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 Post subject: MeanDoku NC X 11
PostPosted: Fri Aug 03, 2018 3:31 am 
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Joined: Wed Apr 23, 2008 6:04 pm
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Location: Lethbridge, Alberta, Canada
In the MeanDoku thread HATMAN posted the link

http://forum.enjoysudoku.com/post257549.html#p257549

This was for MeanDoku NC 2 but if you scroll down you will find MeanDoku NC X 11. Another good one for those new to MeanDoku NCs to try. It's also unusual in that each nonet has the maximum 12 coloured marks.

Here is my walkthrough for MeanDoku NC X 11:
Cells adjacent to green marks must total less than 10, blue must total 10, red must total more than 10. Also NC so horizontally/vertically adjacent cells cannot be {12}, {23}, … {78}, {89}, so at least one of the cells adjacent to each green mark must contain one of 1,2,3 as they cannot be {45}; similarly at least one of the cells adjacent to each red mark must contain one of 7,8,9 as they cannot be {56}. However since this appeared to be an easier puzzle I didn’t use that property; if I had my walkthrough would have been a bit shorter.

This is a Killer-X.

Prelims.
Delete 9 from cells either side of green marks.
Delete 5 from cells either side of blue marks.
Delete 1 from cells either side of red marks.
Clean-ups only as stated.

1. R1C1 = 1 (hidden single on D\, also for N1 but I spotted it on the diagonal first), no 2 in R1C2 + R2C1 (NC)
1a. R2C5 = 1 (hidden single in C5), no 2 in R13C5 + R2C46 (NC)
1b. R3C9 = 1 (hidden single in R3), no 2 in R24C9 + R3C8 (NC)
1c. R4C8 = 1 (hidden single in C8), no 2 in R4C7 + R5C8 (NC)
1d. R5C3 = 1 (hidden single in R5), no 2 in R46C3 + R5C24 (NC)
1e. R9C2 = 1 (hidden single in C2), no 2 in R8C2 + R9C13 (NC)
1f. R6C4 = 1 (hidden single in C4), no 2 in R6C5 + R7C4 (NC)
1g. R7C6 = 1 (hidden single in C6), no 2 in R68C6 + R7C57 (NC)
1h. R8C7 = 1 (hidden single in C7), no 2 in R8C8 + R9C7 (NC)

2. R9C9 = 9 (hidden single on D\, also for N9 but I spotted it on the diagonal first), no 8 in R8C9 + R9C8 (NC)
2a. R8C5 = 9 (hidden single in R8), no 8 in R79C5 + R8C46 (NC)
2b. R7C1 = 9 (hidden single in R7), no 8 in R68C1 + R7C2 (NC)
2c. R6C2 = 9 (hidden single in C2), no 8 in R5C2 + R6C3 (NC)
2d. R5C7 = 9 (hidden single in R5), no 8 in R46C7 + R5C68 (NC)
2e. R4C6 = 9 (hidden single in R4), no 8 in R3C6 + R4C5 (NC)
2f. R3C4 = 9 (hidden single in R3), no 8 in R24C4 + R3C35 (NC)
2g. R2C3 = 9 (hidden single in R2), no 8 in R1C3 + R2C2 (NC)
2h. R1C8 = 9 (hidden single in R1), no 8 in R1C79 + R2C8 (NC)

Time for some clean-ups.
Blue marks
No 2 in R1C5 -> no 8 in R1C4
No 2 in R4C3 -> no 8 in R4C2
No 2 in R4C9 -> no 8 in R5C9
No 8 in R6C1 -> no 2 in R5C1
No 8 in R6C7 -> no 2 in R6C8
No 8 in R9C5 -> no 2 in R9C6
Green marks
No 1 in R1C7 -> no 8 in R2C7
No 1,2 in R2C1 -> no 7 in R2C2 -> no 3 in R1C2 (blue)
No 1 in R2C2 -> no 8 in R2C1 + R3C2
No 1,2 in R2C4 -> no 7 in R1C4 -> no 3 in R1C5 (blue)
No 1 in R2C8 -> no 8 in R3C8
No 1,2 in R3C5 -> no 7 in R3C6 -> no 3 in R2C6 (blue)
No 1,2 in R3C8 -> no 7 in R2C8 -> no 3 in R2C9 (blue)
No 1 in R4C2 -> no 8 in R4C1
No 1 in R4C5 -> no 8 in R5C5
No 1,2 in R5C2 -> no 7 in R4C2 -> no 3 in R4C3 (blue)
No 1 in R5C6 -> no 8 in R6C6
No 1,2 in R5C8 -> no 7 in R5C9 -> no 3 in R4C9 (blue)
No 1 in R5C9 -> no 8 in R6C9
No 1,2 in R6C6 -> no 7 in R5C6
No 1 in R7C2 -> no 8 in R7C3
No 1 in R7C3 -> no 8 in R8C3
No 1 in R7C89 -> no 8 in R7C89
No 1 in R8C1 -> no 8 in R9C1
No 1 in R8C4 -> no 8 in R9C4
No 1,2 in R9C1 -> no 7 in R8C1 -> no 3 in R8C2 (blue)
No 1,2 in R9C7 -> no 7 in R9C8 -> no 3 in R8C8 (blue)
No 1 in R9C8 -> no 8 in R9C7
Red marks
No 9 in R1C2 -> no 2 in R1C3
No 9 in R1C5 -> no 2 in R1C6
No 8,9 in R2C1 -> no 2,3 in R3C1
No 8,9 in R2C7 -> no 2,3 in R3C7
No 9 in R2C9 -> no 2 in R1C9
No 9 in R3C1 -> no 2 in R3C2 -> no 7 in R3C3 (green)
No 9 in R3C7 -> no 2 in R2C7 -> no 7 in R1C7 (green)
No 8,9 in R4C1 -> no 3 in R5C1 -> no 7 in R6C1 (blue)
No 8,9 in R4C4 -> no 3 in R5C4
No 9 in R5C1 -> no 2 in R4C1
No 9 in R5C4 -> no 2 in R4C4 + R5C5 -> no 7 in R4C5 (green)
No 8,9 in R5C8 -> no 3 in R6C8 -> no 7 in R6C7 (blue)
No 8,9 in R6C6 -> no 3 in R6C5
No 9 in R6C8 -> no 2 in R6C9
No 8,9 in R7C5 -> no 3 in R7C4 -> no 7 in R8C4 (blue)
No 9 in R7C7 -> no 2 in R7C8 -> no 7 in R7C9 (green)
No 8,9 in R7C8 -> no 3 in R7C7
No 9 in R8C2 -> no 2 in R7C2 + R8C3 -> no 7 in R7C3 (green)
No 8,9 in R8C3 -> no 3 in R9C3
No 8,9 in R8C6 -> no 3 in R9C6 -> no 7 in R9C5 (blue)
No 9 in R8C8 -> no 2 in R8C9

3a. 2 in N5 only in R4C5 + R5C6, no 3 in R5C5 (NC)
3b. 8 in N5 only in R5C4 + R6C5, no 7 in R5C5 (NC)
3c. R5C5 = {456} -> no 4,5,6 in R5C4 + R6C5 (red + NC)
3d. Naked pair {78} in R5C4 + R6C5, locked for N5, no 6 in R5C5 (NC)
3e. R5C5 = {456} -> no 4,5,6 in R4C5 + R5C6 (green + NC)
3f. Naked pair {23} in R4C5 + R5C6, locked for N5, no 4 in R5C4 (NC)
3g. R5C5 = 5, placed for both diagonals
3h. Naked pair {46} in R4C4 + R6C6, locked for D\
Clean-up: no 4,6 in R1C2 + R9C8 (blue)
3i. Naked pair {23} in R2C2 + R3C3, locked for N1, no 4 in R3C2 (NC)
3j. R1C2 = {78} -> no 7 in R1C3 (NC)
3k. Naked pair {78} in R7C7 + R8C8, locked for N9, no 6 in R7C8 (NC)
3l. 8 in N7 only in R8C2 + R9C3, no 7 in R8C3 (NC)
3m. R8C3 = {3456} -> no 4,5,6 in R8C2 + R9C3 (red + NC)
3n. Naked pair {78} in R8C2 + R9C3, locked for N7, no 6 in R8C3 (NC)
Clean-up: no 4,6 in R8C1 (blue)
3o. R9C3 = {78} -> no 7 in R9C4 (NC)
3p. 5 in N7 only in R7C2 + R8C3, no 4,6 in R7C3 (NC)
3q. Naked pair {23} in R7C3 + R8C2, locked for N7
3r. Naked pair {23} in R37C3, locked for C3
3s. Naked pair {78} in R18C2, locked for C2
3t. R8C3 = {45} -> no 4 in R8C4 (NC)
Clean-up: no 6 in R7C4 (blue)
3u. R3C2 = {56} -> no 4,5,6 in R3C1 (red + NC)
3v. Naked pair {78} in R1C2 + R3C1, locked for N1
3w. R3C1 = {78}, no 7 in R4C1 (NC)
3x. R35C1 = {78} (hidden pair in C1), no 6 in R4C1 (NC)
Clean-up: no 4,6 in R6C1 (blue)
3y. Naked pair {23} in R68C1, locked for C1
3z. R4C1 = {45} -> no 4,6 in R4C2 (green + NC)
Clean-up: no 4,6 in R4C3 (blue)
3aa. Naked pair {23} in R4C2 + R6C1, locked for N4
3ab. Naked pair {78} in R4C3 + R5C1, locked for N4
3ac. Naked pair {23} in R4C25, locked for R4

4a. 2 in N2 only in R1C45 = [28] (blue) or R23C6 = [82] (blue), 8 in R1C5 + R2C6, locked for N2, no 7 in R1C6 (NC)
4b. R1C6 = {3456} -> no 4,6 in R1C5 + R2C6 (red + NC)
Clean-up: no 4,6 in R1C4 + R3C6 (blue)
4c. Naked pair {23} in R1C4 + R3C6, locked for N2
4d. Naked pair {78} in R1C5 + R2C6, locked for N2, no 6 in R1C6 (NC)
4e. R1C6 = {45} -> no 4,5 in R1C7 (NC)
4f. R2C6 = {78} -> no 7 in R2C7 (NC)
4g. R2C7 = {3456} -> no 4,6 in R3C7 (red + NC)
4h. R3C7 = {78} -> no 7 in R3C8 + R4C7 (NC)
4i. Naked pair {78} in R3C7 and R8C2, locked for D/
4j. R2C9 + R3C7 = {78} (hidden pair in N3)
Clean-up: no 4,6 in R2C8 (blue)
4k. Naked pair {23} in R2C8 + R7C3, locked for D/
4l. R2C8 = {23} -> no 3 in R2C7 + R3C8 (NC)
4m. R1C7 + R2C8 = {23} (hidden pair in N3), no 4 in R2C7 (NC)

5a. R4C39 = {78} (hidden pair in R4)
Clean-up: no 4,6 in R5C9 (blue)
5b. Naked pair {78} in R24C9, locked for C9
5c. R6C9 = {3456} -> no 4,6 in R6C8 (red + NC)
Clean-up: no 4,6 in R6C7
5d. Naked pair {23} in R5C9 + R6C7, locked for N6
5e. Naked pair {78} in R4C9 + R6C8, locked for N6
5f. Naked pair {23} in R16C7, locked for C7
5g. Naked pair {23} in R29C8, locked for C8
5h. R7C8 = {45} -> no 4,5,6 in R7C9 (green + NC)
5i. Naked pair {23} in R7C9 + R9C8, locked for N9
5j. Naked pair {23} in R57C9, no 4 in R6C9 (NC)
5k. R57C4 = {78} (hidden pair in C4), no 7 in R7C5 (NC)
Clean-up: no 6 in R8C4 (blue)
5l. R9C36 = {78} (hidden pair in R9), no 7 in R8C6 (NC)
Clean-up: no 4,6 in R9C5 (blue)
5m. Naked pair {23} in R8C4 + R9C5, locked for N8, no 4 in R9C4 (NC)
5n. Naked pair {78} in R7C4 + R9C6, locked for N8

[Now some short forcing chains to place the remaining 5s.]
6a. R1C4 = 2 => R1C7 = 3, no 4 in R1C6 (NC)
or R1C4 = 3, R1C7 = 2, R2C8 = 3 => R2C9 = 7 (blue), no 6 in R1C9 (NC) => R1C9 = 4
-> R1C6 = 5
6b. R9C4 = 5 (hidden single in C4)
6c. R4C3 = 7 => R4C2 = 3 (blue), no 4 in R4C1
or R4C3 = 8, R5C1 = 7, no 6 in R5C2 (NC) => R5C2 = 4
-> R4C1 = 5
6d. R6C9 = 5 (hidden single in R6)
6e. R2C7 = 5 (hidden single in R2)
6f. R3C2 = 5 (hidden single in R3)
6g. R7C8 = 5 (hidden single in R7)
6h. R8C3 = 5 (hidden single in R8)

Then working through the options starting from one of the {23} cells and applying NC leads to two possible solutions.

As HATMAN said, there are two solutions, but that doesn't spoil this puzzle:
1 7 4 2 8 5 3 9 6
6 3 9 4 1 7 5 2 8
8 5 2 9 6 3 7 4 1
5 2 8 6 3 9 4 1 7
7 4 1 8 5 2 9 6 3
3 9 6 1 7 4 2 8 5
9 6 3 7 4 1 8 5 2
2 8 5 3 9 6 1 7 4
4 1 7 5 2 8 6 3 9

and

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

With hindsight I spotted:
With the symmetry of the placements of 1 and 9, it’s hardly surprising that R5C5 = 5.
It was only after I’d finished the puzzle that I noticed the complete symmetry and checked the symmetry of the blue marks, and the corresponding pairs of green and red marks.
This is similar to symmetry which has appeared in a few Assassins in the Killer forum.
If corresponding cells, cages in the case of killers, or marks in the case of MeanDoku NCs, are all complimentary about the centre of the puzzle, then it is symmetrical.
In this puzzle each of the pairs of blue marks, for example in R1C45 and R9C56, are symmetrical about R5C5. Similarly each green mark has a red mark in the corresponding position, for example green in R1C12 and red in R9C89.
With total symmetry it follows that R5C5 must be 5, which could be used as a shortcut.


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 Post subject: Re: MeanDoku NC X 11
PostPosted: Fri Aug 24, 2018 10:30 am 
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 549
Hi Andrew

To my memory I did not notice the symmetry. Well noted.

Maurice


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