Anti Chess, NC and Forbidden Pairs (FP) puzzles

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Re: Anti Chess, NC and Forbidden Pairs (FP) puzzles

Postby creint » Mon Feb 11, 2019 7:41 pm

I think I still don't fully understand your rules:
No adjacent cells can sum, multiply, divide or subtract to give you 5 or 10
Toroidal grid: The grid displays a top-bottom right-left wrapping to
give you a toroidal (doughnut) shape

And look at this board state, which steps do solve this puzzle?
Code: Select all
+-----------+-----------+-----------+
|  11 4  3  |  1  8  7  |  6  2  9  |
|  9  2  6  |  3  4  11 |  8  1  7  |
|  8  1  7  |  6  2  9  |  . .  .  |
+-----------+-----------+-----------+
|  1  7  8  |  9  6  2  |  .  . .  |
|  2  6  9  |  11 3  4  |  7  8  1  |
|  4  3  11 |  7  1  8  |  9  6  2  |
+-----------+-----------+-----------+
|  3  11 4  |  8  7  1  |  2  9  6  |
|  6  9  2  |  4  11 3  |  1  7  8  |
|  7  8  1  |  2  9  6  |  3  4  11 |
+-----------+-----------+-----------+

Do you mean with adjacent all 8 surrounding, or 4 with + or 4 with x?
And the math operators, on which cell are they used?
And 1 operator for the target adjacent cells?
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Re: Anti Chess, NC and Forbidden Pairs (FP) puzzles

Postby tarek » Mon Feb 11, 2019 8:35 pm

Hi creint,

I'm following the Sudoku federation terminology regarding the words "Adjacent" and "Neighbouring":

Adjacent cell means any cell that shares an edge. That means on our rectangular grid with square cells that each cell can have a maximum of 4 adjacent cells (1 in each orthogonal direction). On a toroidal grid each cell will have 4 adjacent cells. On a grid without a continuity plane (non toroidal) then the cells at the edge of the board will have less adjacent cells and the corner cells will have only 2 adjacent cells each.

Neighbouring cell means any cell that shares an edge or a point. That means on our rectangular grid with square cells that each cell can have a maximum of 8 neighbouring cells (4 adjacent cells in each orthogonal direction and 4 cells sharing a point in each diagonal direction). On a toroidal grid each cell will have 8 neighbouring cells. On a grid without a continuity plane (non toroidal) then the cells at the edge of the board will have less neighbouring cells and the corner cells will have only 3 neighbouring cells each.

with the no XV puzzle The rules state that we don't have 5 nor 10 as clues and that no adjacent cells can give you 5 or 10 through arithmetic operations. The possibilities therefore are:
Code: Select all
1 + 4 = 5
1 + 9 = 10
2 + 3 = 5
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
6 - 1 = 5
7 - 2 = 5
8 - 3 = 5
9 - 4 = 5
11- 1 = 10
11- 6 = 5
Each of these pairing is a forbidden pair and therefore can't occupy adjacent cells which should make solving those empty cells straightforwrad
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Re: Anti Chess, NC and Forbidden Pairs (FP) puzzles

Postby Mathimagics » Tue Feb 12, 2019 3:56 am

tarek wrote:with the no XV puzzle The rules state that we don't have 5 nor 10 as clues and that no adjacent cells can give you 5 or 10 through arithmetic operations. The possibilities therefore are:
Code: Select all
1 + 4 = 5
1 + 9 = 10
2 + 3 = 5
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
6 - 1 = 5
7 - 2 = 5
8 - 3 = 5
9 - 4 = 5
11- 1 = 10
11- 6 = 5
Each of these pairing is a forbidden pair and therefore can't occupy adjacent cells which should make solving those empty cells straightforwrad



If the definition is "arithmetic operations" then the list should include 1 x 5 = 5, and 2 x 5 = 10, shouldn't it ?
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Re: Anti Chess, NC and Forbidden Pairs (FP) puzzles

Postby tarek » Tue Feb 12, 2019 12:08 pm

Mathimagics wrote:If the definition is "arithmetic operations" then the list should include 1 x 5 = 5, and 2 x 5 = 10, shouldn't it ?
the digit 5 is not there as clue as per the instructions. That is why it is not included. The clues are 1,2,3,4,6,7,8,9,11 we have therefore 11 - 6 = 5 & 11 - 1 = 10 as possibilities and therefore should be forbidden pairs.

The idea is to:
Remove 5 to have 1,2,3,4,6,7,8,9,10
Remove 10 to have 1,2,3,4,6,7,8,11 to make it a "no XV" in both clues and arithmetic operations
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Re: Anti Chess, NC and Forbidden Pairs (FP) puzzles

Postby creint » Tue Feb 12, 2019 8:16 pm

Yes it solves now.
In the picture:
Adjacent cells can't combine to give 5 or 5 through arithmetic operations

Which was in my opinion something like operations on the four cells: a+b+c+d not equal 5 or 10.
The clue that was missing for me was always 2 cells and center cell + one of the four adjacent.
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Re: Anti Chess, NC and Forbidden Pairs (FP) puzzles

Postby tarek » Tue Feb 12, 2019 11:45 pm

creint wrote:Which was in my opinion something like operations on the four cells: a+b+c+d not equal 5 or 10.
The clue that was missing for me was always 2 cells and center cell + one of the four adjacent.


Thanks, I agree that the wording needs to be as clear as possible. A possible better option is "adjacent cells can't give 5 or 10 through arithmetic operations" or "adjacent cells can't give 5 or 10 through +,-,x,/". At the moment I think that "adjacent cells" should mean "any 2 adjacent cells" and therfore didn't elaborate on that further!
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