The New Sudoku Players' Forum

by **HATMAN** » Mon Jan 21, 2008 7:18 pm

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.

by **Smythe Dakota** » Mon Jan 21, 2008 11:25 pm

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

by **HATMAN** » Tue Jan 22, 2008 1:57 pm

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

by **evert** » Tue Feb 12, 2008 1:06 am

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

by **HATMAN** » Tue Feb 12, 2008 12:05 pm

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

by **evert** » Tue Feb 12, 2008 11:12 pm

I'll have to correct myself.

Code: Select all: 123456789 000000000 000000000 000000000 000000000 000000000 000000000 000000000 000000000

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.

by **HATMAN** » Wed Feb 13, 2008 1:36 pm

Wow - I await your results

by **evert** » Wed Feb 13, 2008 11:33 pm

If I'm right this is a solution:

Code: Select all: 129687354 543219876 768435192 687354921 912876543 435192768 354921687 876543219 291768435

And a puzzle based on it:

Code: Select all: 100000000 000000800 000000000 000000000 010070000 000000760 300000080 000540000 000060400

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

(Took my program about 4 hrs

)

by **evert** » Thu Feb 14, 2008 12:23 am

Still playing around with this.
Finding a whole grid seems to be tough but deriving puzzles from it ...

Code: Select all: 100000000 500000000 700000000 000000000 000000000 000000700 000000080 070540000 000000000

This one should be really fun!

by **HATMAN** » Thu Feb 14, 2008 12:34 pm

Well done

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

by **HATMAN** » Thu Feb 14, 2008 6:35 pm

Evert

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

by **evert** » Fri Feb 15, 2008 2:08 am

Code: Select all: 000000000 000000000 000009080 000000000 000800000 000000700 000007000 000040000 600000000

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

by **HATMAN** » Fri Feb 15, 2008 11:48 am

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

by **HATMAN** » Fri Feb 15, 2008 2:30 pm

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.

by **tarek** » Fri Feb 15, 2008 2:41 pm

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

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