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PostPosted: Fri Jul 08, 2016 7:38 am 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
NC Killer X 6 Ortho or Diag

Para recently published a puzzle pair (Inside and Outside Sudoku) on his website:
http://puzzleparasite.blogspot.com/ (For outside the clues apply in the first three cells and for inside in cells 2,3,4)

I decided to try to create something similar: a killer using standard (orthogonal) non-consecutive and then fers (diagonal) non-consecutive.

It is X.
The black cages are standard non-repeat killer.
The red cage has a single repeat.

Solve it as a standard (orthogonal) non-consecutive first (easier).

Then solve it as a fers (diagonal) non-consecutive. (harder - but probably not assassin level).


Image

JSCode for the killer cages:
3x3:5:k:7169:7169:8:9:11:12:13:4355:4355:7169:7169:14:15:16:17:18:4355:4355:3334:19:20:21:22:23:24:25:26:3334:27:28:29:30:31:32:33:34:3334:3594:35:36:37:38:39:40:41:3334:3594:42:43:44:45:46:47:48:3591:4612:4612:49:50:51:52:53:54:3591:4612:4612:3589:3589:3589:3589:7170:7170:55:56:57:58:59:60:61:7170:7170:

Ortho NC Sol:
851396247
693742815
247518639
724185963
369427581
185963724
518639472
936274158
472851396


Diag NC (Fers) Sol:
893257641
652841739
741639825
174365982
289174563
365982174
936528417
527416398
418793256


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PostPosted: Wed Jul 27, 2016 4:29 pm 
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Grand Master
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Very ingenious! I found the diagonal NC at least assassin level.

Here is a WT for that.

NC Killer 6 - Diag:
1. Whatever is duplicated in 17(3) is in r3c2, r45c3, and in r789c1
28(4) contains (89) -> max r3c2 = 7
Max r12c2 = +16 -> Min r12c1 = +12 -> Max r9c1 = 6
-> 7 not in r789c1 -> 7 not in r3c2 -> max r3c2 = 6
Since 14(2)r5c4 contains one of (56) -> 17(3) cannot be [6{56}] ->Max r3c2 = 5
-> 17(3) from [5{57}] or [4{49}]
Either way 14(2)r5c2 cannot be {59}
-> 14(2)r5c2 = {68}
-> 8 in r12c1
-> 14(2)r7c1 = {59}
-> 9 in r12c2

2. HS 7 in n4 -> r4c2 = 7
-> 17(3) = [4{49}
-> 28(4) = {5689}
-> HS 7 in c1 -> r3c1 = 7
-> r456c1 = {123}
-> r6c3 = 5
-> r56c2 = [86]
-> r45c3 = [49]
Also r78c1 = [95]
Also r9c1 = 4
Also 28(4) from [8965] or [6589]
Also r789c2 = {123}
-> r789c3 = {678}
-> r123c3 = {123}

3. 14(4)r8 cannot contain a 9
-> 9 in n8 in r9c456
-> 9 in n9 in r8c89
r8c2 from (12) -> 14(4)r8 cannot contain 7 or 8
-> Since 5 already in r8 -> 14(4)r8 = {1346}
-> r8c2 = 2
Remaining innies n7 r9c23 = +9(2) = [18] or [36]
-> HS 7 in n7-> r8c3 = 7
-> r8c89 = {89}
-> r9c89 = {56}
-> r9c23 = [18]
-> r7c23 = [36]

4. NQ in D\r1289 = {5689}
-> r3c3 and r4c4 both from (123) and non-consecutive
-> r3c3,r4c4 = {13}
-> NS 7 in D\ -> r5c5 = 7
-> NP in D\r67 = {24}

5. 8 in n5 only in r46c5
-> HS 8 in n8 -> r7c6 = 8
-> 8 in n2 in r123c4
6 in n5 only in r4c5 or r5c6
-> 5 cannot be either of those
-> HS 5 in n5 -> r4c6 = 5

6. 7 in n8 in a corner cell.
-> 6 not in r8c5, must be in r8c4 or r8c6
-> HS 5 in n8 -> r7c4 = 5
-> 4 in n5 in r56c6
Also -> r8c5 from (13)
-> 2 in n8 in r7c5 or r9c5
-> 14(4)r8 = [4163] or [4361]
-> HS 6 in n5 -> r4c5 = 6
-> r6c5 = 8
Also -> r6c4 = 9

7. 7 in n8 only in r9c46
-> 7 in n9 in r7c89
Since 7 in r6 in r6c89
-> 7 in n3/c7 in r12c7
6 in r5/n6 in r5c89
-> 6 in n3/c7 in r12c7 (i.e., r12c7 = {67})
-> HS 6 in n2/r3 -> r3c4 = 6
-> 8 in n2 in r12c4
-> HS 8 on D/ -> r3c7 = 8
-> NP on D/r12 = {13}
-> r1c8,r2c9 = {49}
-> r3c89 = [25]
-> r9c89 = [56]
-> 28(4)n1 = [8965]
-> r8c89 = [98]
etc.


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PostPosted: Tue Oct 04, 2016 1:33 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
The standard NC version is straightforward, probably about the level of newspaper killers plus NC.

Here is walkthrough for NC Killer X 6 Ortho:
This puzzle has two versions with different solutions. This version is normal non-consecutive (NC) horizontally and vertically. 17(3) cage at R3C2 has one number repeated.

Prelims

a) R78C1 = {59/68}
b) R56C2 = {59/68}
c) 28(4) cage at R1C1 = {4789/5689}, no 1,2,3
d) 13(4) cage at R3C1 = {1237/1246/1345}, no 8,9
e) 14(4) cage at R8C4 = {1238/1247/1256/1346/2345}, no 9
f) 28(4) cage at R8C8 = {4789/5689}, no 1,2,3
g) 17(3) cage at R3C2 with repeated number = {449/557/665/773/881}, no 2

1a. 28(4) cage at R1C1 = {5689} (cannot be {4789} because of NC), locked for N1
1b. Naked quad {5689} in R1278C1, locked for C1
1c. Naked quad {5689} in R1256C2, locked for C2
1d. 28(4) cage at R8C8 = {5689} (cannot be {4789} because of NC), locked for N9
1e. Naked quad {5689} in R1C1 + R2C2 + R8C8 + R9C9, locked for D\

2. 13(4) cage at R3C1 = {1237} (only remaining combination), locked for C1 -> R9C1 = 4, placed for D/
2a. R9C1 = 4 -> no 5 in R8C1, no 3 in R9C2 (NC), clean-up: no 9 in R7C1
2b. 45 rule on N7 2 remaining innies R9C23 = 9 = [18/27/72]

3. The repeated number in 17(3) cage at R3C2 must be in R3C2 -> 17(3) cage = {449} (only remaining combination, cannot be {773} which clashes with 13(4) cage at R3C1) -> R3C2 = 4, R45C2 = {49}, locked for C3 and N4, no 5 in R2C2, no 3 in R3C13 + R4C2 (NC), clean-up: no 5 in R56C2
3a. Naked pair {68} in R56C2, locked for C2 and N4 -> R2C2 = 9, placed for D\, R1C2 = 5 -> no 6 in R1C1, no 8 in R2C1 (NC)
3b. R1C1 = 8, placed for D\, R2C1 = 6 -> no 7 in R3C1 (NC)
3c. R6C3 = 5 (hidden single in N4) -> no 4 in R5C3, no 6 in R6C24 + R7C3 (NC)
3d. R56C2 = [68] -> no 7 in R4C2 + R56C1 + R7C2 (NC)
3e. R45C3 = [49] -> no 3 in R4C4, no 8 in R5C4 (NC)
3f. R78C1 = [59], R8C3 = 6 (hidden single in N7), R8C89 = [58], R9C89 = [96] -> no 7 in R7C3 + R8C24 + R9C3 (NC)
3g. R9C2 = 7 (hidden single in N7) -> R9C3 = 2 (step 2b) -> no 1,3 in R9C4 (NC)
3h. Naked pair {13} in R78C2, locked for C2 and N7, R4C2 = 2
3i. Naked pair {13} in R56C1, locked for C1 -> R4C1 = 7, R4C4 = 1, placed for D\, R3C3 = 7, placed for D\, no 2,6,8 in R3C4, no 2 in R5C4 (NC)
3j. R7C3 = 8, placed for D/, no 7,9 in R7C4 (NC)

4. 14(4) cage at R8C4 = {1247} (only remaining combination), locked for R8C4 -> R8C2 = 3, placed for D/, R7C2 = 1
4a. R5C5 = 2, placed for both diagonals -> no 3 in R4C5 + R5C46 + R6C5 (NC)
4b. 1 in N9 only in R89C7, locked for C7
4c. R6C6 = 3 (hidden single in N5), placed for D\, R56C1 = [31], R7C7 = 4 -> no 4 in R5C6 + R6C5, no 2 in R6C7 + R7C6, no 3 in R7C8 (NC)
4d. R5C4 = 4 (hidden single in N5), R8C4 = 2 -> no 3 in R7C4, no 1 in R8C5 (NC)
4e. R7C4 = 6 -> no 7 in R6C4 + R7C5 (NC)
4f. R6C4 = 9, placed for D/
4g. R6C89 = {24} (hidden pair in R6) -> no 3 in R7C9 (NC)
4h. Naked pair {27} in R7C89, locked for R7 and N9 -> R7C56 = [39], R89C7 = [13], no 4 in R8C5 (NC)
4i. R8C56 = [74], R6C57 = [67], R4C6 = 5, placed for D/, R3C7 = 6, R4C5789 = [8963], R5C6 = 7, no 5 in R2C7, no 9 in R3C5, no 8 in R5C7 (NC)
4j. R1C7 = 2, R2C7 = 8 -> no 1 in R1C6, no 1,3 in R1C8, no 7 in R2C8 (NC)

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

Rating Comment:
I set up the puzzle in SudokuSolver with the red 17(3) cage set as [449]. It gave a SS score of 0.85. In practice this is equivalent to a newspaper level puzzle, since SS is optimised for puzzles in the 1.0 to 1.5 range.


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PostPosted: Tue Oct 04, 2016 3:05 am 
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Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
As HATMAN said the Fers diagonal version is quite a bit harder. My first five steps were fairly straightforward, then I had to think harder how to continue until I found where to start nibbling away at candidates but nothing technically harder than FNC and CPE, so my solving path wasn't as hard an modern Assassins. wellbeback and I did those later stages in fairly similar ways; confirming my thought when I did my step 6 that this puzzle has a fairly narrow solving path.

Here is walkthrough for NC Killer X 6 Diag:
This puzzle has two versions with different solutions. This version is Fers non-consecutive (FNC) diagonally. 17(3) cage at R3C2 has one number repeated.

Prelims

a) R78C1 = {59/68}
b) R56C2 = {59/68}
c) 28(4) cage at R1C1 = {4789/5689}, no 1,2,3
d) 13(4) cage at R3C1 = {1237/1246/1345}, no 8,9
e) 14(4) cage at R8C4 = {1238/1247/1256/1346/2345}, no 9
f) 28(4) cage at R8C8 = {4789/5689}, no 1,2,3
g) 17(3) cage at R3C2 with repeated number = {449/557/665/773/881}, no 2

Steps resulting from Prelims
1a. 28(4) cage at R1C1 = {4789/5689}, 8,9 locked for N1
1b. 13(4) cage at R3C1 = {1237/1246/1345}, 1 locked for C1
1c. 28(4) cage at R8C8 = {4789/5689}, 8,9 locked for N9

2a. R1C1 + R2C2 or R2C1 + R1C2 cannot be {89} (FNC) -> either R1C12 or R2C12 = {89}
2b. R8C8 + R9C9 or R8C9 + R9C8 cannot be {89} (FNC) -> either R8C89 or R9C89 = {89}
2c. Killer pair 8,9 in R1C1 or R2C2 + R8C8 or R9C9, locked for D\
2d. Killer pair 8,9 in R12C1 and R78C1, locked for C1
2e. Killer pair 8,9 in R12C2 and R56C2, locked for C2

3. 45 rule on C1 2 outies R12C2 = 1 innie R9C1 + 10
3a. Max R12C2 (because of step 2a) = 16 -> max R9C1 = 6

4. 17(3) cage at R3C2 with repeated number must have repeated number in R3C2 = {449/557/665/773}, no 1,8 -> R3C2 = {4567}
4a. 7 in C1 only in R123456C1 -> 17(3) cage cannot be {773}, no 7 in R3C2, no 3 in R45C3
4b. 17(3) cage cannot be {665} (which clashes with R56C2) -> 17(3) cage = {449/557}, no 6
4c. R56C2 = {68} (cannot be {59} which clashes with 17(3) cage), locked for C2 and N4
4d. 8 in N1 only in R12C1, locked for C1, clean-up: no 6 in R78C1
4e. R78C1 = {59}, locked for C1 and N7
4f. Naked pair {68} in R56C2 -> no 7 in R456C13 (FNC)
4g. 17(3) cage = {449} (only remaining combination) -> R3C2 = 4, R45C3 = {49}, locked for C3 and N4
4h. R3C2 = 4 -> no 3,5 in R2C3, no 3 in R4C1 (FNC)
4i. Naked triple {123} in R456C1, locked for C1 and N4 -> R6C3 = 5, R4C2 = 7, no 6 in R3C13, no 6 in R5C2, no 4,6 in R57C4 (FNC)
4j. R3C1 = 7, naked pair {68} in R12C1, locked for C1 and N1 -> R9C1 = 4, placed for D/, no 3 in R8C2 (FNC)
4k. R56C2 = [86] -> no 9 in R4C3, no 5 in R7C1, no 7 in R7C3 (FNC)
4l. R78C1 = [95]
4m. 45 rule on N9 2 remaining innies R9C23 = 9 = [18/27/36]
4n. Naked triple {123} in R123C3, locked for C3
4o. 3 in C3 only in R13C3 -> no 2,4 in R2C4 (FNC)
4p. R7C3 = {68} -> no 7 in R68C4 (FNC)
4q. R45C3 = [49] -> no 3,5 in R35C4, no 8 in R6C4 (FNC)

5. 14(4) cage at R8C4 = {1346} (cannot be {1238/1247} which clash with R8C2), locked for R8
5a. 28(4) cage at R8C8 = {5689} (only remaining combination), no 7
5a. Naked pair {89} in R8C89, locked for R8 and N9
5b. Naked pair {56} in R9C89, locked for R9 and N9
5c. R8C2 = 2, placed for D/, R8C3 = 7, R9C3 = 8 -> R9C2 = 1 (step 4m), R7C2 = 3, R7C3 = 6, placed for D/, no 2 in R6C1, no 8 in R7C4 (FNC)
5d. 3 in N9 only in R89C7, locked for C7
5e. Naked quad {5689} in R1C1 + R2C2 + R8C8 + R9C9, locked for D\
5f. 8 in C4 only in R123C4, locked for N2

6! 4 on D\ only in R6C6 + R7C7 -> no 4 in R6C7 + R7C6 (CPE), no 3 in R6C6 (FNC)
6a! 3 on D\ only in R3C3 + R4C4 + R5C5 -> no 2 in R4C4 (FNC)
6b. R4C4 = {13} -> no 2 in R3C3 (FNC)
6c. Naked pair {13} in R3C3 + R4C4, locked for D\ -> R5C5 = 7, placed for both diagonals, no 8 in R4C6 (FNC)
6d. Naked pair {13} in R3C3 + R4C4 -> no 1 in R3C4 (CPE)
6e. R4C4 = {13} -> no 2 in R3C5 (FNC)
6f. Naked pair {24} in R6C6 + R7C7 -> no 2 in R6C7 + R7C6 (CPE)
6g. 7 in N8 only in R79C46 -> no 6 in R8C5 (FNC)
6h. 6 in N8 only in R8C46 -> no 5 in R7C5 (FNC)
6i. 8 on D/ only in R1C9 + R2C8 + R3C7, locked for N3
6j. 8 on D/ only in R1C9 + R2C8 + R3C7 -> no 9 in R2C8 (FNC)
6k. 5 in N8 only in R7C46 -> no 4 in R68C5 (FNC)
6l. R8C5 = {13} -> no 2 in R7C4 + R9C46 (FNC)
6m. 2 in R9 only in R9C57 -> no 1,3 in R8C4 (FNC)
6n. 2 in N8 only in R79C5, locked for C5
6o. 2 in N8 only in R79C5 -> no 1,3 in R8C4 (FNC)
6p. Naked pair {46} in R8C46, locked for R8 and N8
6q. 4 in N8 only in R8C46 -> no 3 in R9C5 (FNC)
6r. R8C7 = {13} -> no 2 in R7C8 (FNC)

7. R7C6 = 8 (hidden single in C6) -> no 9 in R6C5, no 7,9 in R6C7 (FNC)
7a. R7C4 = 5 (hidden single in R7)
7b. 7 in R7 only in R7C89, locked for N9
7c. 4 in N5 only in R56C6, locked for C6 -> R8C46 [46]
7d. R4C5 = 6 (hidden single in N5) -> no 5 in R35C6 (FNC)
7e. R4C6 = 5 (hidden single in N5), placed for D/
7f. R6C5 = 8 (hidden single in N5), R6C7 = 1, R6C1 = 3, R6C4 = 9, placed for D/, R3C7 = 8, R8C57 = [13], R9C57 = [92], R7C5 = 2, R7C7 = 4, placed for D\, R6C6 = 2, R5C4 = 1, R4C4 = 3, placed for D\

8. 7 in C7 only in R12C7, locked for N3
8a. Naked pair {13} in R1C9 + R2C8, locked for N3
8b. R1C9 + R2C8 = {13} = 4 -> R1C8 + R2C9 = 13 = {49}, locked for N3

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

Rating Comment:
I set up the puzzle in SudokuSolver with the red 17(3) cage set as [449]. It gave a SS score of 2.15. I've no idea why that score is so high; there must be some steps which wellbeback and I used which Sudoku Solver isn't programmed to find, because they're not commonly used steps.


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