Knight Non-Consecutive

For fans of Killer Sudoku, Samurai Sudoku and other variants

Knight Non-Consecutive

I've been investigating a possible Restrained Sudoku formulation:

Cells a knights move apart must be nonconsecutive.

For each value placed it removes up to 16 extra candidates compared to plain sudoku.

I am not at present sure whether it has feasible solutions, but if it does the solution space will be small.

After a weekend of playing around with it manually this is the least unfeasible solution I've found: It contains 14 failures: five of 89, four of 78, three of 67 and two of 56.

I would welcome any thoughts on how to take this further.
HATMAN

Posts: 213
Joined: 25 February 2006

Or, how about the following? Every entry (in the final solution) is a knight's move away from another entry which is either consecutive or identical? This sounds so restrictive that you almost shouldn't need any clues at all.

To make it even more restrictive, allow digit wrap-around, i.e. consider 9 and 1 to be adjacent. Maybe even allow wrap-around with respect to rows and columns as well, e.g. r9c4 is a knight's move away from r2c5.

Bill Smythe
Smythe Dakota

Posts: 546
Joined: 11 February 2006

Bill

I have used the nonconsecutive loop in NC90 as OverKillers 3 and 4 at:
http://www.djape.net/sudoku/forum/viewtopic.php?t=1188&start=0

The OverKiller idea is to have ten numbers instead of 9 distributed almost evenly so there are 9 of one number and 8 of each of the others - it works well as a Killer and I'm trying to do it on a Vanilla basis. My first vanilla overkiller posted on Ruud's site was a total wimp - which does not go well with the ethos on that site.

I am not convinced the knight nonconsecutive is solvable - never mind making it harder. I have (with udosuk's help) compiled a long list of "impossibles" (simple ones like NC Windoku fail) and I've a feeling that this is another one.

Maurice
Last edited by HATMAN on Wed Feb 27, 2008 6:51 pm, edited 1 time in total.
HATMAN

Posts: 213
Joined: 25 February 2006

I did some programming on this. There seem to be no solutions at all.
I welcome everybody to search for an elegant ** mathematical ** proof.
evert

Posts: 186
Joined: 26 August 2005

Evert

Thanks for confirming that - from my T&E I was coming to the same conclusion. I think the primary problem is knight non-consecutive within a Nonet. So I've been trying the less constrained version where you only apply the night non-consecutive constraint to cell that are in different nonets. I have not got a solution yet but I've come much closer.

If you have some time to spare please try this out.

Thank you

Maurice
HATMAN

Posts: 213
Joined: 25 February 2006

I'll have to correct myself.
Code: Select all
`123456789000000000000000000000000000000000000000000000000000000000000000000000000`
has no solutions.

However, the general conclusion that there is no solution, is not justified.
Because not all numbers 1 to 9 play exactly the same role.

So today, I ran an algorithm that decides if a grid has no solution, one solution or more than one solution. The conclusion - after several hours - is that valid AN-grids do exist.

However it's very hard to find.
Right now I'm running another algorithm that tries to find a solution.
I'm afraid it will run for hours and have my computer crash.
evert

Posts: 186
Joined: 26 August 2005

Wow - I await your results
HATMAN

Posts: 213
Joined: 25 February 2006

If I'm right this is a solution:
Code: Select all
`129687354543219876768435192687354921912876543435192768354921687876543219291768435`

And a puzzle based on it:
Code: Select all
`100000000000000800000000000000000000010070000000000760300000080000540000000060400`

Could you do a manual check if it's correct?

(Took my program about 4 hrs )
evert

Posts: 186
Joined: 26 August 2005

Still playing around with this.
Finding a whole grid seems to be tough but deriving puzzles from it ...
Code: Select all
`100000000500000000700000000000000000000000000000000700000000080070540000000000000`

This one should be really fun!
evert

Posts: 186
Joined: 26 August 2005

Well done

I'll check it and then try and solve them.
HATMAN

Posts: 213
Joined: 25 February 2006

Evert

I've checked it and it is valid - well done. I'll do the puzzle later
HATMAN

Posts: 213
Joined: 25 February 2006

Code: Select all
`000000000000000000000009080000000000000800000000000700000007000000040000600000000`

This puzzle is based upon an essentially different grid.
HATMANS brilliant idea, this whole knight non consecutive, my role is only bit of stupid programming and then sit next to my computer for 4 hrs
evert

Posts: 186
Joined: 26 August 2005

Evert

Flattery will get you everywhere with me.

I’ve not been able to try to solve any yet – too busy at work and on the Guinness last night.

I note with your last one that you’ve got the givens below 8 – well done. Given the very limited solution space we should be able to get to quite a low number of givens.

The next stage is adapting some of the non-consecutive techniques. Would anyone solving these please post any techniques they use.

Maurice
HATMAN

Posts: 213
Joined: 25 February 2006

KNAC 1

Took about 3/4 hr almost all singles and plain KNAC elimination except:
Diagonal NP r4c2r3c5 = {28} -> r3c4 ~1379 =2|4
On redoing it this is not needed.
HATMAN

Posts: 213
Joined: 25 February 2006

I won't probably attempt solving this by hand.

however it should be easy to include non-consecutive, A-King or A-Knight in a solver. I'm optimizing mine the moment & hopefully will see how it goes after that.

tarek

tarek

Posts: 2699
Joined: 05 January 2006

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