The New Sudoku Players' Forum

by **coloin** » Tue Sep 09, 2008 5:34 am

Oct-doku

Another varient I dreamt up ! Probably only useful as "tea-time quickies"

Same as 9*9 Vanilla sudoku

But only eight clue values and a blank cell in each box.

Possibly already described

Code: Select all: +---+---+---+ |*..|...|...| |...|*..|...| |...|...|*..| +---+---+---+ |.*.|...|...| |...|.*.|...| |...|...|.*.| +---+---+---+ |..*|...|...| |...|..*|...| |...|...|..*| +---+---+---+

I can use my vanilla programs to give this 13-clue example [probably the minimum] [plagered from a 17 with x4 of one clue value]

Code: Select all: +---+---+---+ |*23|...|...| |4..|*1.|...| |...|...|*5.| +---+---+---+ |.*.|...|.6.| |..5|.*.|...| |...|.3.|.*4| +---+---+---+ |..*|6..|...| |...|5.*|7..| |3..|...|..*| +---+---+---+ "mild"

Might be useful for unaswered questions re vanilla 17s/18s ?

Probably a vanilla 17 with x5 of one clue value doesnt exist.

Which would indicate a 12-clue oct-doku doesnt exist - unless we are able to find a 18-clue vanilla with x6 of one clue value.

Time will tell.

C

by **tarek** » Tue Sep 09, 2008 6:44 am

So :

1. You uncovered the nine positions of a certain clue in a vanilla puzzle .....
2. Minimized the puzzle so that only the minimal puzzles with 8 positions are present & uncovered
3. cover up those 8 positions ......

Is that correct ?

tarek

by **coloin** » Tue Sep 09, 2008 7:36 am

Sort of, not sure about 3.

Code: Select all: +---+---+---+ |923|...|...| |4..|91.|...| |...|...|95.| +---+---+---+ |.9.|...|.6.| |..5|.9.|...| |...|.3.|.94| +---+---+---+ |..9|6..|...| |...|5.9|7..| |3..|...|..9| +---+---+---+ mild

This is a 22-clue vanilla non-minimal puzzle

5 clues of the 9-rookery can be removed to leave us with a 17-clue vanilla.

Code: Select all: +---+---+---+ |.23|...|...| |4..|.1.|...| |...|...|95.| +---+---+---+ |.9.|...|.6.| |..5|...|...| |...|.3.|..4| +---+---+---+ |..9|6..|...| |...|5.9|7..| |3..|...|...| +---+---+---+ 17 clue from gordon's list

Removing all the 9s leaves a 13-clues oct-duku [as in post above].

Ive posted to gsf to see if there is mileage in making vanilla 17s utilizing the oct-duku reductions !

Essentially the blank cells are fixed in one position.
There are only 8 clues [only 7 clue values needed]
There are only 72 potential cells

How many different 14-clue oct-duku puzzles are there ?
- there are usually several from each vanilla-17.

How easy is it to generate random 15-clue oct-doku puzzles ?

C

by **coloin** » Tue Sep 09, 2008 9:39 am

Ah Ha

you will recognize this oct-duko puzzle

Code: Select all: +---+---+---+ |...|8..|.39| |8..|..1|..5| |..3|.5.|8..| +---+---+---+ |..8|.9.|..6| |.7.|..2|..8| |1..|4.8|...| +---+---+---+ |..9|.8.|.5.| |.2.|...|68.| |48.|7..|...| +---+---+---+ Gonden Nuggett with 6 more "8"s SE 9.3

scrambled to the format

Code: Select all: +---+---+---+ |*..|.1.|.5.| |...|*..|.83| |.3.|..5|*..| +---+---+---+ |.*.|..8|.6.| |1..|4*.|...| |..7|.2.|.*.| +---+---+---+ |4.*|7..|...| |.8.|..*|..5| |..2|...|6.*| +---+---+---+ SE still presumably 9.3

Hmmmm

How easy is it to generate these puzzles again ?

C

by **Pat** » Tue Sep 09, 2008 9:51 am

you can call it a "13-clue" oct-duko --
but it is equivalent to a plain SuDoku puzzle
having 13 + 9 = 22 clues

by **coloin** » Tue Sep 09, 2008 10:01 am

Yes they are equivalent. And yes you are right - Oct-Doku is what it should be coined.

But what is it doing to the "sudoku puzzle space ?"

Another one from the hardest archive

Code: Select all: +---+---+---+ +---+---+---+ |1..|...|...| |1..|...|...| |.2.|4..|.6.| |.2.|4..|.6.| |..3|...|5.1| |4.3|...|5.1| +---+---+---+ +---+---+---+ |.4.|.86|...| |.4.|.86|...| |...|.49|.8.| |...|.49|.8.| |...|2..|...| |...|2..|...| +---+---+---+ +---+---+---+ |5.7|...|3..| |5.7|..4|3..| |.6.|9..|.4.| |.6.|9..|.4.| |...|...|..7| |..4|...|..7| +---+---+---+ "cloudy bay" SE 10.9, +---+---+---+ with 4 singles inserted !

http://forum.enjoysudoku.com/viewtopic.php?t=4212&start=840

scrambled and the rookery completed

Code: Select all: +---+---+---+ |9.1|...|43.| |.2.|9..|..5| |3..|...|9..| +---+---+---+ |.9.|.85|...| |...|.96|..8| |...|2..|.9.| +---+---+---+ |..9|...|.7.| |4.7|..9|1..| |.5.|6..|..9| +---+---+---+ with the 4 clue rookery filled SE 10.5

reduced to oct-doku

Code: Select all: +---+---+---+ |*.1|...|43.| |.2.|*..|..5| |3..|...|*..| +---+---+---+ |.*.|.85|...| |...|.*6|..8| |...|2..|.*.| +---+---+---+ |..*|...|.7.| |4.7|..*|1..| |.5.|6..|..*| +---+---+---+ SE presumably still a whopping 10.5

C

by **tarek** » Tue Sep 09, 2008 11:54 am

there is still something confusing about this coloin,

if we KNOW 9 positions of a clue then the extra non minimal clues would allow removal of other clues outside this this 9 position clue...

Minimality is then achived when removal of a clue would result in multiple solutions....

I think you may be able to achieve less than 13 with that 17 clue seed from gordon's list (if you can remove redundant clues other than 9s in the 22 clue version)

tarek

by **coloin** » Wed Sep 10, 2008 4:55 am

tarek wrote:if we KNOW 9 positions of a clue then the extra non minimal clues would allow removal of other clues outside this this 9 position clue.......I think you may be able to achieve less than 13 with that 17 clue seed from gordon's list (if you can remove redundant clues other than 9s in the 22 clue version)tarek

In the puzzles with less than 15 clues there are not many of these 15 that can be removed from a 15 plus 9 vanilla.

I agree in oct-doku puzzles with around 20 clues many of the 20 can be removed from a 20 plus 9 vanilla.

The search space is being compressed - especially for the 14 clue oct-doku. That is why I think we could generate them

We already have many from Gordon's list [all the puzzles with a 14 plus 3 configuration] [Almost all of Gordon's list have this configuration].
[18-puzzles with a 14 plus 4 configuration]
[19-puzzles with a 14 plus 5 configuration]
[20-puzzles with a 14 plus 6 configuration] [?exists]

The search space is being compressed - there is one less clue value and 9 less clue positions for these 14 clues - but I dont know if these puzzles are within doable limits. They are possibly all within a {-2+2} of each other too.

Can you get a program to chuck these out ?

Im anticipating a confirmatory post from gsf !

Coloin

by **gsf** » Wed Sep 10, 2008 9:44 am

coloin wrote:Can you get a program to chuck these out ?

Im anticipating a confirmatory post from gsf !

its a neat idea
won't have anything this week though

by **coloin** » Wed Sep 10, 2008 9:54 am

OK gsf
BTW whats the code which performs this count

Code: Select all: 7 15 011122334 175 226 011123333 197 315 011222234 5908 7537 011222333 12 25 012222224 8377 10028 012222233 730 850 022222223 10 15 111113333 81 121 111122234 2220 2847 111122333 13 21 111222224 11091 13394 111222233 4104 4696 112222223 5 5 122222222 ------- ------ 32930 40095

tarek wrote:I think you may be able to achieve less than 13 with that 17 clue seed from gordon's list (if you can remove redundant clues other than 9s in the 22 clue version) tarek

Yes you may be able to remove a clue other than the nine.

This would be a 12 plus 9 scenario.

It cant be a 12 plus 5 {I dont think there are any of these in Gordons list}{see above]

The best it can be would be a 12 plus 6 = 18 clue vanilla

[You cant have a minimal puzzle with 7 clues in a rookery !]

Interesting if we were to find a 12.

If we can generate all the 14s, we can easily test these all for new 17s......and put this little matter to rest.

C

by **gsf** » Wed Sep 10, 2008 12:04 pm

coloin wrote:OK gsf
BTW whats the code which performs this count

Code: Select all
7 15 011122334 175 226 011123333 197 315 011222234 5908 7537 011222333 12 25 012222224 8377 10028 012222233 730 850 022222223 10 15 111113333 81 121 111122234 2220 2847 111122333 13 21 111222224 11091 13394 111222233 4104 4696 112222223 5 5 122222222 ------- ------ 32930 40095

refresh me on what the columns represent

by **coloin** » Wed Sep 10, 2008 12:20 pm

Sorry, they are the distribution of clue values in Gordons 17-puzzles. Note no "********5" in the list.

Code: Select all: +---+---+---+ |.23|...|...| |4..|.1.|...| |...|...|95.| +---+---+---+ |.9.|...|.6.| |..5|...|...| |...|.3.|..4| +---+---+---+ |..9|6..|...| |...|5.9|7..| |3..|...|...| +---+---+---+

This is the clue value occurance in this puzzle [011122334]
1-1 times
2-1 times
3-3 times
4-2 times
5-3 times
6-2 times
7-1 times
8-0 times
9-4 times

I want to look at a batch of 18s

I doubt whether there is a minimal [011122236]

If there is - it means there is a 12 clue oct-doku.

by **gsf** » Wed Sep 10, 2008 1:01 pm

coloin wrote:Sorry, they are the distribution of clue values in Gordons 17-puzzles. Note no "********5" in the list.

generated by my solver and a few unix commands

Code: Select all: sudoku -f%+#oP g.dat | sort | uniq -c

where g.dat is Gordon's catalog
the result for the current 17s

Code: Select all: 26 011122334 295 011123333 470 011222234 9598 011222333 32 012222224 11734 012222233 947 022222223 22 111113333 170 111122234 3586 111122333 33 111222224 15761 111222233 5227 112222223 8 122222222 ----- 47909

by **tarek** » Wed Sep 10, 2008 2:25 pm

My lack of knowledge of the sudoku space shows ....

tarek

by **coloin** » Wed Sep 10, 2008 3:21 pm

No cigar yet........

The "sudoku puzzle space" issue is vast - but at least its finite !

For every way of completing a 14 clue oct-doku there will be many of the isomorphs which will have the identical blank cell [9 clue] rookery.

1 per each of the 9 boxes = x9
diagonal reflection = x2
[and of course the 8!]

Edit - this is less than I first calculated.

Looking at a few distributions from the puzzle archives
[11122335] & [011222235] did occur - but very much at the edge of the 18-space.

Code: Select all: 011123334 205 011133333 1172 011222235 2 011222244 3 011222334 2294 011223333 43721 012222234 1740 012222333 94817 022222224 4 022222233 17691 111113334 10 111122334 845 111123333 12350 111222234 2495 111222333 114942 112222224 59 112222233 97709 122222223 8506 222222222 8 Total 398573

Not many [< ~ 2%] [********4] in the 18s
Not many [********5] on a batch of 19s either.

There would have to be an awful lot of these 14 clues to overwhelm us now.

Following on, it isnt too hard to test/add 3 clues into 9 spaces for all of these.

Worringly, doing a {-2+2} on 14-plus-9 - isnt a very productive or quick way of making new 14-clue oct-doku puzzles......

Selectivly removing 3 clues and adding 3 more didnt have a good yield either.......

Attempting a {-1+2} on a 13-plus-9 oct-doku.......this did generate new 14 plus 9 puzzles.......

If we were to find a 12-plus-9 oct-doku......that might just make it a bit easier !

C