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Mean 38 and Mean ORC 39
http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=13&t=1571
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Author:  HATMAN [ Mon Jul 27, 2020 5:59 am ]
Post subject:  Mean 38 and Mean ORC 39

Mean ORC (not AK) A-S & OL

Meandoku 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
Black: 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:
FNC: Ferz Non-consecutive - diagonally adjacent are not consecutive
NC: adjacent cells are not consecutive

It is not Anti-King
There is the old lace group in the centre and the two reverse snakes that overlap with it.
This is hard or perhaps more correctly intricate, as no individual move is too hard.



Image

Mean 38 LS AK NC FNC OL

This one started life as an ORC but my preferred solution had no repeats in the even rows and columns, so an ordinary Latin square.

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

Note that (although I did not use it)
it is 1 to 9 NC and wrap NC

There are 72 solutions so essentially one; given nine numbers and three symmetries (left-right, top-bottom and increasing-decreasing). In one sloped direction there are keima (knights move) repeats and in the other there is a keima one to nine climb.

Image

Author:  Andrew [ Sun Aug 09, 2020 1:45 am ]
Post subject:  Re: Mean 38 and Mean ORC 39

Thanks HATMAN for a nice puzzle. It started easily, then became harder after finishing with most of the coloured clues. Took me a while to find my step 9, then it got a bit easier again.

Here is my walkthrough for Mean ORC 39:
Cells adjacent to yellow lines must total less than 8, green 8 or 9, red 11 or 12, black more than 12.
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 yellow mark must contain one of 1,2,3 in even rows/columns or just one of 1,2 in odd rows/columns.
No repeats in Reverse Snakes and Old Lace.
Odd numbered rows and columns are normal; repeats are allowed on even numbered rows and columns.

Prelims
Delete 1 from cells either side of red marks.
Delete 1,2,3 from cells either side of black marks.
Delete 7,8,9 from cells either side of yellow marks.
Delete 9 from cells either side of green marks.
Delete 4 from cells either side of green marks in R3 and C5 (NC)
Delete 6 from cells either side of red marks in C3 and C5 (NC)
Clean-ups, FNC and NC, only when stated.

1. R5C5 = 5, placed for R5, C5 and Old Lace
1a. R5C5 = 5 -> R4C5 = 3 (green), placed for C5
1b. R5C5 = 5 -> R6C5 = 7 (red), placed for C5
1c. R4C5 = 3 -> R3C5 = 1 (yellow + NC), placed for R3, C5, Old Lace and upper Reverse Snake
1d. R6C5 = 7 -> R7C5 = 9 (black + NC), placed for R7, C5, Old Lace and lower Reverse Snake
1e. R5C5 = 5 -> R5C6 = {12} (yellow)
1f. R5C5 = 5 -> R5C4 = {89} (black)
Clean-ups:
R3C5 = 1 -> no 2 in R2C5 + R3C4 (NC), no 2 in R24C46 (FNC)
R4C5 = 3 -> no 4 in R4C46 (NC), no 4 in R3C6, no 2 in R5C6 (FNC)
R5C5 = 5 -> no 6 in R4C46, no 4,6 in R6C46 (FNC)
R6C5 = 7 -> no 8 in R6C4 (NC), no 8 in R5C4, no 6 in R7C4,no 6,8 in R7C6 (FNC)
R7C5 = 9 -> no 8 in R8C5 (NC), no 8 in R8C46 (FNC)
R6C6 = {23} -> no 2,3 in R5C7 (FNC + Old Lace)

2a. R5C4 = 9, placed for R5
2b. R5C6 = 1, placed for R5
2c. R5C6 = 1 -> R6C6 = 3 (NC), placed for Old Lace
2d. Naked pair {78} in R4C46, locked for Old Lace
2e. R6C4 = 2, placed for Old Lace
2f. Naked pair {46} in R5C37, locked for R5
2g. R5C23 = [24] (yellow + NC), placed for R5, 4 placed for C3
2h. R5C7= 6, placed for C7
2i. R5C7 = 6 -> R4C6 = 8 (FNC) -> R4C4 = 7 (Old Lace)
2j. R5C2 = 2 -> R6C2 = 9 (red)
Clean-ups:
R4C4 = 7 -> no 6,8 in R3C4 + R4C3 (NC), no 6,8 in R3C3 (FNC)
R4C6 = 8 -> no 7,9 in R3C6 + R4C7 (NC), no 7,9 in R3C7 (FNC)
R5C2 = 2 -> no 3 in R4C2 + R5C1 (NC), no 3 in R4C1 + R6C3, no 1,3 in R4C3 + R6C1 (FNC)
R5C3 = 4 -> no 5 in R46C3 (NC), no 5 in R4C2 (FNC)
R5C6 = 1 -> no 2 in R46C7 (FNC)
R5C7 = 6 -> no 5 in R4C7, no 7 in R5C8, no 5,7 in R6C7 (NC), no 5,7 in R46C8 (FNC)
R6C2 = 9 -> no 8 in R6C3 + R7C2 (NC), no 8 in R5C1 (FNC)
R6C4 = 2 -> no 1,3 in R7C4 (NC), no 3 in R7C3 (FNC)
R6C6 = 3 -> no 4 in R6C7, no 2,4 in R7C6 (NC), no 2,4 in R7C7 (FNC)

3. R5C1 = 7, placed for R5 and C1
Clean-ups:
R5C1 = 7 -> no 6,8 in R4C1, no 6 in R6C1 (NC), no 6,8 in R4C2 (FNC)
Naked pair {38} in R5C89 -> no 2,4,9 in R4C8, no 2,4,7,9 in R4C9, no 2,4 in R6C8, no 2,4,7 in R6C9 (NC+FNC)

4. R3C67 = [58/68/85] (black), no 4, 8 locked for R3
4a. R3C89 = {49} (hidden pair in R3)
Clean-up:
Naked pair {49} in R3C89 -> no 3,5,8 in R2C89 + R4C9, no 3,8 in R4C8 (NC+FNC)
4b. R4C89 = [66] (red), 6 placed for C9
Clean-up:
R4C8 = 6 -> no 5 in R3C7 (FNC)
4c. R3C7 = 8, placed for R3 and C7
Clean-up:
R3C7 = 8 -> no 7,9 in R2C7, no 9 in R3C8 (NC), no 7,9 in R2C68 (FNC)
4d. R3C89 = [49], 9 placed for C9 and upper Reverse Snake
Clean-up:
R3C8 = 4 -> no 3,5 in R2C79, no 3,5 in R2C8, no 3 in R4C7 (FNC)
R3C9 = 9 -> no 8 in R2C8 (FNC)

5a. R67C3 = [75/92] (red), no 2 in R6C3
5b. R7C34 = [24/25/52] (yellow), 2 locked for R7
Clean-ups:
2 in R7 only in R7C34 -> no 1,3 in R8C34 (NC+FNC)
8 in R7 only in R7C89 -> no 7 in R8C89 (NC+FNC)
9 in C7 only in R68C7 -> no 8 in R7C8 (FNC)

6. R7C9 = 8 (hidden single in R7), placed for C9 and lower Reverse Snake
6a. R5C89 = [83], 3 placed for C9
6b. R6C89 = [35/81] (green), no 1,6 in R6C8
Clean-ups:
R5C8 = 8 -> no 9 in R6C7 (FNC)
R7C9 = 8 -> no 7 in R7C8 (NC)
6c. R8C7 = 9 (hidden single in C7)
Clean-up:
R8C7 = 9 -> no 8 in R9C68 (FNC)

7. R4C12 = {29}/[47/57] (red), no 4 in R4C2
7a. Consider combinations for R4C12
R4C12 = {29}/[47] => no 3 in R3C12 (NC or FNC) => 3 in R3 only in R3C34 = {35} (green), 5 locked for R3
or R4C12 = [57] => no 6 in R3C12 (NC+FNC) => R3C6 = 6 (hidden single in R3)
-> R3C6 = 6, placed for R3
Clean-up:
R3C6 = 6 -> no 5 in R2C6 (NC)
7b. R3C12 = [27]/{35} (green), no 2 in R3C2
7c. R3C34 = [27]/{35} (green), no 7 in R3C3
7d. R3C1234 = [27]{35}/[3527] (cannot be [5327], NC), no 5 in R3C1, no 3 in R3C2
Clean-ups:
R3C1 = {23} -> no 2,3 in R2C1, no 2 in R4C1 (NC), no 2,3 in R2C2 (FNC + upper Reverse Snake)
R3C2 = {57} -> no 6 in R2C1 (FNC), no 6 in R2C2 (NC)
R3C34 = [27]/{35} -> no 2 in R24C3 (C3 + NC+FNC)
2 in R3 only in R3C13 -> no 2 in R1C3 (C3 + upper Reverse Snake)
7 in R3 only in R3C24 -> no 6,8 in R2C3 (FNC)
7e. Naked pair {79} in R46C3, locked for C3
7f. R4C12 = [47/57/92], no 9 in R4C2

8. R67C1 = [24/25/41/51] (yellow + NC), no 3,6 in R7C1

[Getting harder, it took me a while to spot this.]
9. R3C34 = {35} (green) (cannot be [27] because R37C3 = [25] clashes with R2C3, NC), locked for R3
9a. R3C1 = 2, placed for C1 and upper Reverse Snake, R3C2 = 7
9b. R6C1 = {45} -> R7C1 = 1 (yellow), placed for R7, C1 and lower Reverse Snake
9c. R2C3 = 1 (hidden single in C3)
Clean-ups:
R2C3 = 1 -> no 2 in R1C24 (FNC)
R3C2 = 7 -> no 8 in R2C1 (FNC), no 8 in R2C2 (NC)
R7C1 = 1 -> no 2 in R8C2 (FNC)
R2C8 = {46} -> no 5 in R1C79 (FNC), no 5 in R1C8 (NC)
R3C3 = {35} -> no 4 in R2C24 (FNC)
R3C4 = {35} -> no 4 in R2C5 (FNC)
R2C5 = {68} -> no 7 in R1C46 (FNC), no 7 in R2C4 (NC)

10. Consider positions for 4 in R7
4 in one of R7C24 => no 5 in R78C3 (NC+FNC)
or R7C8 = 4 => R7C2 = 6 (hidden single in R7), no 5 in R78C3 (NC+FNC)
-> R7C3 = 2, placed for R7 and C3
and no 5 in R8C3
10a. R7C3 = 2 -> R6C3 = 9 (red), placed for C3 -> R4C3 = 7
Clean-ups:
R7C3 = 2 -> no 3 in R7C2 (NC), no 3 in R8C2 (FNC)
R8C3 = {68} -> no 7 in R7C2 (FNC), no 7 in R8C24 (NC)
10b. 7 in lower Reverse Snake only in R8C6 + R9C7 -> no 6 in R8C6 (FNC), no 6 in R9C6 (NC)
10c. 5 in C7 only in R79C7 -> no 4 in R8C6, no 4,6 in R8C8 (FNC)
10d. R6C89 = [35/81] (green) -> no 4 in R7C8 (NC+FNC)
10e. Consider placement for 5 in C7
R7C7 = 5 => no 5,6 in R7C8 (NC) => R7C8 = 3 => no 2 in R8C8 (NC), R8C8 = {35} => no 4 in R9C7 (FNC)
or R9C7 = 5
-> no 4 in R9C7
10f. 4 in lower Reverse Snake only in R8C24 -> no 3,5 in R9C3 (FNC)
10g. R9C3 = 6, placed for R9, C3 and lower Reverse Snake -> R8C3 = 8, placed for C3
Clean-ups:
R9C3 = 6 -> no 5 in R8C24 (FNC), no 5,7 in R9C24 (NC)
10h. R8C24 = [42], 2 placed for lower Reverse Snake
10i. R2C7 = 2 (hidden single in C7)
Clean-ups:
R2C7 = 2 -> no 1,3 in R1C68 (FNC), no 3 in R1C7 + R2C6 (NC)
R8C2 = 4 -> no 5 in R7C2, no 3,5 in R8C1, no 3 in R9C2 (NC), no 3,5 in R9C1 (FNC)
R8C3 = 8 -> no 9 in R9C24 (FNC)
R8C4 = 2 -> no 1,3 in R9C4 (NC)
R8C8 = {35} -> no 4 in R8C9 + R9C8 (NC), no 4 in R9C9 (FNC)

11a. R1C1 = 3 (hidden single in C1), placed for R1
11b. R1C3 = 5, placed for R1, C3 and upper Reverse Snake
11c. R3C34 = [35]
11d. R2C2 = 7, R1C7 = 4, placed for R1 and C7, R2C468 = [386], all upper Reverse Snake
11e. R46C7 = [13], 3 placed for C7
11f. R89C1 = [68] (hidden pair in C1), 8 placed for R9
11g. Naked pair {24} in R9C45, locked for R9 -> R9C2 = 1, placed for R9
11h. Naked pair {57} in R9C79, locked for R9
Clean-ups:
R1C1 = 3 -> no 4 in R2C1 (NC)
R1C3 = 5 -> no 6 in R1C24 (NC)
R2C2 = 7 -> no 8 in R1C2 (NC)
R2C4 = 3 -> no 2 in R1C5 (FNC)
R2C8 = 6 -> no 7 in R1C8 + R2C9 (NC), no 7 in R1C9 (FNC)
R3C3 = 3 -> no 2 in R4C2 (FNC)
R3C4 = 5 -> no 6 in R2C5 (FNC)
R9C5 = {24} -> no 3 in R9C6 (NC)
11i. R12C5 = [68], 6 placed for R1
11j. R4C2 = 7 -> R4C1 = {45} (red)
Clean-up:
R2C5 = 8 -> no 9 in R1C46 (FNC)
11k. R9C6 = 9, placed for R9 -> R9C8 = 3
11l. R1C28 = [79] (hidden pair in R1)
Clean-up:
R9C8 = 3 -> no 2 in R8C9 (FNC)
11m. Naked pair {15} in R68C9, locked for C9 -> R9C9 = 7, placed for R9
11n. R9C7 = 5, placed for C7 and lower Reverse Snake -> R7C7 = 7, placed for R7, R8C68 = [73]
Clean-ups:
R7C7 = 7 -> no 6 in R7C8 (NC), no 8 in R6C8 (FNC)
R8C6 = 7 -> no 6 in R8C5 (NC)
R8C5 = {24} -> no 3 in R7C6 (FNC)
R7C6 = 5 -> no 4 in R8C5 (FNC)
11o. R7C2468 = [6453]
Clean-up:
R7C2 = 6 -> no 5 in R6C1 (FNC)
11p. R6C8 = 3 -> R6C9 = 5 (green)

and the rest is singles in R1, R9, C1, C5 and C9

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

Author:  tarek [ Mon Aug 10, 2020 7:45 pm ]
Post subject:  Re: Mean 38 and Mean ORC 39

I also had a go it Puzzle #39 thanks. Like all of these overlapping puzzles, It takes a while!

With it being a Latin Square as it combines NC & FNC should we just call it King non-consecutive or KNC. Looking at the cell with 8 neighbours made me see more eliminations that the usual 4 that I normally see.

This would be a cool addition to Sukaku Explainer if I have the time!

tarek

Author:  Andrew [ Wed Aug 12, 2020 4:16 am ]
Post subject:  Re: Mean 38 and Mean ORC 39

Then I had a try at Mean 38, expecting to only get as far as alternative solutions but, much to my surprise, I seem to have reached a unique solution. Amazing considering that there are only 4 colour clues, the Old Lace, AK, NC, FNC, rows and columns.

Have I done something wrong?!

My start:
Cells adjacent to yellow lines must total less than 8, green 8 or 9, black more than 12.
AK so no diagonal repeats (the rows and columns prevent horizontal and vertical repeats).
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 yellow mark must contain one of 1,2,3 in even rows/columns or just one of 1,2 in odd rows/columns.

Prelims
Delete 1,2,3 from cells either side of the black mark.
Delete 7,8,9 from cells either side of the yellow mark
Delete 4,9 from cells either side of green marks (NC).
Clean-ups, AK, FNC and NC, only when stated.

1a. R5C5 = {56}
Clean-up:
R5C5 = {56} -> no 5,6 in R46C5 + R5C46 (NC), no 5,6 in R46C46 (AK+FNC)
1b. R5C5 = {56} -> R6C5 = {12} (yellow)
Clean-up:
R6C5 = {12} -> no 1,2 in R6C46 + R7C5 (NC), no 1,2 in R57C46 (AK+FNC)
1c. R5C5 = {56} -> R5C6 = 3 (green), placed for R5 + C6
Clean-up:
R5C6 = 3 -> no 2,4 in R4C6, no 2 in R5C7, no 4 in R6C6 (NC), no 4 in R4C5, no 2 in R6C5 (FNC), no 2,3,4 in R46C7 (AK+FNC)
1d. R6C5 = 1, placed for R6 and C5
1e. R5C5 = {56} -> R4C5 = {89} (black + NC)
Clean-ups:
R4C5 = {89} -> no 8,9 in R3C5 + R4C46 (NC), no 8,9 in R3C46 + R5C4 (AK+FNC)
R6C6 = {789} -> no 8 in R6C7 + R7C6 (NC), no 8 in R5C7 + R7C57 (AK+FNC)
1f. R5C45 = [46/75] (NC)
Clean-ups:
R5C45 = [46/75] (NC) -> no 4,7 in R46C4 (AK+FNC+NC), no 5,6 in R5C3 (NC)
R4C4 = {123} -> no 2 in R3C4 + R4C3 (NC), no 2 in R3C5 + R5C3 (AK+FNC)

2a. R4C4 = 2 (hidden single in Old Lace), placed for R4 and C4
Clean-up:
R4C4 = 2 -> no 1,3 in R3C4 + R4C3 (NC), no 1,2,3 in R3C3 (AK+FNC), no 3 in R3C5, no 1 in R5C3 (FNC)
2b. 3 in Old Lace only in R6C4 + R7C3 -> no 4 in R7C3 (FNC)

3. R5C78 = [17/18/62/71/72] (green), no 5, no 6 in R5C8

4. R5C45 (step 1f) = [46/75]
4a. Consider placements for 5 in Old Lace
R3C5 = 5 => R5C3 = 4 (hidden single in Old Lace)
or R5C5 = 5 or R7C5 = 5 => R6C6 = 3 (hidden single in Old Lace), no 4 in R5C4 (NC)
-> R5C45 = [75], placed for R5, 7 placed for C4, 5 placed for C5

Then continue as before with placements and clean-ups, gradually working outwards towards the edges and corners.

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

Author:  HATMAN [ Wed Sep 02, 2020 8:41 am ]
Post subject:  Re: Mean 38 and Mean ORC 39

Your solution to 38 is correct Andrew.

I am very pleased with this one as four clues is minimal: one to lock the number and three more to lock the three symmetries.

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