568); R3C8 <> 6,7 since R5C7 <= 8
g) ! 23(6): R56C8+R567C9 <> 6 since R5C7 = (568)
h) 6 locked in R456C7 @ N6 for C7
i) 6 locked in 23(4) @ N3 = 69{17/35}
j) 8 locked in 12(2) @ N3 = {48} locked for C9+N3

2. C789+N4
a) 23(6) = 1234{58/67} -> 4 locked for C8+N6
b) 27(4) = 79{38/56} -> 7 locked for N9
c) Innies N9 = 10(2) = {28} -> R7C9 = 2, R9C7 = 8
d) 3(2) = {12} locked for R5+N4
e) 23(6) = {123458} -> R5C7 = 5, R5C9 = 3, R6C9 = 1
f) Hidden Single: R3C7 = 7 @ C7
g) 23(4) = {3569} locked for N3; 3 also locked for C8
h) 8(3) = {134} -> R7C8 = 1
i) R3C8 = 2, R4C7 = 6 -> R3C6 = 1, R6C7 = 2, R2C7 = 1, R4C1 = 8, R5C1 = 9

3. N25
a) 6(2) = {24} locked for R1+N2
b) 9(3) = {135} -> 3,5 locked for C6+N2
c) 13(2) = {67} -> R3C5 = 6, R2C5 = 7
d) 31(5) = {25789} -> R6C5 = 5; 7,9 locked for C6
e) Hidden Single: R7C4 = 5 @ N8
f) 27(5) = 589{14/23} -> R4C4 = (12); 8,9 locked for C4

4. N457
a) 26(4) = 58{49/67} -> 8 locked for C3+N7
b) Innies N7 = 21(3) <> 3
c) 16(3) = 3{49/67} -> 3 locked for R6+N4
d) 27(5) = {14589} -> R4C4 = 1; 4 locked for R4+N4
e) 23(5) = {23468} -> R4C5 = 3, R4C6 = 2, R5C5 = 8; 4,6 locked for C4
f) 26(4) = {5678} since R6C3 = (67) -> R7C3 = 6, R6C3 = 7, R8C3 = 8
g) Innie N7 = R7C2 = 7
h) 16(4) = {1249} -> R7C1 = 4, R8C2 = 9, R9C1 = 1, R8C1 = 2
i) R7C7 = 3, R6C6 = 9

5. Rest is singles without considering diagonals.

Rating:
Hard 0.75?. I used IOD.


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 Post subject: Re: Assassin 314 X
PostPosted: Wed Apr 01, 2015 2:04 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
Thanks HATMAN for your new Assassin.

I found it harder than Afmob did, partly because it took me a long time to spot an important step.

Here is my walkthrough for Assassin 314 X:
Thanks Afmob for your comments and corrections.
Prelims

a) R1C45 = {15/24}
b) R23C5 = {49/58/67}, no 1,2,3
c) R23C9 = {39/48/57}, no 1,2,6
d) R45C1 = {89}
e) R4C89 = {79}
f) R5C23 = {12}
g) R89C4 = {19/28/37/46}, no 5
h) R9C23 = {17/26/35}, no 4,8,9
i) 9(3) cage at R1C6 = {126/135/234}, no 7,8,9
j) 8(3) cage at R7C7 = {125/134}
k) 26(4) cage at R6C3 = {2789/3689/4589/4679/5678}, no 1
l) 27(4) cage at R8C8 = {3789/4689/5679}, no 1,2
m) 23(6) cage at R4C7 = {123458/123467}, no 9

Steps directly and indirectly resulting from Prelims
1a. Naked pair {79} in R4C89, locked for R4 and N6 -> R45C1 = [89]
1b. Naked pair {12} in R5C23, locked for R5 and N4
1c. 8(3) cage at R7C7 = {125/134}, 1 locked for N9
1d. 27(4) cage at R8C8 = {3789/4689/5679}, 9 locked for N9
1e. 7 in N4 only in R6C123, locked for R6
1f. 23(6) cage at R4C7 = {123458/123467}, 1 locked for R6 and N6
1g. 7 of {123467} must be in R7C9 -> no 6 in R7C9
1h. 9 in C7 only in R13C7, locked for N3, clean-up: no 3 in R23C9

2. 45 rule on R123 2 innies R23C4 = 1 outie R4C7 + 11
2a. Min R4C7 = 2 -> min R23C4 = 13, no 1,2,3 in R23C4
2b. 3 in N2 only in R123C6, locked for C6

3. 45 rule on N7 3 innies R7C23 + R8C3 = 21 = {489/579/678}, no 1,2,3

4. 45 rule on N9 2 innies R7C9 + R9C7 = 10 = {28/37}/[46], no 5, no 4 in R9C7

5. 45 rule on C123 2 innies R4C23 = 1 outies R7C4 + 4
5a. Min R4C23 = 7 -> min R7C4 = 3
5b. Max R4C23 = 11 -> max R7C7 = 7

6. 45 rule on C1234 3 innies R156C4 = 12
6a. Min R15C4 = 4 -> max R6C4 = 8
6b. 9 in R6 only in R6C56, locked for 31(5) cage at R5C6, no 9 in R7C6

7. 45 rule on R1234 2 remaining innies R4C56 = 5 = {14}/[32], no 2 in R4C5
7a. 45 rule on R1234 3 remaining outies R5C45 + R6C5 = 18 = {378/468/567}, no 2
7b. R4C23 = R7C4 + 4 (step 5)
7c. Min R4C23 = 8 (R4C23 cannot be {34} which clashes with R4C56) -> min R7C4 = 4

8. 45 rule on N7 2 outies R6C3 + R7C4 = 1 innie R7C2 + 5, IOU no 5 in R6C3
8a. Max R6C3 + R7C4 = 13 -> max R7C2 = 8

9. 45 rule on C1234 4(1+3) outies R1C5 + R4C56 + R5C5 = 17, R4C56 (step 7) = 5 -> R15C5 = 12 = [48/57], clean-up: no 4,5 in R1C4
9a. R23C5 = {49/67} (cannot be {58} which clashes with R15C5), no 5,8
9b. Killer pair 4,7 in R15C5 and R23C5, locked for C5, clean-up: no 1 in R4C6 (step 7)

10. R7C9 + R9C7 (step 4) = {28/37}/[46]
10a. 45 rule on N6 2 innies R46C7 = 1 outie R7C9 + 6, R7C9 = {23478} -> R46C7 = 8,9,10,13,14 = {26/36}/[58/68] (cannot be {46} which clashes with R7C9 + R9C7 = [46], killer combo clash, other combinations eliminated because R46C7 must contain 6 except when R7C9 = 7), no 4 in R4C7, no 4,5 in R6C7, no 4 in R7C9, clean-up: no 6 in R9C7
10b. Killer pair 2,3 in 8(3) cage at R7C7 and R7C9 + R9C7, locked for N9

11. 45 rule on N5 2 outies R6C7 + R7C6 = 1 innie R4C4 + 9, min R6C7 + R7C6 = 10, max R6C7 = 8 -> min R7C6 = 2

12. 45 rule on N3 2 outies R3C6 + R4C7 = 1 innie R2C7 + 6, IOU no 6 in R3C6

[I ought to have seen this 45 earlier]
13. 45 rule on N3 3 innies R2C7 + R3C78 = 10 = {127/136/235} (cannot be {145} which clashes with R23C9), no 4,8,9
13a. 16(4) cage at R3C6 = {1267/1357/1456/2347/2356} (cannot be {1249/1348} because 4,8,9 only in R3C6, cannot be {1258} because no 4,7 in R2C7), no 8,9 in R3C6
13b. R1C7 = 9 (hidden single in C7)

14. 8 in N2 only in R23C4, locked for C4, clean-up: no 2 in R89C4
14a. R23C4 = R4C7 + 11 (step 2) -> R23C4 = {58/68/89}, R4C7 = {236}
14b. 27(5) cage at R2C4 contains 8 = {14589/23589} (cannot be {13689} which clashes with R4C5) -> R23C4 = {89}, locked for C4 and N2, R4C7 = 6, R4C4 = {12}, clean-up: no 4 in R23C5, no 1 in R89C4
14c. Naked pair {67} in R23C5, locked for C5 and N2 -> R5C5 = 8, placed for both diagonals, R1C5 = 4 (step 9), R1C4 = 2, R4C4 = 1, placed for D\, R4C5 = 3, R4C6 = 2 (step 7), placed for D/
14d. R4C56 = [32], R5C5 = 8 -> R56C4 = 10 = {46}, locked for C4 and N5
14e. Naked triple {135} in R123C6, locked for C6 -> R5C6 = 7, R6C6 = 9, placed for D\, R6C5 = 5 -> R6C7 + R7C6 = 10 -> R6C7 = 2, R7C6 = 8
14f. R9C7 = 8 (hidden single in C7), R7C9 = 2 (step 4)
14g. 8(3) cage at R7C7 = {134} (only remaining combination), 4 locked for N9
14h. Naked triple {345} in R5C789, locked for R5 and N6 -> R5C4 = 6, R6C4 = 4, placed for D/

15. R3C7 = 7 (hidden single in C7), placed for D/, clean-up: no 5 in R23C9
15a. R2C7 + R3C78 (step 13) = {127} (only remaining combination) -> R2C7 = 1, R3C8 = 2, R3C6 = 1 (cage sum)
15b. Naked pair {34} in R78C7, locked for C7 -> R5C7 = 5, R7C8 = 1, R6C89 = [81], R7C5 = 9

16. R7C4 = 5 (hidden single in C4), R7C3 = 6, placed for D/, R68C3 = 15 = {78} -> R6C3 = 7, R8C3 = 8
16a. R6C12 = {36} -> R7C2 = 7 (cage sum)
16b. R9C23 = {35} (only remaining combination), locked for R9 and N7 -> R7C1 = 4, R7C7 = 3, placed for D\, R9C4 = 7, R9C9 = 6, placed for D\
16c. Naked pair {57} in R1C1 + R8C8, locked for D\ -> R3C3 = 4

and the rest is naked singles, without using the diagonals.
Afmob pointed out that step 16c isn't needed to reach naked singles without using the diagonals. However the finish is a lot quicker if step 16c is used.

Rating Comment:
I'll rate my walkthrough for A314 X at 1.25 for step 10a, a killer combo clash.


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