http://forum.enjoysudoku.com/viewtopic.php?t=3351&postdays=0&postorder=asc&start=15

sq wrote:Just to round off the discussion; Shi Doku has

288 solutions of which 2 are essentially different

13579680 puzzles of which 85632 are irreducible

1536 6-clue, 58368 5-clue and 25728 4-clue irreducible puzzles

4710 essentially different puzzles of which 36 are irreducible (13 4-clues, 22 5-clues and 1 6-clue)

What about the 3x3 ?

Just how many minimal puzzles are there in a grid ?

I dont think anyone has come up with a sensible estimate - quite rightly !

The generation of of 1 million minimal sudoku puzzles has been performed for several grids and the clue statisics have been shown

dukuso wrote:

- Code: Select all
`counts of clues in randomly generated minimal`

sudokus over sf :

average:24.104503 , 1000000 samples

19 3

20 229

21 6277

22 61494

23 227035

24 352839

25 248868

26 86121

27 15453

28 1589

29 89

30 3

Concerns over the proportions must be made due to the randomization/computation methods which produces the puzzles.

1.common size 24 clue may well be over represented / rarer sizes under.

2.duplication of puzzles by a quirk in the randomization

If the above could be excluded, and this is a big if, if we find the average seed value at which puzzles start to get duplicated - this would be proportional to the overall [finite] number of puzzles in that particular grid.

The 24 clue puzzle is the commonest

If the seed value that we reach a single duplicate is on average 50,000 then perhaps this could be extrapolatable that there are 900 million puzzles of that size. [Complete guesswork on the figures here !]

I have a hunch that certain grids have more puzzles than others - e.g the grids which have a low minimal - specifically the SF grid.

Certainly - if you generate enough puzzles you will start to get duplicates - the less puzzles there actually are - the sooner you will get duplicates.

Any thoughts into whether this is practical - or possible ?

see http://mathforum.org/dr.math/faq/faq.birthdayprob.html

There is a 50% chance that 2 out of 23 people will share the same birthday - therefore number of days in the year = 365 !

C

Apologies to G.Orwell