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 Post subject: Mean ORC 1 and 1A
PostPosted: Sat Dec 09, 2017 4:03 pm 
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Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 551
Mean ORC 1 and 1A

I decided to combine the two puzzle types I've been doing recently 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 1
Image

And a slightly harder one
Mean ORC 1A
Image

Solution:
162738495
384951617
516273849
738495162
951627384
273849516
495162738
627384951
849516273


Last edited by HATMAN on Tue Mar 26, 2019 8:00 pm, edited 1 time in total.

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 Post subject: Re: Mean ORC 1 and 1A
PostPosted: Sat Mar 23, 2019 9:58 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1651
Location: Lethbridge, Alberta, Canada
Having previously done SkyScraper Sum ORCs and MeanDoku NCs, I found the combination of MeanDoku and ORC fairly easy to understand.

Mean ORC 1 was straightforward. Just apply the various conditions as often as possible and it's all naked singles and pairs and hidden singles.

The following may be helpful to those new to AK, FNC, NC or to ORC.

My approach to this puzzle.:
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 marks in odd rows and columns (4 because of NC).
Delete 5 from cells either side of blue marks in odd rows and columns.
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.

A further note about the use of AK, FNC and NC.

After doing the Prelims R1C2 = {56} could be used to eliminate 5,6 from R1C13 and R2C1, but not from R2C2 because that's in an even column.

Similarly, after the Prelims, R8C8 = {456} could be used to eliminate 5 from R7C9 and R9C7, but not from R8C7 because that's in an even row.


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 Post subject: Re: Mean ORC 1 and 1A
PostPosted: Sat Mar 23, 2019 10:05 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1651
Location: Lethbridge, Alberta, Canada
Mean ORC was a bit harder, which is hardly surprising since 9 coloured marks have been removed from the R123C789 area.

First time through I made a silly mistake, thinking that I'd found a simple way to crack it but forgetting (just for that step) that repeats are allowed in even numbered rows and columns, so I re-worked using a forcing chain. Then I had to rework my walkthrough again because I'd made some incorrect assumptions, forgetting that repeats are allowed for coloured marks in even rows and columns.

Here is my walkthrough for Mean ORC 1A:
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 marks in odd rows and columns (4 because of NC).
Delete 5 from cells either side of blue marks in odd rows and columns.
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. R1C2 = {56} -> no 6 in R2C3
1b. R23C6 = [46] (blue), placed for C3, 6 placed for R3, no 5 in R1C2, no 3,5 in R1C3
1c. R1C2 = 6 -> R1C1 = 1 (yellow), R1C3 = 2, all placed for R1, 1 placed for C1, 2 placed for C3, no 2,5,6 in R2C1, no 5,7 in R2C2
1d. R2C1 = 3 -> R3C1 = 5 (green), both placed for C1, 5 also placed for R3
1e. R1C2 = 6 -> R2C2 = 8 (grey) -> R3C2 = 1 (green), 1 placed for R3
Clean-ups:
R1C3 = 2 -> no 3 in R1C4, no 1,2,3 in R2C4
R2C3 = 4 -> no 4,5 in R1C4, no 5 in R2C4, no 3,4 in R3C4
R3C1 = 5 -> no 4,6 in R4C1, no 4,5,6 in R4C2
R3C2 = 1 -> no 2 in R4C12, no 1 in R4C3
R3C3 = 6 -> no 6,7 in R2C4, no 7 in R3C4 + R4C2, no 5,7 in R4C3, no 5,6,7 in R4C4
R4C1 = {789} -> no 8 in R5C12

2a. R8C8 = {456} -> R8C7 = {789} (grey), no 8 in R79C7
2b. R8C8 = {456} -> R8C9 = {123} (yellow)
2c. R7C78 = [64/73] (blue), no 7 in R8C7, no 6 in R8C8
2d. R7C8 = {34} -> R7C9 = {78} (red)
2e. R7C9 = {78} -> R8C9 = {12} green, no 1,2 in R9C9
2f. R9C89 = [64/73] (blue), no 4 in R8C8
2g. R8C8 = 5 -> R7C8 = 3 (green), placed for R7, no 6 in R9C8
2h. R7C8 = 3 -> R7C7 = 7 (blue), placed for R7 and C7, no 8 in R8C7
2i. R7C9 = 8 -> R8C9 = 1 (green), both placed for C9, 8 placed for R7
2j. R9C8 = 7 -> R9C7 = 2 (green), both placed for R9, 2 placed for C7
2k. R9C8 = 7 -> R9C9 = 3 (blue), placed for R9 and C9
2l. R8C7 = 9, placed for C7
Clean-ups:
R7C7 = 7 -> no 6,7,8 in R6C68 + R8C6, no 6,8 in R6C7, no 6 in R7C6
R7C8 = 3 -> no 3,4 in R6C7, no 2,4 in R6C89
R7C9 = 8 -> no 9 in R6C8, no 7,9 in R6C9
R8C7 = 9 -> no 9 in R7C6, no 8,9 in R9C6
R9C7 = 2 -> no 1,2,3 in R8C6, no 1 in R9C6
R6C9 = {56} -> no 5,6 in R5C89
R9C6 = {456} -> no 5 in R89C5

3a. R12C7 = [46] (blue), both placed for C7, 4 also placed for R1
Clean-ups:
R1C7 = 4 -> no 3,5 in R1C68, no 3,4,5 in R2C68
R2C7 = 6 -> no 7 in R123C68

4a. R1C5 = 3 (hidden single in R1), placed for C5
4b. R1C9 = 5 (hidden single in R1), placed for C9
4c. R1C4 = 7 (hidden single in R1)
4d. R6C9 = 6, placed for C9
4e. R12C8 = [82/91] (blue)
Clean-ups:
R1C4 = 7 -> no 8 in R2C4, no 6,7,8 in R2C5
R1C5 = 3 -> no 4 in R2C4, no 2,4 in R2C5, no 2 in R2C6
R1C9 = 5 -> no 4 in R2C9
R2C4 = 9 -> no 8 in R3C4, no 8,9 in R3C5
R6C9 = 6 -> no 7 in R5C89, no 5 in R6C8
R1C6 = {89} -> no 9 in R2C5
R1C8 = {89} -> no 9 in R2C9
R2C8 = {12} -> no 2 in R3C9
R6C8 = {13} -> no 2 in R5C9

[At this stage, first time through, I made a silly mistake which seemed to crack the puzzle
R12C8 = [91] (blue) (cannot be [82] which clashes with R2C9, FNC)
Forgetting that R2C89 = [22] is allowed in an even row.
So I’ll try a forcing chain.]

5. Consider permutations for R12C8 (step 4e) = [82/91]
R12C8 = [82], clean-ups: no 7 in R2C9, no 3 in R3C78
R2C9 = 2, clean-up: no 2 in R3C8
R3C6 = 3 (hidden single in R3), clean-up: no 2,4 in R3C5
R3C4 = 2 (hidden single in R3)
or R12C8 = [91], clean-up: no 2 in R2C9 + R3C8
R2C9 = 7, placed for C9, clean-up: no 8 in R3C8
R4C9 = 2 (hidden single in C9), clean-up: no 3 in R3C8
Naked pair {49} in R3C89, locked for R3
R3C4 = 2, placed for R3
R3C5 = 7, clean-up: no 8 in R3C6
R3C67 = [38]
-> R3C4567 = [2738], placed for R3, 7 placed for C5, 8 placed for C7, clean-up: no 9 in R3C8
R3C89 = [49], 9 placed for C9
R5C9 = 4, placed for R5 and C9
Clean-ups:
R3C4 = 2 -> no 1 in R2C5, no 3 in R4C3, no 1,3 in R4C4, no 1,2 in R4C5
R3C5 = 7 -> no 6,8 in R2C6 + R4C5, no 8 in R4C4, no 6,7,8 in R4C6
R3C6 = 3 -> no 4 in R4C5, no 2,4 in R4C6, no 3 in R4C7
R3C7 = 8 -> no 9 in R24C6, no 7,8,9 in R4C8
R3C8 = 4 -> no 5 in R4C7, no 3,5 in R4C8
R5C9 = 4 -> no 4 in R4C8, no 3 in R56C8

[Much easier now. Almost back to the Simpler Version.]

6a. R4C7 = 1, R6C7 = 5, R5C7 = 3, placed for R5
6b. R2C5 = 5, R4C5 = 9, both placed for C5
Clean-ups:
R4C5 = 9 -> no 8,9 in R5C46, no 8 in R5C5
R4C7 = 1 -> no 2 in R4C8, no 1,2 in R5C68
R5C7 = 3 -> no 3 in R4C6, no 2,3,4 in R6C6
R6C7 = 5 -> no 5,6 in R5C6, no 4,5 in R7C6
R7C6 = {12} -> no 2 in R6C5, no 1,2 in R78C5

7a. R59C5 = [21] (hidden pair in C5), 2 placed for R5, 1 placed for R9
7b. R5C6 = 7, placed for R5
Clean-ups:
R5C5 = 2 -> no 2 in R4C4, no 1 in R4C6 + R5C4 + R6C6, no 2,3 in R6C4
R5C6 = 7 -> no 6,8 in R6C5
R9C5 = 1 -> no 1,2 in R8C4
R5C4 = {56} -> no 5 in R56C3

8a. R6C5 = 4, placed for C5, clean-up: no 5 in R5C4
8b. R7C5 = 6, placed for C5 and R7
8c. R8C5 = 8
8d. R5C4 = 6, placed for R5
8e. R5C1 = 9, placed for R5 and C1, clean-up: no 8 in R46C1
8f. R4C1 = 7, placed for C1
8g. R5C8 = 8, R5C23 = [51], 1 placed for C3
Clean-ups:
R5C1 = 9 -> no 8,9 in R46C2
R5C2 = 5 -> no 4,6 in R6C12
R5C3 = 1 -> no 1 in R4C2, no 1,2 in R6C2
R5C4 = 6 -> no 7 in R6C3, no 5,7 in R6C4
R5C8 = 8 -> no 7 in R4C9
R6C5 = 4 -> no 5 in R6C6, no 4,5 in R7C4
R7C5 = 6 -> no 6 in R6C4, no 5,6,7 in R8C4, no 5 in R8C6
R8C5 = 8 -> no 9 in R7C4 + R8C46, no 8,9 in R9C4

9a. R4C9 = 2, placed for C9, clean-up: no 1 in R4C8
9b. R2C9 = 7, clean-up: no 8 in R1C8
9c. R1C8 = 9, placed for R1
9d. R1C8 = 9 -> R2C8 = 1 (blue)

10a. R6C5 = 4 -> R6C4 = 8 (red), clean-ups: no 9 in R67C3
10b. R7C3 = 5, placed for R7 and C3
10c. R68C3 = [37] (hidden pair in C3), clean-up: no 8 in R9C3
10d. R9C3 = 9, placed for R9 and C3
Clean-ups:
R4C3 = 8 -> no 9 in R4C4
R6C3 = 3 -> no 2,4 in R7C2, no 2 in R7C4
R7C3 = 5 -> no 5 in R6C2, no 4,5,6 in R8C2, no 4 in R8C4
R8C3 = 7 -> no 8 in R8C24, no 6,8 in R9C2, no 6 in R9C4

11a. R67C1 = [24], placed for C1, clean-up: no 3 in R8C2
11b. R9C1 = 8 (hidden single in R9), placed for C1
11c. R8C12 = [62] (green)
Clean-ups:
R6C1 = 2 -> no 3 in R6C2, no 1 in R7C2
R8C1 = 6 -> no 5 in R9C2

The rest is naked singles, without using AK, NC, FNC or coloured marks.
Now to try some more of these puzzles, until the next Assassin appears on the Killer forum.


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