The New Sudoku Players' Forum

[BlueSpark]

Here's a project: how many 16 by 16 sudokus are there that contain a 9 by 9 sudoku within them somewhere?

I am hoping that the answer is zero and that someone can provide the reason why, but I suspect that some such sudokus do exist and I am very afraid of what it might take to answer the question.

May Fate bless anyone who dares walks down this road.

Cheers

[Karyobin]

25

[PaulIQ164]

I don't know exactly what you mean by "contain", but if you're asking how many 16x16 sudokus there are for which you can draw a 9x9 box somewhere in that contains a valid sudoku, then it's zero. Because wherever you draw that 9x9 box, it'll contain an entire one of the main sudokus' 4x4 boxes. So the 9x9 grid'll have 16 different sumbols in it and so not be a valid sudoku.

Otherwise, yeah, it's 25.

[BlueSpark]

Thank you for the replies. I have never seen a 16 x 16 sudoku--I didn't realize that it had internal boxes as well. I suppose I was thinking of just a 16 X 16 square. So I got my wish--the answer is zero. How many 9 x 9 sudokus exist in a plain old 16 x 16 square might be an interesting question for someone, but it is not really a sudoku question, is it?

[Pat]

I have never seen a 16 x 16 sudoku--I didn't realize that it had internal boxes as well.

a box-size of 2x5 implies a 10-square SuDoku puzzle (100 cells).

a box-size of 2x8 or 4x4 implies a 16-square SuDoku puzzle (256 cells);
i assume we all prefer the more-balanced arrangment i.e. 4x4.


and back to the original question:
we'd like to take a validly-filled 16-square SuDoku;
choose 7 symbols to drop,
drop all cells containing those 7 symbols,
and push it together horizontally ( an arbitrary choice ) to get 16 rows of 9 cells;
carefully choose 7 rows to drop, ending with a 9-square;
and now we ask, is it possible to have ended with a validly-filled 9-square SuDoku?? ( always? never? sometimes? )

- Pat

[Pat]

... and it's not such a crazy question

( but may drive you insane trying to find an answer ? )

- Pat

[BlueSpark]

Pat, thank you for your reply. Whether or not my original question was insane (it was certainly misguided as it misunderstood the properties of 16 x 16 sudokus), your reformation of it has made it insane--in the sense of "I don't want to go anywhere near that!" Oh, who am I kidding, I will probably think about it.

btw, my edit above was to correct verb use. It was a disappointing mistake--I usually make much grander ones.

Cheers