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 Post subject: NCiX
PostPosted: Sun Dec 31, 2017 10:27 pm 
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Posts: 24
I decided to make a Non-Consecutive X puzzle. I found it difficult to generate solution grids. If someone knows a good way to make them please let me know.

ImageImage
SS Score: 2.20

The Sudoku Solver Score is inaccurate to the real difficulty of the puzzle, so please do not be intimidated. This puzzle is non-consecutive, meaning no two consecutive candidates can appear in orthogonally adjacent cells, the puzzle is also X, candidates do not repeat on the diagonals.

Code: paste into solver:
3x3:d:k:3851:3851:4874:4874:3599:3599:0000:2822:2822:3851:1557:1557:4874:0000:3599:2327:2072:2822:0000:2832:2832:4873:11540:3848:2072:2327:3847:4108:4108:4873:4873:11540:3848:3848:3847:3847:4108:0000:11540:11540:11540:11540:11540:0000:3598:3840:3840:3841:3841:11540:2821:2821:3598:3598:3840:2838:3091:3841:11540:2821:2322:2322:0000:4866:3091:2838:4109:0000:2820:3601:3601:3843:4866:4866:0000:4109:4109:2820:2820:3843:3843:


Solution:
247915836
915368472
683724159
368472915
724159683
591836247
159683724
836247591
472591368


As always, any feedback or suggestions are appreciated.


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 Post subject: Re: NCiX
PostPosted: Tue Jan 02, 2018 6:57 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Very pleasant I particularly liked the crossover effect - I did not use symmetry

To get an initial solution I use JSudoku. I put in some sparse pattern I like either numbers or Killer, then run recursively solve. If it has no solution I take out clues until it solves. With multiple solutions I add feasible clues one at a time until it is unique.
For NC X do not put too many clues in as it is very restrained.


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 Post subject: Re: NCiX
PostPosted: Tue Apr 03, 2018 3:49 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks ixsetf for a nice puzzle. Unlike HATMAN I used the step which isn't programmed into SudokuSolver. This made it an easy puzzle.

Here is my walkthrough for NCix:
This puzzle if a Killer-X and non-consecutive horizontally and vertically.

Prelims

a) R2C23 = {15/24}
b) 9(2) cage at R2C7 = {18/27/36/45}, no 9
c) 8(2) cage at R2C8 = {17/26/35}, no 4,8,9
d) R3C23 = {29/38/47} (cannot be {56} NC), no 1,5,6
e) 11(2) cage at R7C2 = {29/38/47/56}, no 1
f) 12(2) cage at R7C3 = {39/48/57}, no 1,2,6
g) R7C78 = {18/27/36} (cannot be {45} NC), no 4,5,9
h) R8C78 = {59/68}
i) 19(3) cage at R1C3 = {289/379/469/478/568}, no 1
j) 11(3) cage at R1C8 = {128/137/146/236/245}, no 9
k) 19(3) cage at R3C4 = {289/379/469/478/568}, no 1
l) 11(3) cage at R6C6 = {128/137/146/236/245}, no 9
m) 19(3) cage at R8C1 = {289/379/469/478/568}, no 1
n) 11(3) cage at R8C6 = {128/137/146/236/245}, no 9
o) And, of course, 45(9) cage at R3C5 = {123456789}

1a. 45 rule on N1 2 innies R1C3 + R3C1 = 13 = {49/58/67}, no 1,2,3
1b. 45 rule on N3 2 innies R1C7 + R3C9 = 17 = {89}, locked for N3, clean-up: no 1 in 9(2) cage at R2C7
1c. R3C9 = {89} -> 15(3) cage at R3C9 = 8{16}/8{25}/9{15}/9{24} (cannot be 8{34} NC), no 3,7,8,9 in R4C89
1d. R1C7 = {89} -> no 8,9 in R1C6 (NC)
1e. 45 rule on N7 2 innies R7C1 + R9C3 = 3 = {12}, locked for N7, clean-up: no 9 in 11(2) cage at R7C2
1f. R7C1 = {12} -> 15(3) cage at R6C1 = {59}1/{68}1/{49}2/{58}2 (cannot be {67}2 NC), no 1,2,3,7 in R6C12
1g. R9C3 = {12} -> no 1,2 in R9C4 (NC)
1h. 45 rule on N9 2 innies R7C9 + R9C7 = 7 = {16/25/34}, no 7,8,9

2a. Hidden killer triple 1,2,3 in 15(3) cage at R1C1, R2C23 and R3C23 for N1, each can only contains one of 1,2,3 -> R3C23 = {29/38}, no 4,7
2b. Killer pair 8,9 in R3C23 and R3C9, locked for R3, clean-up: no 4,5 in R1C3 (step 1a)
2c. Hidden killer triple 7,8,9 in R7C78, R8C78 and 15(3) cage at R8C9 for N7, each can only contains one of 7,8,9 -> R7C78 = {18/27}, no 3,6
2d. Killer pair 1,2 in R7C1 and R7C78, locked for R7, clean-up: no 5,6 in R9C7 (step 1h)

3. One can invoke symmetry because all the corresponding 2-cell cages sum to 20, the 3-cells cages to 30 and the 45(9) cage is symmetrical about the centre of the grid -> R5C5 = 5, placed for both diagonals, clean-up: no 1 in R2C3, no 3 in 8(2) cage at R2C8, no 7 in 12(2) cage at R7C3, no 9 in R8C7
3a. R5C5 = 5 -> no 4,6 in R46C5 + R5C46 (NC)
3b. 9(2) cage at R2C7 = {36/45} (cannot be {27} which clashes with 8(2) cage at R2C8), no 2,7
3c. 11(2) cage at R7C2 = {47/56} (cannot be {38} which clashes with 12(2) cage at R7C3), no 3,8
3d. 11(3) cage at R1C8 = {137/236/245} (cannot be {146} which clashes with both the other cages in N3)
3e. 2 of {245} and 6 of {236} must be in R1C9 (NC) -> no 6 in R1C8 + R2C9, no 4 in R1C9
3f. 19(3) cage at R8C1 = {379/478/568} (cannot be {469} which clashes with both the other cages in N7)
3g. 4 of {478} and 8 of {568} must be in R9C1 (NC) -> no 4 in R8C1 + R9C2, no 6 in R9C1

4a. R2C23 = [15] (cannot be {24} which clashes with R3C23 using NC), 1 placed for D\, no 2 in R1C2 + R2C1 + R3C2, no 6 in R1C3, no 4,6 in R2C4 (NC), clean-up: no 8 in R1C3, no 7 in R3C1 (both step 1a), no 9 in R3C3, no 7 in R3C7, no 4 in R3C8, no 6 in R7C2, no 8 in R7C8
4b. R8C78 = [59] (cannot be {68} which clashes with R7C78 using NC), 9 placed for D\, no 8 in R8C9 + R9C8, no 4,6 in R8C6, no 4 in R9C7 (NC), clean-up: no 3 in R7C3, no 3 in R7C9, no 2 in R9C7 (both step 1h)
4c. R1C3 = {79} -> no 8 in R1C24 (NC)
4d. R3C1 = {46} -> no 5 in R4C1 (NC)
4e. R7C9 = {46} -> no 5 in R6C9 (NC)
4f. R9C7 = {13} -> no 2 in R9C68 (NC)
4g. 7 in R3 only in R3C456, locked for N2
4h. 3 in R7 only in R7C456, locked for N8

5a. 15(3) cage at R1C1 = {249/267/348}
5b. 2 only in R1C1, 8 of {348} must be in R1C1 (NC) -> R1C1 = {28}, no 8 in R2C1
5c. 15(3) cage at R8C9 = {168/267/348}
5d. 2 of {267} must be in R9C9 (NC), 8 only in R9C9 -> R9C9 = {28}, no 2 in R8C9
5e. Naked pair {28} in R1C1 + R9C9, locked for D\, CPE no 2 in R1C9, no 8 in R9C9
5f. R3C3 = 3, placed for D\, R3C2 = 8, R3C9 = 9 -> R1C7 = 8, R1C1 = 2, R7C7 = 7, placed for D\, R7C8 = 2, R7C1 = 1 -> R9C3 = 2, R9C9 = 8, no 2,4 in R3C4, no 7,9 in R4C2, no 4 in R4C3, no 6 in R6C7, no 1,3 in R6C8, no 6,8 in R7C6, no 3 in R9C2 (NC), clean-up: no 6 in R23C7, no 4 in R78C3
5g. R3C8 = {56} -> no 6 in R2C8, no 5,6 in R4C8 (NC)
5h. R2C8 = 7 -> R3C7 = 1, both placed for D/, no 2 in R3C6 + R4C7, no 6 in R3C8 (NC)
5. R3C8 = 5 -> R2C7 = 4, R1C8 = 3, R1C9 = 6, placed for D/, R2C9 = 2, R7C9 = 4, R9C7 = 3, R8C9 = 1, R9C8 = 6
5i. R56C1 = {37} -> R6C8 = 4 (cage sum) -> R56C1 = [37] (NC), R4C89 = [15]
5j. R7C2 = 5 -> R8C3 = 6, no 6 in R6C2, no 4 in R8C2 (NC)
5k. R8C2 = 3 -> R7C3 = 9, R9C1 = 4, all placed for D/, R9C2 = 7, R8C1 = 8, R23C1 = [96], R1C2 = 4, R6C12 = [59], R45C1 = [37], R4C236 = [682]
5l. R9C7 = 3 -> R89C6 = 8 = [71]

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

Rating Comment:
The technically hardest step is the use of symmetry to place R5C5, which I've previously rated at 1.5. Apart from that my technically hardest steps were 4a and 4b, which are probably in the 1.25 range.


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 Post subject: Re: NCiX
PostPosted: Tue Apr 03, 2018 7:21 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
And then I did it the other way without using symmetry. This made it a more interesting and enjoyable puzzle; the crossovers, after using the hidden pair in each of those nonets, were surprisingly powerful.

Here is my start, doing it this way:
This puzzle if a Killer-X and non-consecutive horizontally and vertically.

Prelims

a) R2C23 = {15/24}
b) 9(2) cage at R2C7 = {18/27/36/45}, no 9
c) 8(2) cage at R2C8 = {17/26/35}, no 4,8,9
d) R3C23 = {29/38/47} (cannot be {56} NC), no 1,5,6
e) 11(2) cage at R7C2 = {29/38/47/56}, no 1
f) 12(2) cage at R7C3 = {39/48/57}, no 1,2,6
g) R7C78 = {18/27/36} (cannot be {45} NC), no 4,5,9
h) R8C78 = {59/68}
i) 19(3) cage at R1C3 = {289/379/469/478/568}, no 1
j) 11(3) cage at R1C8 = {128/137/146/236/245}, no 9
k) 19(3) cage at R3C4 = {289/379/469/478/568}, no 1
l) 11(3) cage at R6C6 = {128/137/146/236/245}, no 9
m) 19(3) cage at R8C1 = {289/379/469/478/568}, no 1
n) 11(3) cage at R8C6 = {128/137/146/236/245}, no 9
o) And, of course, 45(9) cage at R3C5 = {123456789}

1a. 45 rule on N1 2 innies R1C3 + R3C1 = 13 = {49/58/67}, no 1,2,3
1b. 45 rule on N3 2 innies R1C7 + R3C9 = 17 = {89}, locked for N3, clean-up: no 1 in 9(2) cage at R2C7
1c. R3C9 = {89} -> 15(3) cage at R3C9 = 8{16}/8{25}/9{15}/9{24} (cannot be 8{34} NC), no 3,7,8,9 in R4C89
1d. R1C7 = {89} -> no 8,9 in R1C6 (NC)
1e. 45 rule on N7 2 innies R7C1 + R9C3 = 3 = {12}, locked for N7, clean-up: no 9 in 11(2) cage at R7C2
1f. R7C1 = {12} -> 15(3) cage at R6C1 = {59}1/{68}1/{49}2/{58}2 (cannot be {67}2 NC), no 1,2,3,7 in R6C12
1g. R9C3 = {12} -> no 1,2 in R9C4 (NC)
1h. 45 rule on N9 2 innies R7C9 + R9C7 = 7 = {16/25/34}, no 7,8,9

2a. Hidden killer triple 1,2,3 in 15(3) cage at R1C1, R2C23 and R3C23 for N1, each can only contains one of 1,2,3 -> R3C23 = {29/38}, no 4,7
2b. Killer pair 8,9 in R3C23 and R3C9, locked for R3, clean-up: no 4,5 in R1C3 (step 1a)
2c. Hidden killer triple 7,8,9 in R7C78, R8C78 and 15(3) cage at R8C9 for N7, each can only contains one of 7,8,9 -> R7C78 = {18/27}, no 3,6
2d. Killer pair 1,2 in R7C1 and R7C78, locked for R7, clean-up: no 5,6 in R9C7 (step 1h)

[And now to try to solve this puzzle without invoking symmetry, which makes it an easy puzzle.]
3a. R2C23 = {15} (cannot be {24} which clashes with R3C23 using NC), locked for R2 and N1, clean-up: no 8 in R1C3 (step 1a), no 3,7 in R3C7, no 4 in R3C8
3b. R8C78 = {59} (cannot be {68} which clashes with R7C78 using NC), locked for R8 and N9, clean-up: no 6 in R7C2, no 3,7 in R7C3, no 2 in R9C7 (step 1h)

4a. 8(2) cage at R2C8 = [35/71] (cannot be {26} which clashes with 9(2) cage at R2C7 = {27/36} and clashes with [45] NC) -> R2C8 = {37}, R3C7 = {15}
4b. 9(2) cage = [45] (cannot be {27/36} which clash with R2C8 NC), R3C7 = 1 -> R2C8 = 7, both placed for D/, clean-up: no 5 in R7C3
4c. 11(3) cage at R1C8 = {236} -> 6 must be in R1C9 (NC), placed for D/, clean-up: no 7 in R3C1 (step 1a), no 4 in R9C7 (step 1h)
4d. 12(2) cage at R7C3 = [93] (cannot be {48} which clashes with 11(2) cage at R7C2 = {38/47} and clashes with [56] NC) -> R7C3 = 9, R8C2 = 3, both placed for D/
4e. 11(3) cage = [56] (cannot be {47} which clashes with R8C2 NC)
4f. 19(3) cage at R8C1 = {478} -> 4 must be in R9C1 (NC), placed for D/

5a. R1C3 = 7, R3C1 = 6
5b. R2C2 = 1 -> no 2 in R1C2 + R2C1 + R3C2 (NC)
5c. 2 in N1 only in R1C1 + R3C3, locked for D\
5d. R9C7 = 3 -> R7C9 = 4
5e. R8C8 = 9 -> no 8 in R7C8 + R8C9 + R9C8 (NC)
5f. 8 in N9 only in R7C7 + R9C9, locked for D\
5g. R5C5 = 5, naked pair {28} in R4C6 + R6C4, locked for N5

[Now make all the NC eliminations which I didn’t find necessary for those steps. Then continue as in my previous walkthrough.]

Rating Comment:
This way the puzzle is in the 1.25 range. I can only guess that SudokuSolver isn't programmed for the crossover steps and the important NC eliminations in N1 and N9; if so, I find that surprising.


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 Post subject: Re: NCiX
PostPosted: Wed Apr 04, 2018 2:32 pm 
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Posts: 791
Based on your assurances, I will give this one a try. As most of you know by now, I am no where near the advanced solver that many of you are.


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