## Knight Non-Consecutive

For fans of Killer Sudoku, Samurai Sudoku and other variants
Speaking of limited solution space:
Code: Select all
`000000001000000009000000000000000000000000000000000000000000000000000000190000000`

... has zero solutions.
I travel for my work, during two train rides I could solve one of these kind of puzzles.
After getting used to the new constraint it's not t h a t hard.
By the way the first valid grid has a nice feature if we take a better look ...
evert

Posts: 186
Joined: 26 August 2005

The 1 and 9 placements are critical in non-consecutive so it is not too surprising that there is no solution - I wonder how many solutions if you move the lower 9 to r8c1?

Horizontal and vertical triplets - many Restrained Sudokus have this property see the ML2 solution.
HATMAN

Posts: 214
Joined: 25 February 2006

Interesting variant. Here is a Knight Non-Consecutive I designed. It can be solved by logic but should require using techniques specific to Non-Consecutive.

Code: Select all
`+-------+-------+-------+| . . . | . . 1 | . . . || 9 . . | . . . | . . 5 || . . . | . . . | . . . |+-------+-------+-------+| . . . | 6 . . | . 5 . || . . . | . 9 . | . . . || . 4 . | . . 3 | . . . |+-------+-------+-------+| . . . | . . . | . . . || 4 . . | . . . | . . 2 || . . . | 8 . . | . . . |+-------+-------+-------+`

PS: The cells at a knight move may hold the same digit, unless they are in the same block/nonet of course. Indeed, I also tried using both anti-knight and non-cons knight, but it cannot work together; an exhaustive search didn't find any valid grid.
Jean-Christophe

Posts: 149
Joined: 22 January 2006

JC

Nice puzzle - I had to work the NC right to the end

+-------+-------+-------+
| 6 8 4 | 3 5 1 | 9 2 7 |
| 9 7 2 | 4 6 8 | 1 3 5 |
| 5 1 3 | 2 7 9 | 8 4 6 |
+-------+-------+-------+
| 7 2 9 | 6 8 4 | 3 5 1 |
| 1 3 5 | 7 9 2 | 4 6 8 |
| 8 4 6 | 5 1 3 | 2 7 9 |
+-------+-------+-------+
| 3 5 1 | 9 2 7 | 6 8 4 |
| 4 6 8 | 1 3 5 | 7 9 2 |
| 2 9 7 | 8 4 6 | 5 1 3 |
+-------+-------+-------+

Techniques so far (in small in case anyone wants to develop them themselves):

running pair (56): remove both from knight within nonet
running triplet (678): remove middle (7) from knight within nonet
split pair (35): remove middle (4) from all knight
Any strongly linked pair of cells (only two cell with a 2 in N7 are r7c2, r8c3): remove adjacents from any knight intersections (r6c4 ~13)
HATMAN

Posts: 214
Joined: 25 February 2006

Well done.
Here is another Knight Non-Consecutive. Should be harder to solve.

Code: Select all
`+-------+-------+-------+| . . . | . . . | . . . || . . . | 7 . . | . . . || . . . | . . . | . 9 . |+-------+-------+-------+| . 1 . | 6 . . | . . 8 || . . . | . . . | . 5 . || . . . | . . 7 | . . . |+-------+-------+-------+| . . . | . . . | . . . || . . 3 | . 5 . | . . 9 || . . . | 2 . . | . 6 . |+-------+-------+-------+`
Jean-Christophe

Posts: 149
Joined: 22 January 2006

I've found that knight non consecutive does not go together
with 2 diagonals. So a valid NNC-X does not exist.
evert

Posts: 186
Joined: 26 August 2005

I'll add that to my impossibles list
HATMAN

Posts: 214
Joined: 25 February 2006

knight non consecutive with windoku/nrc: no solutione either
evert

Posts: 186
Joined: 26 August 2005

Evert

noted - no surprise as NC only works with two windows (either straight or diagonal). Can you make this work with just one window?

JC

I am completely stuck with just two placements. I've been over your NC techniques and you have obviously found something I've missed - HELP please?
HATMAN

Posts: 214
Joined: 25 February 2006

Tripple click to read the hints that I wrote:I guess you got these 2:
r8c8 = 8 (HS @ n9)
r4c7 = 9 (HS @ c7)

Next one:
r9c8 = 6 -> r7C79 <> {57}
5 @ n9 locked @ r9c79 -> r7c8 <> 4, 5 locked for r9
5 @ n68 -> r7c79, r9c7 <> 4
4 @ n9 locked @ r8c7, r9c9 -> r9c9 <> {35}
r9c7 = 5 (HS @ n9)

To unlock the puzzle, consider the placements of {789} @ n8 in relation with NC
7 @ n8 locked @ r79c5
r6c6 = 7 -> r7c4 <> 8
8 @ n8 locked @ r79c56
Thus {78} @ n8 locked @ r79c56, two pairs of NC: r7c5+r9c6 and r7c6+r9c5
None of these pairs of NC cells may hold both {78}
Each of them must include either 7 or 8 (I call this a complex hidden pair)

r8c8 = 8 -> r79c6 <> 9
9 @ n8 locked @ r7c45, r9c5

r79c5 <> 9 because it would otherwize force one NC to include both {78}
eg r7c5 = 9 -> r9c6 <> 8 -> r7c6+r9c5 = {78} which is not possible
Similarly for r9c5
-> r7c4 = 9 (HS @ n8)
Jean-Christophe

Posts: 149
Joined: 22 January 2006

JC

Thanks I missed the 4s in N9 implication - excellent.
HATMAN

Posts: 214
Joined: 25 February 2006

JC

I solved it but I used about half a dozen fishes, were these necessary or did I miss any other NC bits?

Maurice
HATMAN

Posts: 214
Joined: 25 February 2006

I didn't use any fish to solve it. It can be solved using only "simple" vanilla and NC techniques.

Triple click to read the other hint that I wrote:In my previous hint I deduced:
r8c8 = 8, r4c7 = 9, r9c7 = 5, r7c4 = 9

From there:
{35} @ n789 -> r7c2 = 4 (HS @ r7)
r4c6 = 5 (HS @ n5)
7 @ n2 -> r13c6 <> 6
5 @ n2 locked @ r13c4 -> r2c6 <> 6
5 @ n9 -> r7c6 <> 6
r8c6 = 6 (HS @ c6)
5 @ n8 -> r7c1 = 6
r7c3 = 5
r7c56 = [78] (HS @ r7)
4 @ n8 locked @ r8c4, r9c6 -> r9c6 <> 3
r9c5 = 3 (HS @ n8)
-> r8c7 <> 4 = 7
r9c9 = 4, r8c4 = 4, r9c6 = 1
2 @ n8 -> r7c12 = [12]
6 @ n58 -> r359c2 <> 7
r1c2 = 7 (HS @ c2), r3c9 = 7, r4c8 = 7
7 @ n68 -> r6c2 = 6 (HS @ r6)
7 @ n12, 5 @ n6 -> r3c5 = 6, r2c3 = 6
r6c1 = 5, r3c4 = 5, r2c2 = 5, r1c9 = 5
r1c7 = 6, r5c9 = 6
r4c5 = 4 (HS @ r4)
r4c13 = [32]
...
Jean-Christophe

Posts: 149
Joined: 22 January 2006

Here is a variant in the same mood.

Instead of Knight moves, cells at Fers moves hold non consecutive digits. Fers or Ferz moves diagonally 1 cell: eg r5c5 is not consecutive with r46c46.

Should be easier than my second Knight NC but harder than my first one.

Code: Select all
`+-------+-------+-------+| . . . | 4 . . | 2 . . || . . . | . . 9 | . . . || . 2 . | 1 . . | . . . |+-------+-------+-------+| . . . | . . . | 1 . 7 || . . . | . 4 . | . . . || 1 . 2 | . . . | . . . |+-------+-------+-------+| . . . | . . 5 | . 1 . || . . . | 3 . . | . . . || . . 3 | . . 4 | . . . |+-------+-------+-------+`
Jean-Christophe

Posts: 149
Joined: 22 January 2006

JC

I've used a few fishes and am at a dead stop - help?

+-----------------+-----------+----------------+
| 3789 16789 6789 | 4 57 38 | 2 56789 16 |
| 578 1578 4 | 2 6 9 | 38 78 138 |
| 38 2 679 | 1 57 38 | 49 579 469 |
+-----------------+-----------+----------------+
| 6 3 5 | 9 8 2 | 1 4 7 |
| 789 789 79 | 5 4 1 | 6 3 2 |
| 1 4 2 | 67 3 67 | 589 89 589 |
+-----------------+-----------+----------------+
| 2 678 678 | 678 9 5 | 34 1 34 |
| 4 589 1 | 3 2 67 | 789 689 5689 |
| 5789 6789 3 | 678 1 4 | 578 2 5689 |
+-----------------+-----------+----------------+
HATMAN

Posts: 214
Joined: 25 February 2006

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