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 Post subject: Assassin 318X
PostPosted: Thu May 14, 2015 8:17 pm 
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Joined: Sat Mar 28, 2015 8:36 pm
Posts: 24
Here is the assassin I promised, I hope it is enjoyable. As the other members of this forum have not been active recently, I will temporarily slow my posting of puzzles in order to give them time to catch up.

ImageImage
SS: 1.35

Things to note. This is a killer X, clues cannot repeat on the main diagonals. There are disconnected cages, 19 at r1c1 contains r1c1 r4c4 r7c7, 26n1 contains the rest of D\ 45 at r1c4 has r7c1 and connected cells, and 45 at r1c7 contains r4c1 and connected cells.

Code: Paste into solver:
3x3:d:k:4884:4609:4609:11522:4355:4355:11524:2821:2821:5126:6677:4609:4615:11522:4355:6152:11524:2821:5126:5126:6677:4615:4615:11522:6152:6152:11524:11524:4105:4105:4884:4618:4618:11522:3339:3339:1548:11524:4105:1805:6677:4618:3854:11522:3339:1548:1548:11524:1805:1805:6677:3854:3854:11522:11522:3343:3343:11524:4624:4624:4884:2833:2833:3602:11522:3343:3859:11524:4624:4096:6677:2833:3602:3602:11522:3859:3859:11524:4096:4096:6677:


Solution:
487569132
913842756
652371894
874956213
165237489
239418567
341795628
598624371
726183945


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 Post subject:
PostPosted: Fri May 15, 2015 1:19 pm 
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Joined: Mon Apr 21, 2008 9:44 am
Posts: 310
Location: MV, Germany
Thanks for the new Assassin, ixsetf! It was quite confusing sometimes, especially those two 45(9) cages.

A318 Walkthrough:
1. N345
a) 6(3) = {123} locked for N4
b) Innies N4 = 23(3) = {689} locked for N4+45(9)
c) 7(3) = {124} locked for N5
d) 6 locked in 11(3) @ N3 = 6{14/23}
e) 5 locked in Innies N3 = 10(3) = 5{14/23} locked for 45(9)
f) Naked quad (1234) locked in R6C1245 for R6

2. N156
a) Innies N1 = 7(3) = {124} locked for N1+D\
b) 19(3) <> 3,5 since R1C1 <= 4
c) Hidden Killer pair (12) locked in R4C7+13(3) @ R4 for N6 since 13(3) can only have one of (12) -> R4C7 = (12)
d) 15(3) = 5{37/46} since R6C78 <> 3,4 -> R5C7 = (34); 5 locked for R6+N6
e) Killer pair (34) locked in R5C7 + 13(3) for N6
f) Killer pair (67) locked in 15(3) + Innies N6 = 17(3) = {179/269/278} for N6
g) Hidden Killer pair (35) in R5C5 @ N5 since 18(3) can only have one of them -> R5C5 = (35)

3. N569 !
a) Innies N9 = 18(3) = {369/378/567}
b) 11(3) <> 3,7 since 3{17/26} blocked by Killer pairs (36,37) of Innies N9
c) R6C6 <> 7 since it sees all 7 of C9
d) 7 locked in R6C789 @ R6 for N6
e) ! Innies+Outies N9: 1 = R1C1+R4C4 - (R8C8+R9C9): R8C8+R9C9 <> 9 since R8C8 >= 3 and R8C8+R9C9 sees R1C1+R4C4 and R1C1 <= 4
f) 9 locked in R456C9 @ C9 for N6
g) Innies N6 = 2{69/78} since R5C8 = (68) -> R4C7 = 2; R6C9 = (79)

4. R123
a) Innies N2 = 10(3) = 1{36/45} -> 1 locked for N2+45(9)
b) Hidden Killer pairs (79,89) in each of 18(3) + 17(3) for R1 since each can only have one of them -> R2C36 <> 7,8,9; 18(3) = 3{69/78} -> 3 locked for N1; 17(3) = {269/278/359} <> 4
c) 17(3) = 2{69/78} since {359} blocked by Killer pair (35) of Innies N2 -> 2 locked for N2
d) Hidden triple (789) in R2C147 for R2 -> R2C147 = (789)
e) 20(3) = 5{69/78} -> 5 locked for R3

5. N569 !
a) ! R5C5 <> 5 since it sees all 5 of R2
b) R5C5 = 3, R5C7 = 4
c) Innies N5 = 17(2) = {89} locked for N5+D\
d) 13(3) = {139} -> R5C9 = 9
e) Innies N6 = 15(2) = {78} -> R6C9 = 7, R5C8 = 8
f) 5 locked in R789C9 @ C9 for N9
g) Innies N9 = 18(3) = {567} -> R9C9 = 5; 6,7 locked for N9
h) 19(3) = 4{69/78} since R7C7 = (67) -> R1C1 = 4
i) 16(3) = {349} -> R9C8 = 4; 3,9 locked for C7

6. N2345
a) 18(3) = 3{69/78} since {468} blocked by Killer pair (46) of Innies N2 -> R3C4 = 3
b) Innies N3 = 10(3) = {145} -> R3C9 = 4; 1 locked for N3+45(9)
c) Innies N2 = 10(3) = {145} -> R3C6 = 1, R1C4 = 5, R2C5 = 4
d) R3C3 = 2, R2C2 = 1, R1C7 = 1, R2C8 = 5
e) 6(3) = {123} -> 1 locked for C1
f) 7(3) = {124} -> R6C4 = 4
g) Hidden Single: R7C3 = 1 @ D/

7. Rest is singles without considering diagonals.

Rating:
Easy 1.25. I used CPEs, Hidden Killer pairs and a small IOD combo analysis.


Last edited by Afmob on Mon May 25, 2015 4:48 am, edited 1 time in total.

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 Post subject: Re: Assassin 318X
PostPosted: Sun May 24, 2015 2:34 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1658
Location: Lethbridge, Alberta, Canada
Thanks ixsetf for your first Assassin. I look forward to more of them.

An easy start but then I found it hard to find further moves, but I really ought to have spotted my key breakthrough step more quickly. I use coloured cages on my worksheet, so didn't have any problems with the disjoint cages including the 45s. Even with the disjoint cages there are still plenty of 45s.

Here is my walkthrough for Assassin 318X:
Prelims

a) 11(3) cage at R1C8 = {128/137/146/236/245}, no 9
b) 20(3) cage at R2C1 = {389/479/569/578}, no 1,2
c) 24(3) cage at R2C7 = {789}
d) 6(3) cage at R5C1 = {123}
e) 7(3) cage at R5C4 = {124}
f) 11(3) cage at R7C8 = {128/137/146/236/245}, no 9
g) 19(3) disjoint cage at R1C1 = {289/379/469/478/568}, no 1

Steps resulting from the Prelims
1a. Naked triple {789} in 24(3) cage at R2C7, locked for N3
1b. Naked triple {123} in 6(3) cage at R5C1, locked for N4
1c. Naked triple {124} in 7(3) cage at R5C4, locked for N5

2. 1,2 in R4 only in R4C789, locked for N6
2a. Hidden killer pair 1,2 in R4C7 and R4C89 for R4, R4C89 cannot contain both of 1,2 -> R4C7 = {12}, R4C89 must contain one of 1,2 -> 13(3) cage at R4C8 = {139/148/157/238/247/256} (cannot be {346} which doesn’t contain 1 or 2)
2b. 15(3) cage at R5C7 = {348/357/456}, no 9
2c. 13(3) cage = {139/148/157/238/256} (cannot be {247} which clashes with 15(3) cage)

3. 45 rule on N1 3 innies R1C1 + R2C2 + R3C3 = 7 = {124}, locked for N1 and D\

4. 45 rule on N4 3 innies R4C1 + R5C2 + R6C3 = 23 = {689}, locked for N4 and 45(9) disjoint cage at R1C7

5. 7 in 45(9) disjoint cage at R1C7 only in R7C4 + R8C5 + R9C6, locked for N8
5a. 45 rule on N8 3 innies R7C4 + R8C5 + R9C6 = 12 = {147/237}, no 5

6. 6 in N3 only in 11(3) cage at R1C8 = {146/236}, no 5

7. 45 rule on N2 3 innies R1C4 + R2C5 + R3C6 = 10 = {136/145/235} (cannot be {127} which clashes with R4C7), no 7,8,9
7a. Killer pair 1,2 in R1C4 + R2C5 + R3C6 and R4C7, locked for 45(9) disjoint cage at R1C4

8. R1C1 = {24} -> 19(3) disjoint cage at R1C1 = {289/469/478}, no 3,5

9. 45 rule on N6 3 innies R4C7 + R5C8 + R6C9 = 17 = {179/269/278} (other combinations don’t contain 1 or 2 for R4C7), no 3,4,5

10. 45 rule on N7 3 innies R7C1 + R8C2 + R9C3 = 18 = {369/378/459/468} (cannot be {567} which clashes with R4C7 + R5C8 + R6C9)

11. Hidden killer pair 8,9 in 18(3) cage at R1C2 and 17(3) cage at R1C5 for R1, neither can have both of 8,9 -> 18(3) cage and 17(3) cage must each contain one of 8,9 in R1 -> no 8,9 in R2C3 and R2C6
11a. 18(3) cage = {369/378} (cannot be {567} which doesn’t contain 8 or 9), no 5, 3 locked for N1
11b. 17(3) cage = {179/269/278/368/458} (cannot be {359} which clashes with R1C4 + R2C5 + R3C6, cannot be {467} which doesn’t contain 8 or 9)
11c. Hidden killer pair 7,9 in 18(3) cage at R1C2 and 17(3) cage at R1C5 for R1, 18(3) cage cannot contain both of 7,9 -> 17(3) cage must contain at least one of 7,9 in R1 = {179/269/278} (cannot be {368/458} which don’t contain 7 or 9), no 3,4,5
11d. 18(3) cage at R2C4 = {369/378/459/468} (cannot be {189/279/567} which clash with 17(3) cage), no 1,2

12. Hidden killer pair 1,2 in R3C3 and 13(3) cage at R7C2 for C3, 13(3) cage cannot contain both of 1,2 -> R3C3 = {12}, no 1,2 in R7C2

13. 45 rule on R3 3 outies R2C147 = 3 innies R3C369 + 17 -> R2C147 = 23,24, R3C369 = 6,7
13a. R2C147 = 23,24 = {689/789}, no 3,4,5
13b. R3C369 = 6,7 = {123/124}, no 5,6
13c. 5 in N1 only in R3C12, locked for R3

14. 18(3) cage at R2C4 (step 11d) = {369/378/468}
14a. R1C4 + R2C5 + R3C6 (step 7) = {145/235} (cannot be {136} which clashes with 18(3) cage), no 6, 5 locked for 45(9) cage at R1C4)

15. 45 rule on R6 3 innies R6C369 = 3 outies R5C147 + 17 -> R5C147 = 6,7, R6C369 = 23,24
15a. R5C147 = 6,7 -> R5C14 = {12}, R5C7 = {34}
15b. R6C369 = 23,24 = {689/789}, no 3,5, 8 locked for R6
15c. 15(3) cage at R5C7 (step 2b) = {357/456}, 5 locked for N6
15d. R5C7 = {34} -> no 3,4 in R6C78
15e. Killer pair 6,7 in R5C8 + R6C9 and 15(3) cage, locked for N6
15f. 5 in C9 only in R789C9, locked for N9

16. 45 rule on N5 3 innies R4C4 + R5C5 + R6C6 = 20 = {389/569/578}
16a. 3,5 only in R5C5 -> R5C5 = {35}

17. 45 rule on N9 3 innies R7C7 + R8C8 + R9C9 = 18 = {369/378/567}
17a. 11(3) cage at R7C8 = {128/146/245} (cannot be {137/236} which clash with R7C7 + R8C8 + R9C9), no 3,7
17b. 16(3) cage at R8C7 = {169/178/349} (cannot be {268/367} which clash with R7C7 + R8C8 + R9C9), no 2
17c. 2 in N9 only in 11(3) cage = {128/245}, no 6

18. 45 rule on C9 3 innies R369C9 = 3 outies R147C8 + 10
18a. Max R369C9 = 21 -> max R147C8 = 11, no 9 in R4C8

19. 45 rule on C7 3 innies R369C8 = 3 outies R147C7 + 10
19a. Min R147C7 = 9 -> min R369C8 = 19, no 1 in R9C8

[I ought to have spotted this sooner.]
20. 16(3) cage at R8C7 (step 17b) = {169/178/349}
20a. 9 of {349} must be in R89C7 (R89C7 cannot be {34} which clashes with R5C7)
20b. Killer quad 6,7,8,9 in R23C7, R7C7 and R89C7, locked for C7 -> R6C7 = 5
20c. R2C8 = 5 (hidden single in N3), placed for D/
20d. R1C4 = 5 (hidden single in N2)

21. R5C5 = 3, placed for both diagonals
21a. R9C9 = 5 (hidden single on D\) -> R7C7 + R8C8 + R9C9 (step 17) = {567}, 6,7 locked for N9 and D\
21b. Naked pair {89} in R4C4 + R6C6, locked for N5
21c. R5C7 = 4 -> R6C8 = 6 (cage sum), R8C8 = 7, R7C7 = 6
21d. 16(3) cage at R8C7 (step 20) = {349} (only remaining combination) -> R9C8 = 4, R89C7, = {39}, locked for C7
21e. R6C9 = 7 (hidden single in R6), placed for disjoint 45(9) cage at R1C4
21f. Naked triple {124} in R268C5, locked for C5
21g. R1C4 + R2C5 + R3C6 (step 7) = {145/235}
21h. 3 of {235} must be in R3C6 -> no 2 in R3C6

22. R3C8 = 9 (hidden single in N3)

23. R5C8 = 8, placed for 45(9) disjoint cage at R1C4
23a. R4C7 + R5C8 + R6C9 (step 9) = {278} (only remaining combination) -> R4C7 = 2, placed for 45(9) disjoint cage at R1C4, R5C9 = 9, R5C2 = 6
23b. R1C4 + R2C5 + R3C6 (step 7) = {145} (only remaining combination), 1,4 locked for N2 and 45(9) disjoint cage at R1C4 -> R8C2 = 9, R7C1 = 3, R9C3 = 6

24. Naked pair {12} in R56C1, locked for C1 and N4 -> R1C1 = 4, R6C2 = 3

25. 18(3) cage at R1C2 = {378} (only remaining combination), 7,8 locked for N1, 8 also locked for R1 -> R3C12 = [65], R2C1 = 9, R4C1 = 8, R89C1 = [57], 7 placed for D/, R9C2 = 2 (cage sum)

26. R2C2 = 1, R2C5 = 4
26a. R6C4 = 4 (hidden single in N5), R3C7 = 8, both placed for D/ -> R7C3 = 1

and the rest is naked singles, without using the diagonals.

Rating Comment:
I'll rate my walkthrough for A318X at Easy 1.25. I used hidden killer pairs, a killer quad and simple IOD analysis.


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