Quest for THE 16 GIVEN SUDOKU

coloin · Posted: Thu Apr 10, 2008 11:20 pm Post subject:

Thank-you, Hmmmm, Rolling Eyes

You can nearly always rely on these grids to always throw up an exception.......

Heres a random grid

coloin · Posted: Thu Apr 10, 2008 11:32 pm Post subject:

The fact that DrZ didnt return is probably an indication of its value.

Its easy to make a sum add up to 17.

I think it is a spoof.

C

JPF · Posted: Fri Apr 11, 2008 12:31 am Post subject:

coloin · Posted: Fri Apr 11, 2008 10:19 am Post subject:

So you have searched 362880 and not found one ?

A while ago, using a version of gsfs software, which canonicolizes these sub-puzzles [normalizes them to a minlex version]sudoku space

I looked at a NAR clue positon template for many grids.

The 9NAR with 9 different clue values [rainbow] wasnt uncommon, I will repeat it again.

number of essentially different ways to have 1 clue [any value] in a box with NAR clue positions

Lunatic · Posted: Fri Apr 11, 2008 10:31 am Post subject:

JPF · Posted: Fri Apr 11, 2008 1:35 pm Post subject:

coloin · Posted: Fri Apr 11, 2008 2:24 pm Post subject:

Well 18 NAR is fair, dont know if there will be a grid without any.

Confusing these numbers [for me]

The 9^9 refers to any clue positions, any clue value in each of the 9 boxes
The 9! [you are correct] refers correctly to any clue position with different clue values [rainbow] in each of the 9 boxes.

There are of course a 1-clue rookerys worth of NAR combinations

9*9*9*4*4*2*2*1*1 for B1B5B9B2B4B6B8B3B9 is easier to see than the 6^6, both = 46656.

I think I remember I got around 20 9/9 NAR when I generated 46656 rookery templates. I will repeat, there are only 439 differnt non-equivalent combinations.

Thats why I thought all grids would have at least one.

The test I havent done is the how many essentially different there are out of the 9^9.

Im thinking now there will be not as many as you would initially think.

This computation is of relevance to all puzzles which have at least one clue in every box. Value to be determined.

C

daj95376 · Posted: Fri Apr 11, 2008 3:37 pm Post subject:

coloin · Posted: Fri Apr 11, 2008 3:56 pm Post subject:

Ha Ha.

And very suitable information.

Of course you can subdevide solution grids into two, which increases the number of constant clues, and reduces options.

Concerning the clue @ r2c3
Those with a 6 - have one or more bands with a repeating minirow [~30%]
Those with a 7 - those grids that dont have a repeatring minirow in any of the 6 bands. [~70%]

17 puzzles are twice as likely to have a repeating minirow. [the SF grid has 2 bands like this]

here is a repeating minirow/tupel

daj95376 · Posted: Fri Apr 11, 2008 5:30 pm Post subject:

If I were to look for a 16 Sudoku, I would start by examining the 17 Sudokus.

1) Canonicalize the solutions and the grids
2) examine each canonical grid to see how many units have no givens
3) examine each canonical grid to see how many units have one given
4) see if I can construct a canonical 16 within the minimum/maximum found in (2) & (3)

coloin · Posted: Fri Apr 11, 2008 8:59 pm Post subject:

you mean this.....when there was ~32930 known puzzles Ocean published this http://www.sudoku.com/boards/viewtopic.php?t=2312&start=4

frequency of puzzles with distribution of number of clues in boxes

gsf · Posted: Fri Apr 11, 2008 9:46 pm Post subject:

coloin · Posted: Fri Apr 11, 2008 9:58 pm Post subject:

That program demands respect

Do you think we will get a new 17 out of all this ?

C

JPF · Posted: Fri Apr 11, 2008 10:44 pm Post subject:

gsf, where do you get the up to date |G|= 47733 catalog ?

This site is blocked at |G|=47621.

JPF

gsf · Posted: Fri Apr 11, 2008 10:54 pm Post subject: