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 Post subject: Mean ORC 2,3,4,5
PostPosted: Sun Dec 24, 2017 4:30 pm 
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Grand Master
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Posts: 552
Mean ORC 2,3,4,5

More of these for Christmas, so:

Meandoku (strictly extra) The following colour clues apply:
Green: the sum of the two adjacent cells is 8 or 9 only
Blue: the sum of the two adjacent cells is ten
Red: the sum of the two adjacent cells is 11 or 12 only
Yellow: the sum of the two cells is below eight
Grey: the sum of the two cells is above twelve

Odd Row and Column - ORC - so it is:
ORC: odd rows and columns are 1-9 no repeat; even ones are not (i.e. they can repeat).
NN: no nonets

For all cells:
AK: Anti-King - diagonally adjacent are not equal
FNC: Ferz Non-concecutive - diagonally adjacent are not consecutive
NC: adjacent cells are not consecutive

I solve these in JSudoku control-right click allows you to remove the row and column constraints. Note recursively solve works but deduce a move is flawed.

I would be grateful for your views on difficulty.



Mean ORC 2
Image
Mean ORC 2 Solution
928361574
466181319
293146857
557191111
829157463
664739918
382915746
155579222
731924685


Mean ORC 2E
The solution to 2 is quite hard and awkward so I have added another clue to make it more straightforward.
Image

Mean ORC 3
Image


Mean ORC 4
Image


Mean ORC 5
Image


Last edited by HATMAN on Wed Mar 27, 2019 2:00 pm, edited 1 time in total.

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 Post subject: Re: Mean ORC 2,3,4,5
PostPosted: Tue Dec 26, 2017 9:22 pm 
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Joined: Mon Apr 21, 2008 11:35 pm
Posts: 40
:cheers:
Although I'm stuck on 1, I am excited to see the next four in the series. A fun combination between logic and rule-following.
Hatman, I think I know the answer, but I have to ask the question, anyway:
--Does the fact that we have AK and NC mean that we do NOT have NE? In other words - in the even-numbered rows - you can have two adjacent cells both be the same integer, right?

Thanks again for all of your puzzle-making skills, and for sharing them here with us!


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 Post subject: Re: Mean ORC 2,3,4,5
PostPosted: Thu Dec 28, 2017 2:41 pm 
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Posts: 552
Correct on even rows and columns two adjacent cells can be the same number.


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 Post subject: Re: Mean ORC 2,3,4,5
PostPosted: Tue Jan 16, 2018 8:36 pm 
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Thanks. After several unsuccessful attempts, finally figured what was leading me to dead-ends. (On the ERCs, was using old-school blue square logic.) Ready for new, successful attempts on these fun puzzles!


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 Post subject: Re: Mean ORC 2,3,4,5
PostPosted: Wed Jan 17, 2018 1:03 am 
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Very pretty! :santa: :applause: The rules are complicated (to me), so I'm not sure I could manage these.


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 Post subject: Re: Mean ORC 2,3,4,5
PostPosted: Wed Jan 17, 2018 11:27 pm 
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Not *too* complicated, enxio - pretty sure you could manage! :cheesey:

Hatman, I finally brought one to successful conclusion! (Mean ORC 3) At least, without seeing your solution, I'm pretty sure it is correct. :pray: Can't wait to try a couple of the others that had me stymied before yesterday's epiphany.


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 Post subject: Re: Mean ORC 2,3,4,5
PostPosted: Mon Apr 15, 2019 7:41 pm 
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Location: Lethbridge, Alberta, Canada
I also made several attempts, having at first made the same mistake as for Mean ORC 1 and Mean ORC 1A. Then restarts because I hadn't been thorough enough with my clean-ups.

Mean ORC 3 isn't too difficult, a bit between Mean ORC 1 and Mean ORC 1A.

Here is my walkthrough for Mean ORC 3:
Cells adjacent to yellow lines must total less than 8, green total 8 or 9, blue must total 10, red must total 11 or 12, grey total more than 12.
AK so diagonally adjacent cells cannot be equal, also FNC and NC so horizontally/ vertically/diagonally adjacent cells cannot be {12}, {23}, … {78}, {89}, therefore at least one of the cells adjacent to each green or yellow mark must contain one of 1,2,3 as green cannot be {45}; similarly at least one of the cells adjacent to each red or grey mark must contain one of 7,8,9 as red cannot be {56}.
Odd numbered rows and columns are normal; repeats are allowed on even numbered rows and columns.

Prelims.
Delete 7,8,9 from cells either side of yellow marks.
Delete 9 from cells either side of green marks in even rows and columns.
Delete 4,9 from cells either side of green mark in R5 (4 because of NC).
Delete 1 from cells either side of red marks in even rows and columns.
Delete 1,6 from cells either side of red mark in C5 (6 because of NC).
Delete 1,2,3 from cells either side of grey marks.
All blue marks are in even rows and columns, so no prelim deletions.
Clean-ups, AK, FNC and NC, separately or together, only when stated.

1a. R5C5 = 5, placed for R5 and C5
1b. R5C5 = 5 -> R5C6 = 3 (green), placed for R5, no 2 in R4C5, no 2,4 in R46C6
1c. R5C5 = 5 -> R4C5 = 1 (yellow), placed for C5
1d. R5C5 = 5 -> R6C5 = 7 (red), placed for C5
1e. R6C5 = 7 -> R6C4 = 3 (blue)
1f. R5C5 = 5 -> R5C4 = {89} (grey)
1g. R5C6 = 3 -> R4C6 = {13} (yellow)
1h. R34C6 (green) -> R3C6 = {56}, R4C6 = 3
1i. R6C4 = 3 -> R6C3 = {56} (green)
1j. R6C5 = 7 -> R6C6 = 1 (green)
1k. R6C6 = 1 -> R6C7 = 9 (blue), placed for C7
1l. R6C7 = 9 -> R6C8 = 1 (blue)
1m. R5C4 = {89} -> R4C4 = {234} (red)
1n. R6C3 = {56} -> R6C2 = {45} (blue)
1o R6C2 = {45} -> R6C1 = {345} (green)
Clean-ups:
R4C5 = 1 -> no 2 in R3C45 + R4C4
R5C5 = 5 -> no 4 in R4C4
R4C4 = 3 -> no 2,3,4 in R3C3, no 4 in R3C4, no 3,4 in R3C5, no 2,4 in R4C3
R4C6 = 3 -> no 2,3,4 in R3C7, no 2,4 in R4C7
R5C6 = 3 -> no 3 in R4C7, no 2,4 in R5C7
R6C4 = 3 -> no 2,4 in R5C3 + R7C4, no 2,3,4 in R7C35
R6C5 = 7 -> no 8 in R5C4, no 6 in R7C46, no 6,8 in R7C5
R6C6 = 1 -> no 1 in R5C7, no 2 in R7C6, no 1,2 in R7C7
R6C7 = 9 -> no 8 in R57C7, no 8,9 in R57C8
R6C8 = 1 -> no 2 in R57C8 + R6C9, no 1,2 in R57C9
R3C6 = {56} -> no 6 in R23C5, no 5,6 in R234C7
R6C2 = {45} -> no 4 in R5C1, no 4,5 in R7C1, no 5 in R7C3
R6C3 = {56} -> no 6 in R5C23 + R7C3, no 5,6 in R7C2, no 5 in R7C4
R7C4 = {13} -> no 2 in R8C345
R6C1 = {345} -> no 4 in R57C2

2a. R4C7 = 1, placed for C7
2b. R4C7 = 1 -> R4C8 = 9 (blue), no 8 in R3C7, no 8,9 in R5C7
2c. R3C7 = 7, placed for R3 and C7, no 6 in R3C6
2d. R3C6 = 5, placed for R3
2e. R7C5 = 9, placed for R7 and C5
2f. R3C5 = 8, placed for R3 and C5
2g. R5C4 = 9, placed for R5
2h. R5C7 = 6, placed for R5 and C7
2i. R3C6 = 5 -> R2C6 = {12} (yellow)
2j. R2C6 = {12} -> R1C6 = {678} (green)
Clean-ups:
R3C5 = 8 -> no 7,8,9 in R2C4
R3C6 = 5 -> no 4 in R2C57
R3C7 = 7 -> no 8 in R2C7, no 6,7,8 in R2C8, no 6 in R3C8
R4C7 = 1 -> no 1,2 in R3C8, no 1 in R5C8
R4C8 = 9 -> no 9 in R3C9, no 8 in R45C9
R5C4 = 9 -> no 8 in R5C3
R5C7 = 6 -> no 7 in R5C8
R2C5 = {23} -> no 2,3 in R1C5
R1C5 = {46} -> no 5 in R12C4
R2C7 = {23} -> no 2,3 in R1C78, no 3 in R3C8

3a. R5C389 = [147], placed for R5, 1 placed for C3, 7 placed for C9, no 2 in R5C2
3b. R5C12 = [28], 2 placed for C1
Clean-ups:
R5C1 = 2 -> no 3 in R46C1, no 2,3 in R4C2
R5C2 = 8 -> no 7,8,9 in R4C1, no 7 in R4C2
R5C8 = 4 -> no 4,5 in R4C9, no 3,4,5 in R6C9
R5C9 = 7 -> no 6 in R46C9

4a. R4C4 = 3 -> R3C4 = 6 (green), placed for R3
4b. R3C4 = 6 -> R2C6 = 6 (red), no 7 in R1C4, no 6 in R1C5
4c. R1C5 = 4, placed for R1 and C5, no 3 in R2C5
4d. R2C5 = 2, placed for C5
4e. R2C4 = 6 -> R1C4 = {89} (grey)
4f. R3C3 = 9, placed for R3 and C3
4g. R4C4 = 3 -> R4C3 = 3 (yellow), placed for C3
4h. R4C3 = 3 -> R4C2 = {56} (green)
4i. R4C2 = {56} -> R4C1 = {56} (red)
4j. R46C9 = [91], placed for C9
4j. Naked pair {36} in R89C5 -> no 3,6 in R9C46
Clean-ups:
R2C4 = 6 -> no 5,6,7 in R1C3, no 5,7 in R2C3
R2C5 = 2 -> no 1 in R2C6
R2C6 = 2 -> no 3 in R2C7
R3C3 = 9 -> no 8,9 in R2C2, no 8 in R2C3
R3C4 = 6 -> no 6 in R2C3
R4C3 = 3 -> no 2,3,4 in R3C2
R6C9 = 1 -> no 1 in R7C8
R1C4 = {89} -> no 8 in R1C3
[With hindsight I missed clean-ups in R89C46 using naked pair {36} in R89C5, which would have given R9C6 = 1 and made things a bit quicker.]

5a. R12C3 = [24], placed for C3, 2 placed for R1
5b. R2C7 = 2, placed for C7
5c. R3C28 = [14], placed for R3
5d. R3C1 = 3, placed for R3 and C1
5e. R3C9 = 2, placed for C9
Clean-ups:
R1C3 = 2 -> 1,3 in R1C2, no 1,2,3 in R2C2
R2C3 = 4 -> no 5 in R12C2
R2C7 = 2 -> no 1 in R1C8, no 1,3 in R2C8
R3C1 = 3 -> no 4 in R2C12
R3C2 = 1 -> no 1 in R2C1
R3C8 = 4 -> no 5 in R2C8, no 3,4,5 in R2C9
R3C9 = 2 -> no 2 in R2C8
R7C3 = {78} -> no 7,8 in R7C2 + R8C23

6a. R1C1 = 1 (hidden single in R1), placed for C1
6b. R1C9 = 3 (hidden single in R1), placed for C9, no 4 in R2C8
6c. R2C8 = 9, no 8 in R1C78 + R2C9
6d. R2C9 = 6, placed for C9, no 5,6,7 in R1C8
6e. R1C48 = [89], placed for R1
6f. R1C7 = 5, placed for C7, no 6 in R1C6
6g. R1C26 = [67]
6h. Naked pair {56} in R68C3 -> no 7 in R7C3
6i. R7C3 = 8, placed for R7 and C3
6j. R9C3 = 7 (hidden single in C3), placed for R9, no 6 in R8C3
6k. R8C3 = 5, placed for C3
6l. R6C3 = 6 -> R6C2 = 4 (blue), no 5 in R6C1
6m. R6C1 = 4, placed for C9
Clean-ups:
R1C2 = 6 -> no 5,6,7 in R2C1, no 7 in R2C2
R6C1 = 4 -> no 3 in R7C2
R7C3 = 8 -> no 9 in R8C2
R8C3 = 5 -> no 4,6 in R8C24, no 4,5,6 in R9C2, no 4,5 in R9C4
R9C3 = 7 -> no 8 in R9C24
R7C1 = {67} -> no 6,7 in R8C1
R7C7 = {34} -> no 3,4 in R7C68 + R8C678
R7C9 = {45} -> no 5 in R78C8, no 4,5 in R8C9

7a. R8C7 = 8, placed for C7, no 8 in R9C8
7b. R8C9 = 8, placed for C9
7c. R89C4 = [19] (blue), 9 placed for R9
7d. R9C1 = 8 (hidden single in R9), placed for C1
7e. R248C1 = [965], R7C1 = 7, placed for R7
7f. R7C8 = 6, no 5 in R7C9
7g. R7C9 = 4, placed for R7 and C9
7h. R7C7 = 3, placed for R7 and C7
7i. R9C79 = [45], placed for R9
7j. R7C246 = [215]
Clean-ups:
R4C1 = 6 -> no 5 in R4C2
R7C2 = 2 -> no 1,3 in R8C2
R7C6 = 5 -> no 6 in R8C56
R7C7 = 3 -> no 2 in R8C68
R8C7 = 8 -> no 7,9 in R8C8
R9C7 = 4 -> no 5 in R8C6, no 3 in R9C8
R9C9 = 5 -> no 6 in R89C8

8a. R89C5 = [36], no 2 in R9C6
8b. R9C268 = [312]
Clean-ups:
R9C2 = 3 -> no 2 in R8C2
R9C8 = 2 -> no 1 in R8C8

The rest is naked singles.

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


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 Post subject: Re: Mean ORC 2,3,4,5
PostPosted: Thu Apr 18, 2019 4:39 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1658
Location: Lethbridge, Alberta, Canada
As with my earlier posts, I had to restart for the same reason.

Mean ORC 4 felt a bit harder to me than Mean ORC 3; that was mainly because I don't have sufficient experience with NCs, those who do won't find it difficult.

Here is my walkthrough for Mean ORC 4:
Cells adjacent to yellow lines must total less than 8, green total 8 or 9, blue must total 10, red must total 11 or 12, grey total more than 12.
AK so diagonally adjacent cells cannot be equal, also FNC and NC so horizontally/ vertically/diagonally adjacent cells cannot be {12}, {23}, … {78}, {89}, therefore at least one of the cells adjacent to each green or yellow mark must contain one of 1,2,3 as green cannot be {45}; similarly at least one of the cells adjacent to each red or grey mark must contain one of 7,8,9 as red cannot be {56}.
Odd numbered rows and columns are normal; repeats are allowed on even numbered rows and columns.

Prelims.
Delete 7,8,9 from cells either side of yellow marks.
Delete 9 from cells either side of green marks in even rows and columns.
Delete 4,9 from cells either side of green mark in R1 (4 because of NC).
Delete 5 from either side of blue mark in R3.
Delete 1 from cells either side of red marks in even rows and columns.
Delete 1,6 from cells either side of red marks in odd rows and columns (6 because of NC).
Delete 1,2,3 from cells either side of grey marks.
Clean-ups, AK, FNC and NC, separately or together, only when stated.

1a. R3C8 = {46} -> R3C9 = {46} (blue), 4,6 locked for R3
1b. R3C8 = {46} -> R2C8 = {89} (grey, R23C8 cannot be [76], NC)
1c. R3C9 = {46} -> R2C9 = {89} (grey, R23C9 cannot be [76], NC)
[Note. R2C89 must be either [88] or [99] (cannot be {89}, NC)
1d. R2C9 = {89} -> R1C9 = {23} (red)
1e. R1C9 = {23} -> R1C8 = {567} (green)
1f. R3C8 = {46} -> R4C8 = {123} (yellow)
Clean-ups:
R1C8 = {567} -> no 6 in R12C7
R2C8 = {89} -> no 8,9 in R13C7
R3C8 = {46} -> no 5 in R234C7 + R4C9
R3C89 = {46} -> no 3 in R4C8, no 3,4,6 in R4C9
R4C8 = {12} -> no 1,2 in R3C7 + R5C79
R4C9 = {12} -> no 1,2 in R5C8

2a. R34C2 (yellow) -> R3C2 = {23}, R4C2 = {45}
2b. R3C2 = {23} -> R3C3 = {89} (red)
2c. R4C2 = {45} -> R5C2 = {89} (grey)
2d. R1C7 = {457} -> R2C7 = {89} (grey, cannot be [77] in odd column)
Clean-ups:
R2C7 = {89} -> no 8,9 in R13C6
R3C2 = {23} -> no 2,3 in R234C1 + R24C3
R3C3 = {89} -> no 8 in R2C34, no 8,9 in R3C4 + R4C34
R4C2 = {45} -> no 5 in R3C1, no 4,5 in R5C13
R5C2 = {89} -> no 8,9 in R4C1 + R56C13

3a. R2C7 = {89} -> R2C6 = {234} (red)
3b. R2C6 = {234} -> R2C5 = {789} (red)
3c. R2C5 = {789} -> R2C4 = {2345} (red)
3d. R2C4 = {2345} -> R2C3 = {4567} (green)
3e. R2C3 = {4567} -> R2C2 = {3456} (blue)
3f. R3C2 = {23} -> R2C2 = {345} (yellow)
3g. R2C2 = {345} -> R2C1 = {567} (blue)
3h. R2C2 = {345} -> R2C3 = {567} (blue)
3i. R2C3 = {567} -> R2C4 = {234} (green)
3j. R2C2 = {345} -> R1C2 = {3456} (green)
Clean-ups:
R2C1 = {567} -> no 6 in R1C12
R1C2 = {345} -> no 4 in R1C13
R2C4 = {234} -> no 3 in R1C35 + R3C5
R2C5 = {789} -> no 8 in R1C45 + R3C5
R2C6 = {234} -> no 3 in R3C7

4a. R3C7 = 7, placed for R3 and C7, no 8 in R2C78, no 6 in R3C8
4b. R2C7 = 9, placed for C7
4c. R2C8 = 9, no 8 in R2C9
4d. R2C9 = 9, placed for C9
4e. R3C89 = [46], 6 placed for C9
4f. R2C7 = 9 -> R2C6 = {23} (red)
4g. R2C6 = {23} -> R2C5 = {89} (red)
4h. R3C3 = {89} -> R3C4 = {23} (red)
Clean-ups:
R3C7 = 7 -> no 6,7,8 in R4C6, no 6,8 in R4C7
R3C8 = 4 -> no 3,4 in R4C7
R1C7 = {45} -> no 4,5 in R1C6
R2C5 = {89} -> no 9 in R1C45 + R3C5
R2C6 = {23} -> no 2 in R13C5
R3C4 = {23} -> no 2,3 in R4C5
R4C7 = {12} -> no 1,2 in R35C6

5a. Naked pair {23} in R3C24, locked for R3
5b. R3C6 = 5, placed for R3
5c. R3C5 = 1, placed for R3 and C5, no 2 in R2C46 + R3C4
5d. R3C4 = 3 -> R3C2 = 2, no 3 in R2C2
5e. R2C2 = {45} -> R2C1 = {56} (blue)
5f. R2C2 = {45} -> R2C3 = {56} (blue)
5g. R2C6 = 3 -> no 4 in R1C57, no 2 in R1C6
5h. R1C7 = 5, placed for R1 and C7, no 6 in R1C8
5i. R1C8 = 7, placed for R1
5j. R1C5 = 6, placed for R1 and C5
5k. R1C8 = 7 -> R1C9 = 2 (green), placed for R1 and C9
5l. R4C9 = 1, placed for C9, no 2 in R4C8
5m. R4C8 = 1 -> no 2 in R4C7
5n. R4C7 = 1, placed for C7
5o. Naked pair {34} in R1C24, locked for R1
5p. R1C6 = 1, placed for R1
5q. Naked pair {89} in R13C1, locked for C1
5r. Naked pair {89} in R13C3, locked for C3
Clean-ups:
R3C2 = 2 -> no 1 in R4C13
R3C4 = 3 -> no 4 in R2C4 + R4C35, no 2,4 in R4C4
R2C4 = 3 -> no 4 in R1C4
R1C4 = 3, placed for R1
R1C2 = 4 -> no 5 in R2C123
R3C5 = 1 -> no 1 in R4C4, no 2 in R4C6
R3C6 = 5 -> no 5 in R4C5, no 4 in R4C6
R4C3 = {567} -> no 6 in R5C4

6a. R2C1 = 6, placed for C1
6b. R2C3 = 6, placed for C3
6c. R4C5 = {789} -> R4C6 = {35} (red)
Clean-ups:
R4C3 = {57} -> no 6 in R4C4
R4C6 = {35} -> no 4 in R5C567
R4C5 = {789} -> no 8 in R5C456

7a. R5C8 = {3456} -> R6C8 = {123} (yellow, cannot be [34], NC), no 2 in R7C7
7b. R567C3 cannot contain all of 1,2,3 -> R9C3 = {123}
7c. 4 in C3 only in R678C3 -> no 3,5 in R7C3
7d. 6 in R5 only in R5C678 -> no 6 in R6C7
7e. R567C7 can only contain one of 2,3 (NC) -> R9C7 = {23}
7f. 4 in C7 only in R678C7 -> no 3,4,5 in R7C68, no 3 in R7C7
Clean-up:
R9C3 = {123} -> no 2 in R9C4
R9C7 = {23} -> no 2,3 in R89C6

8a. R7C8 = {126} -> R8C8 = {489} (blue)
8b. R8C7 = {468} -> R8C8 = {89} (grey)
8c. R8C8 = {89} -> R7C8 = {12} (blue), no 2 in R6C7
8d. R9C7 = 2 (hidden single in C7), placed for R9
8e. 3 in C7 only in R56C7 -> no 3 in R5C6, no 3,4 in R5C8, no 2 in R6C68, no 4 in R6C7
8f. 4 in C7 only in R78C7 -> no 5 in R8C6
8g. R8C3 = {457} -> R8C4 = {789} (grey, cannot be [76], NC)
8h. R8C4 = {789} -> R8C5 = {2345} (red)
8i. R8C56 (blue) -> R8C5 = {234}, R8C6 = {678} (blue)
8j. R8C6 = {678} -> R8C7 = {46} (red)
Clean-ups:
R9C7 = 2 -> no 1 in R9C7
R5C8 = {56} -> no 5 in R56C9
R8C7 = {46} -> no 5 in R9C68
R8C8 = {89} -> no 8 in R7C79 + R9C9
R8C5 = {234} -> no 3 in R79C45

9a. Naked pair {46} in R78C7, locked for C7, no 6,7 in R7C6, no 7 in R8C6
9b. Naked pair {38} in R56C7, no 7,9 in R5C6
9c. Naked pair {56} in R5C68, locked for R5
9d. R8C6 = {68} -> R8C5 = {24} (blue)
9e. R5C8 = {56} -> R6C8 = 1 (yellow), no 2 in R7C8
9f. R7C8 = 1, placed for R7
9g. R7C8 = 1 -> R8C8 = 9 (blue), no 8 in R8C9 + R9C8
9h. 8 in C9 only in R56C9 -> no 7 in R56C9
9i. 5 in C9 only in R789C9 -> no 4 in R8C9
Clean-up:
R5C6 = {56} -> no 5 in R6C5
R7C7 = {46} -> no 5 in R6C6
R8C6 = {68} -> no 7 in R79C5

10a. 5 in C5 only in R79C5 -> no 4 in R8C5
10b. R8C5 = 2, placed for C5, no 2 in R7C6
10c. R8C5 = 2 -> R8C6 = 8 (blue), no 9 in R7C6
10d. R7C6 = 8, placed for R7
10e. R7C6 = 8 -> R6C6 = {34} (red)
10f. R8C6 = 8 -> R8C7 = 4, placed for C7
10g. R7C7 = 6, placed for R7
Clean-ups:
R7C6 = 8 -> no 7,8,9 in R6C5, no 8 in R6C7, no 9 in R7C5
R6C7 = 3 (placed for C7) -> no 4 in R6C6
R6C6 = 3 -> no 4 in R6C5
R6C5 = 3 (placed for C5) -> no 2,3,4 in R5C4, no 2,4 in R67C4, no 4 in R7C5
R7C5 = 5 (placed for R7 and C5) -> no 5,6 in R6C4
R8C6 = 8 -> no 8,9 in R9C5, no 7,9 in R9C6
R9C5 = 4 -> no 4 in R9C68
R5C5 = {79} -> no 8 in R4C5

11a. R5C7 = 8, placed for R5
11b. R5C2 = 9, placed for R5
11c. R5C45 = [17], placed for R5, 7 placed for C5, no 2 in R5C3
11d. R24C5 = [89]
11e. R5C13 = [23], 2 placed for C1, 3 placed for R5 and C3, no 1,3 in R6C1, no 2,4 in R6C3
11f. R5C9 = 4, placed for C9, no 5 in R5C8, no 3 in R6C9
11g. R5C8 = 6, placed for R5
11h. R4C5 = 9 -> R4C6 = 3 (red)
11i. R9C35 = [14], placed for R9
11j. R7C3 = 2 (hidden single in R7/C3)
11k. R8C3 = 4 (hidden single in C3), no 4 in R7C2
11l. Naked pair {79} in R7C24, locked for R7, no 7 in R6C3
11m. R46C3 = [75], no 8 in R3C3
11n. R3C3 = 9, placed for R3 and C3
11o. R3C1 = 8, placed for C1, no 7 in R4C1
11p. R7C9 = 3, placed for R7 and C9
11q. R7C1 = 4, placed for C1
11r. R4C1 = 5, placed for C1, no 4 in R4C2
11s. R689C1 = [713], no 6 in R6C2
11t. R6C3 = 5 -> R6C2 = 7 (red)
11u. R8C3 = 4 -> R8C2 = {78} (red}
11v. R8C3 = 4 -> R8C4 = 9 (grey)
Clean-ups:
R5C3 = 3 -> no 3 in R46C4
R5C5 = 7 -> no 7 in R4C4, no 7,8 in R6C4
R6C1 = 7 -> no 7 in R7C2
R7C2 = 9 (placed for R7) -> no 8 in R8C2
R7C3 = 2 -> no 1 in R6C4
R8C2 = 7 -> no 6,8 in R9C2
R8C3 = 4 -> no 5 in R9C24
R8C4 = 9 -> no 8 in R9C4

12a. R9C9 = 5 (hidden single in R9), placed for C9
12b. R8C9 = 7 -> no 6,7 in R9C8

The rest is naked singles.

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


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 Post subject: Re: Mean ORC 2,3,4,5
PostPosted: Thu Apr 18, 2019 7:59 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1658
Location: Lethbridge, Alberta, Canada
As with my earlier posts, I had to restart for the same reason.

Mean ORC 5 is possibly about the same level of difficulty as Mean ORC 4 if one finds steps 4c and 5a, which I happened to spot easily.

Here is my walkthrough for Mean ORC 5:
Cells adjacent to yellow lines must total less than 8, green total 8 or 9, blue must total 10, red must total 11 or 12, grey total more than 12.
AK so diagonally adjacent cells cannot be equal, also FNC and NC so horizontally/ vertically/diagonally adjacent cells cannot be {12}, {23}, … {78}, {89}, therefore at least one of the cells adjacent to each green or yellow mark must contain one of 1,2,3 as green cannot be {45}; similarly at least one of the cells adjacent to each red or grey mark must contain one of 7,8,9 as red cannot be {56}.
Odd numbered rows and columns are normal; repeats are allowed on even numbered rows and columns.

Prelims.
Delete 7,8,9 from cells either side of yellow marks.
Delete 9 from cells either side of green mark in R8,
Delete 4,9 from cells either side of green marks in odd rows and columns (4 because of NC).
Delete 5 from cells either side of blue marks in R13.
Delete 1 from cells either side of red marks in even rows and columns.
Delete 1,6 from cells either side of red marks in R3 and C13 (6 because of NC).
Delete 1,2,3 from cells either side of grey marks.
Clean-ups, AK, FNC and NC, separately or together, only when stated.

1a. R2C7 = {56} -> R2C8 = {45} (blue)
1b. R2C8 = {45} -> R2C9 = {56} (blue)
1c. R2C7 = {56} -> R1C7 = {23} (green), no 2,3 in R1C6
1d. R1C7 = {23} -> R1C8 = {78} (blue)
1e. R2C7 = {56} -> R3C7 = {12} (yellow)
1f. R3C7 = {12} -> R3C8 = {89} (blue)
1g. R2C9 = {56} -> R1C9 = {12} (yellow)
1h. R2C9 = {56} -> R3C9 = {23} (green)
1i. R1C7 = {23} -> R1C6 = {145} (yellow)
1j. R1C6 = {145} -> R2C6 = {569} (blue)
1k. R2C7 = {56} -> R2C6 = 9 (grey)
1l. R2C6 = 9 -> R1C6 = 1, placed for R1
1m. R1C9 = 2, placed for R1 and C9
1n. R1C7 = 3, placed for R1 and C7
1o. R1C7 = 3 -> R1C8 = 7 (blue), placed for R1
1p. R1C9 = 2 -> R2C9 = 5 (yellow), placed for C9
1q. R2C9 = 5 -> R2C8 = 5 (blue)
1r. R2C8 = 5 -> R2C7 = 5 (blue), placed for C7
1s. R3C9 = 3, placed for R3 and C9
1t. R3C9 = 3 -> R4C9 = 6 (green), placed for C9
1u. R4C9 = 6 -> R4C8 = 6 (red, cannot be [56], NC)
Clean-ups:
R1C6 = 1 -> no 1,2 in R2C5
R2C6 = 9 -> no 8,9 in R13C5, no 8 in R2C5 + R3C6
R2C7 = 5 -> no 4,5,6 in R3C6
R4C8 = 6 -> no 7 in R4C7 + R5C9, no 6,7 in R5C7, no 5,7 in R5C8
R4C9 = 6 -> no 6 in R5C8
R3C7 = {12} -> no 1,2 in R3C6, no 2 in R4C67
R3C6 = {79} -> no 8 in R4C567
R3C8 = {89} -> no 9 in R4C7
R4C7 = {46} -> no 5 in R45C6
R1C5 = {456} -> no 5 in R1C4 + R2C45

2a. R4C7 = {46} -> R4C6 = {67} (red)
2b. R4C6 = {67} -> R4C5 = {34} (blue)
2c. R4C5 = {34} -> R4C4 = {789} (red)
2d. R4C4 = {789} -> R4C3 = {123} (blue)
Clean-ups:
R4C5 = {34} -> no 4 in R3C45, no 3,4 in R5C456
R4C6 = {67} -> no 6,7 in R35C5
R4C3 = {123} -> no 2 in R35C234
R4C4 = {789} -> no 8 in R3C3 + R5C5

3a. R7C2 = {56} -> R7C1 = {89} (grey, cannot be [76], NC)
3b. R7C2 = {56} -> R7C3 = {23} (green)
3c. R78C3 (red) -> R7C3 = 3, R8C3 = 8, both placed for C3, 3 placed for R7
3d. R8C3 = 8 -> R8C2 = 1 (green)
3e. R8C3 = 8 -> R9C3 = {56}
3f. R4C3 = {12} -> R4C4 = {89} (blue)
3g. R7C2 = {56} -> R6C2 = {67} (red, cannot be {56}, NC)
Clean-ups:
R7C3 = 3 -> no 2,4 in R6C3 + R7C4, no 2,3,4 in R68C4
R8C2 = 1 -> no 2 in R8C1 + R9C2, no 1,2 in R9C1
R8C3 = 8 -> no 7,8,9 in R79C4, no 7,9 in R8C4
R4C3 = {12} -> no 1 in R35C234
R4C4 = {89} -> no 9 in R3C3 + R5C5
R6C2 = {67} -> no 6,7 in R5C1, no 6 in R5C3
R5C3 = {45} -> no 4,5 in R45C2, no 5 in R5C4 + R6C34
R7C1 = {89} -> no 8,9 in R6C1
R7C2 = {56} -> no 5,6 in R6C1, no 6 in R6C3, no 5 in R8C1
R7C4 = {56} -> no 5,6 in R678C5
R8C1 = {34} -> no 3 in R9C12
R9C3 = {56} -> no 5,6 in R89C4

4a. Naked pair {56} in R7C24, locked for R7
4b. R9C12 (green) -> R9C1 = {78}, R9C2 = 1, placed for R9
4c. R789C1 (double red) = [847/938], 8 locked for C1
[This seems to be an important step.]
4d. R4C12 (blue) -> R4C1 = {479}, R4C2 = {136}
4e. R7C4 = {56} -> R6C4 = {67} (red)
Clean-up:
R6C4 = {67} -> no 7 in R7C5

5a. 8 in R1 only in R1C24 -> no 9 in R1C3, no 7,9 in R2C3
[Cracked. It gets easier after this.]
5b. R6C3 = 9 (hidden single in C3)
5c. R3C3 = 7 (hidden single in C3), placed for R3, no 6 in R3C24, no 8 in R4C4
5d. R3C6 = 9, placed for R3
5e. R3C8 = 8, placed for R3
5f. R3C4 = 5, placed for R3
5g. R3C2 = 4, placed for R3, no 4 in R4C1
5h. R3C1 = 6 (hidden single in R3), placed for C1, no 7 in R4C1
5i. R4C1 = 9, placed for C1
5j. R4C1 = 9 -> R4C2 = 1 (blue)
5k. R4C4 = 9 -> R4C3 = 1, placed for C3
5l. R4C4 = 9 -> R4C5 = 3 (red), placed for C5, no 2 in R35C5
5m. R4C5 = 3 -> R4C6 = 7 (blue), no 6 in R4C7
5n. R4C7 = 4, placed for C7
5o. R3C5 = 1, placed for R3 and C5
5p. R3C7 = 2, placed for C7
5q. R5C5 = 5, placed for R5 and C5
5r. R5C3 = 4, placed for R5 and C3
5s. R7C1 = 8, placed for R7 and C1
5t. R9C1 = 7, placed for R9 and C1
5u. R9C1 = 7 -> R8C1 = 4 (red), placed for C1
5v. R1C1 = 5, placed for R1
5w. R1C3 = 6, placed for R1 and C3
5x. R1C5 = 4, placed for R1 and C5
5y. R9C3 = 5, placed for R9 and C3
Clean-ups:
R1C1 = 5 -> no 4,5,6 in R2C2
R1C3 = 6 -> no 7 in R2C2, no 6,7 in R2C4
R1C5 = 4 -> no 3,4 in R2C4
R2C3 = 2 -> no 1,3 in R2C2, no 1 in R2C4
R3C2 = 4 -> no 3 in R2C1
R3C3 = 7 -> no 8 in R2C24
R3C4 = 5 -> no 6 in R2C5
R3C5 = 1 -> no 2 in R2C4
R3C6 = 9 -> no 9 in R2C5
R4C2 = 1 -> no 1,2 in R5C1
R4C4 = 9 -> no 8 in R5C4
R4C5 = 3 -> no 2 in R5C6
R4C6 = 7 -> 6,8 in R5C6, no 8 in R5C7
R4C7 = 4 -> no 3 in R5C8
R5C3 = 4 -> no 3 in R5C2
R5C5 = 5 -> no 6 in R56C4, no 4,5,6 in R6C6
R6C3 = 9 -> no 8,9 in R5C2, no 9 in R5C4
R8C1 = 4 -> no 5 in R7C2
R9C3 = 5 -> no 4 in R9C4

6a. R5C1 = 3, placed for C1, no 2 in R6C1
6b. R6C1 = 1, placed for C1
6c. R5C4 = 7, placed for R5
6d. R5C8 = 2 (hidden single in R5), no 1 in R5C7
6e. R5C7 = 9, placed for R5 and C7
6f. R5C9 = 8 (hidden single in R5), placed for C9
6g. R7C2 = 6, placed for R7
6h. R2C4 = 9 -> no 8 in R1C4
6i. R1C4 = 9, placed for R1
Clean-ups:
R1C2 = 8 -> no 9 in R2C2
R5C2 = 6 -> no 7 in R6C2
R5C4 = 7 -> no 7,8 in R6C5
R5C6 = 1 -> no 2 in R6C56, no 1 in R6C7
R5C7 = 9 -> no 8,9 in R6C68, no 8 in R6C7
R5C8 = 2 -> no 1,3 in R6C8, no 1 in R6C9
R5C9 = 8 -> no 7 in R6C8, no 7,9 in R6C9

7a. R6C5 = 9, placed for C5
7b. R7C5 = 2, placed for R7 and C5
7c. R2C5 = 7 -> R89C5 = [86], 6 placed for R9
7d. R9C7 = 8, placed for R9 and C7
Clean-ups:
R7C5 = 2 -> no 1,3 in R6C6, no 1 in R7C6 + R8C4, no 1,2,3 in R8C6
R8C5 = 8 -> no 7,9 in R7C6
R9C5 = 6 -> no 5,6 in R8C6
R8C6 = 4 -> no 3 in R9C6
R9C7 = 8 -> no 7 in R8C7, no 7,8,9 in R8C8, no 9 in R9C8
R6C7 = {67} -> no 7 in R7C78

8a. R678C7 = [716]
8b. R7C6789 = [4197]
8c. R6789C9 = [4719]
Clean-ups:
R6C7 = 7 -> no 6 in R6C8
R6C9 = 4 -> no 5 in R6C8
R7C7 = 1 -> no 2 in R6C8, no 1,2 in R8C8
R7C9 = 7 -> no 6 in R8C8

9a. R8C6 = 4 -> R9C6 = 2 (yellow), placed for R9
9b. R9C4 = 3, placed for R9
9c. R9C8 = 4, no 3,5 in R8C8 -> R8C8 = 4

The remaining cells are already naked singles.

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


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 Post subject: Re: Mean ORC 2,3,4,5
PostPosted: Thu May 02, 2019 10:43 pm 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1658
Location: Lethbridge, Alberta, Canada
Mean ORC 2 is definitely the hardest of this batch of puzzles.

As HATMAN has since commented it is quite hard and awkward. Several weeks ago he told me how he'd cracked it; I've since found an alternative way to look at his hard step, both HATMAN's and my key move are included in my walkthrough.

Here is my walkthrough for Mean ORC 2:
Cells adjacent to yellow lines must total less than 8, green total 8 or 9, blue must total 10, red must total 11 or 12, grey total more than 12.
AK so diagonally adjacent cells cannot be equal, also FNC and NC so horizontally/ vertically/diagonally adjacent cells cannot be {12}, {23}, … {78}, {89}, therefore at least one of the cells adjacent to each green or yellow mark must contain one of 1,2,3 as green cannot be {45}; similarly at least one of the cells adjacent to each red or grey mark must contain one of 7,8,9 as red cannot be {56}.
Odd numbered rows and columns are normal; repeats are allowed on even numbered rows and columns.

Prelims.
Delete 7,8,9 from cells either side of yellow marks.
Delete 9 from cells either side of green marks in even columns.
Delete 4,9 from cells either side of green mark in C5 (4 because of NC).
Delete 5 from cells either side of blue marks in R5.
Delete 1 from cells either side of red mark in R6
Delete 1,6 from cells either side of red marks in odd rows and columns (6 because of NC).
Delete 1,2,3 from cells either side of grey marks.
Clean-ups, AK, FNC and NC, separately or together, only when stated.

1a. R5C5 = 5, placed for R5 and C5
1b. R5C5 = 5 -> R5C6 = 7 (red), placed for R5, no 8 in R6C6
1c. R5C6 = 7 -> R5C7 = 4 (red), placed for R5 and C7
1d. R5C7 = 4 -> R5C8 = 6 (blue), placed for R5
1e. R5C5 = 5 -> R6C5 = 3 (green), placed for C5
1f. R6C5 = 3 -> R6C4 = 7 (blue)
1g. R6C5 = 3 -> R6C6 = 9 (red)
1h. 1 in C5 only in R78C5 -> no 2 in R78C5
1i. R9C5 = 2 (hidden single in C5), placed for R9, clean-up: no 1 in R8C5
1j. R9C5 = 2 -> R9C4 = 9 (red), placed for R9
1k. R7C5 = 1 (hidden single in C5), placed for R7
1l. R5C5 = 5 -> R5C4 = {12} (yellow)
1m. R5C4 = {12} -> R5C3 = {89} (blue)
1n. R5C1 = {89} -> R5C2 = {12} (blue)
1o. R5C9 = 3 (hidden single in R5), placed for C9, clean-up: no 2,4 in R4C9
1p. R5C9 = 3 -> R4C9 = 1 (yellow), placed for C9
1q. R23C5 = {47/48} (red), 4 locked for C5
1r. R1C5 = 6, placed for R1 and C5, clean-up: no 7 in R2C5
1s. R1C5 = 6 -> R1C6 = 1 (yellow), placed for R1
1t. R1C5 = 6 -> R2C5 = 8 (grey), placed for C5
1u. R3C5 = 4 (hidden single in C5), placed for R3
1v. R3C5 = 4 -> R4C5 = 9 (grey), placed for C5
1w. R4C5 = 9 -> R4C4 = 1(blue)
1x. R4C5 = 9 -> R4C6 = 1 (blue)
Clean-ups:
R1C5 = 6 -> no 5,7 in R1C4, no 5,6,7 in R2C46
R1C6 = 1 -> no 2 in R1C7 + R2C6, no 1,2 in R2C7
R2C5 = 8 -> no 8,9 in R1C4, no 9 in R2C46 no 7,8,9 in R3C46
R3C5 = 4 -> no 3,4 in R2C46, no 3,5 in R3C46
R4C4 = 1 -> no 1,2 in R3C3, no 2 in R35C4 + R4C3
R4C6 = 1 -> no 2 in R3C6 + R4C7, no 1,2 in R3C7
R4C9 = 1 -> no 1,2 in R3C8, no 2 in R3C9 + R4C8
R5C6 = 7 -> no 6,7,8 in R46C7
R5C7 = 4 -> no 3,5 in R46C7, no 3,4,5 in R46C8
R5C8 = 6 -> no 7 in R46C8, no 5,6,7 in R6C9
R5C9 = 3 -> no 2 in R6C8, no 2,4 in R6C9
R6C4 = 7 -> no 8 in R5C3, no 6,8 in R6C3 + R7C4, no 6,7,8 in R7C3
R6C5 = 3 -> no 2,3,4 in R7C46
R6C6 = 9 -> no 8 in R7C6, no 8,9 in R7C7
R7C5 = 1 -> no 1,2 in R8C46
R8C5 = 7 -> no 7 in R7C4, no 6,7 in R7C6, no 6,8 in R8C46, no 6,7,8 in R9C6
R9C4 = 9 -> no 8,9 in R8C3, no 8 in R9C3
R9C5 = 2 -> no 3 in R8C46, no 1,3 in R9C6
R1C4 = {234} -> no 3 in R12C3
R6C9 = {89} -> no 8,9 in R7C89
R9C6 = {45} -> no 5 in R89C7

2a. R5C34 = [91], placed for R5, 9 also placed for C3
2b. R5C12 = [82], 8 placed for C1, clean-up: no 7,9 in R4C1
2c. R5C1 = 8 -> R4C1 = {56}
Clean-ups:
R5C1 = 8 -> no 7,8,9 in R46C2, no 7,9 in R6C1
R5C2 = 2 -> no 1,3 in R46C2 + R4C3, no 1,2,3 in R6C13
R5C3 = 9 -> no 8 in R4C3
R4C1 = {56} -> no 5,6 in R3C12
R6C1 = {456} -> no 5 in R7C12

3a. Naked pair {16} in R3C46, locked for R3

4a. Naked pair {59} in R7C46, locked for R7
4b. R7C2 = 8 (hidden single in R7)
Clean-ups:
R7C2 = 8 -> no 7 in R68C3 + R7C1, no 7,9 in R8C12
R7C3 = {234} -> no 3 in R8C23

5a. 2 in R3 only in R3C12 -> no 1,2,3 in R2C1, no 1,3 in R2C2, no 3 in R3C12
5b. 1 in C1 only in R89C1 -> no 2 in R8C12, no 1 in R9C2
5c. 9 in C1 only in R123C1 -> 8 in R2C2
5d. 7 in R7 only in R7C789 -> no 6,8 in R68C8, no 6 in R7C8
5e. 8 in C3 only in R123C3 -> no 7,9 in R2C2, no 7 in R2C3
5f. 2 in C7 only in R678C7 -> no 3 in R7C7, no 2,3 in R7C8
5g. 3 in R7 only in R7C13 -> no 2,4 in R6C2, no 4 in R8C2
Clean-ups:
R6C2 = {56} -> no 6 in R7C1
R6C3 = {45} -> no 4 in R7C3, no 5 in R7C4
R7C3 = {23} -> no 2 in R8C3
R7C1 = {234} -> no 3 in R8C1

6. R7C4 = 9, placed for R7 -> R7C6 = 5
Clean-up:
R7C6 = 5 -> no 6 in R78C7, no 4 in R8C6

7a. No 1,3 in R2C9 -> no 7,9 in R2C8 (blue)
7b. R8C34 = [19/55/64] (blue), R8C3 = {156}, R8C4 = {459}

[This was as far as I managed without using a forcing chain. HATMAN told me how he broke the deadlock.
It is solvable using a complex elimination of R3C4 which is 1/6.
If it is 6 R4C3 is 4 and R3C3 is 8, this means R3C2 is 2 so no value for R2C3.
Hence R3C4 is 1 and R3C6 is 6.]

[I searched for, and eventually found, a forcing chain which gives the same result in a slightly longer way.]
8. Consider placements for R4C3 = {4567} with alternatives for R3C3 = {78} when R4C3 = 4
R4C3 = 4 with R3C3 = 7 => no 6 in R3C4
or R4C4 with R3C3 = 8, no 7,8,9 in R3C2 => R3C2 = 2, no 1,2 in R2C3 => R2C3 = {56} => no 6 in R3C3
or R4C3 = {567} => no 6 in R3C4
-> R3C4 = 1, placed for R3, R3C6 = 6
Clean-ups:
R3C4 = 1 -> no 1,2 in R2C3, no 2 in R2C4
R3C6 = 6 -> no 5,6,7 in R2C7, no 5,7 in R3C7
[Cracked. Now it’s a lot easier.]

9a. R1C7 = 5 (hidden single in C7), placed for R1
9b. R9C7 = 6 (hidden single in C7), placed for R9, no 7 in R8C7, no 5 in R9C6
9c. R7C7 = 7 (hidden single in C7), placed for R7
9d. R7C8 = 4, placed for R7
9e. R7C9 = 6 (hidden single in R7), placed for C9
9f. R9C6 = 4, placed for R9
Clean-ups:
R1C7 = 5 -> no 4 in R1C8, no 4,5,6 in R2C8
R7C7 = 7 -> no 7 in R8C68, no 8 in R8C7
R7C8 = 4 -> no 3 in R8C7, no 3,5 in R8C8, no 4,5 in R8C9
R7C9 = 6 -> no 7 in R8C9
R9C7 = 6 -> no 5 in R8C6, no 5,7 in R9C8

9a. R23C7 = {38} (hidden pair in C7) -> no 3,7,8,9 in R3C8
9b. R3C8 = 5, placed for R3
Clean-up:
R3C8 = 5 -> no 4,5 in R2C9, no 6 in R4C8

10a. R1C9 = 4 (hidden single in C9), placed for R1
10b. R9C9 = 5 (hidden single in C9), placed for R9
10c. Naked pair {23} in R7C13 -> no 1 in R8C2
Clean-ups:
R1C9 = 4 -> no 3 in R12C8 -> no 7 in R2C9 (blue)
R9C9 = 5 -> no 4 in R8C8
R1C4 = {23} -> no 2 in R1C3
R1C3 = {78} -> no 7,8 in R1C2, no 8 in R2C3

11a. R7C3 = 2 (hidden single in C3), placed for R7, no 1 in R8C3
11b. R7C1 = 3, placed for C1
11c. R9C3 = 1 (hidden single in C3), placed for R9
11d. R9C1 = 7, placed for R9 and C1, no 8 in R9C2
11e. R9C28 = [38], no 8,9 in R8C9
11f. R8C9 = 2, placed for C9
11g. R3C9 = 7 (hidden single in C9), placed for R3, no 8 in R2C9
11h. R2C9 = 9, placed for C9
11i. R2C9 = 9 -> R2C8 = 1 (blue)
Clean-ups:
R2C8 = 1 -> no 2 in R1C8
R2C9 = 9 -> no 8,9 in R1C8
R3C9 = 7 -> no 8 in R4C8
R6C9 = 8 -> no 9 in R6C8
R6C8 = 1 -> no 2 in R6C7
R7C1 = 3 -> no 4 in R68C1
R8C9 = 2 -> no 1 in R8C8
R9C1 = 7 -> no 6 in R8C1, no 6,8 in R8C2
R8C2 = 5 -> no 6 in R8C3
R9C8 = 8 -> no 9 in R8C78
R8C8 = 2 -> no 1 in R8C7

12a. R1C8 = 7, placed for R1
12b. R1C3 = 8, placed for C3, no 9 in R1C2
12c. R3C3 = 3, placed for R3
12d. R3C7 = 8, placed for R3 and C7, no 9 in R4C7
12e. R1C1 = 9 (hidden single in R1), placed for C1
12f. R3C1 = 2, placed for R3
12g. R8C1 = 1 (hidden single in C1)
12h. R6C7 = 9 (hidden single in C7)
Clean-ups:
R1C3 = 8 -> no 8 in R2C4
R2C4 = 1 -> no 2 in R1C4
R3C1 = 2 -> no 2 in R24C2
R3C3 = 3 -> no 4 in R24C23
R3C7 = 8 -> no 8 in R2C6, no 9 in R4C8

13a. R1C4 = 3, placed for R1
13b. R8C3 = 5, placed for C3
13c. R8C3 = 5 -> R8C4 = 5 (blue)
13d. R2C3 = 6, placed for C3
Clean-ups:
R2C3 = 6 -> no 5 in R2C2
R4C3 = 7 -> no 6 in R4C2
R6C3 = 4 -> no 5 in R6C2
R6C2 = 6 -> no 5 in R6C1

14. R246C1 = [456]


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