# Off topic question about Sudoku - Hewlett Packard

This is a discussion on Off topic question about Sudoku - Hewlett Packard ; I read somewhere (I think in Scientific American, in an article on Sudoku by a french mathematician) that the minimum number of symbols (numbers 1 to 9) to be filled in in a 9 x 9 Sudoku grid to guarantee ...

# Thread: Off topic question about Sudoku

1. ## Off topic question about Sudoku

I read somewhere (I think in Scientific American, in an article on
Sudoku by a french mathematician) that the minimum number of symbols
(numbers 1 to 9) to be filled in
in a 9 x 9 Sudoku grid to guarantee a unique solution was 17. I can't
remember how he determined this number.

In a similar vein, does anyone know how many symbols-types (e.g.,
numbers 1 to 9) can be ommitted from an initial grid and still have a
unique solution? I have often seen puzzles with one ommitted, but I
don't think I have ever seen puzzles with two symbols absent from the
initial grid. Can one form a solvable puzzle with a unique solution if
two, or if three symbols types are left out the initial starting grid?
I suspect the minimum number of symbols would have to be increased to
uniquely determine the solution.

Silly question and quite off topic I know, but perhaps someone knows
the answer. Perhaps there is a way of writing a program to work out
the answer?

Lance

2. ## Re: Off topic question about Sudoku

"Gary" schrieb im Newsbeitrag
news:5ef8b315-3c0b-4ec7-99e9-cb8d5b755586@e4g2000hsg.googlegroups.com...
>I read somewhere (I think in Scientific American, in an article on
> Sudoku by a french mathematician) that the minimum number of symbols
> (numbers 1 to 9) to be filled in
> in a 9 x 9 Sudoku grid to guarantee a unique solution was 17. I can't
> remember how he determined this number.
>
> In a similar vein, does anyone know how many symbols-types (e.g.,
> numbers 1 to 9) can be ommitted from an initial grid and still have a
> unique solution? I have often seen puzzles with one ommitted, but I
> don't think I have ever seen puzzles with two symbols absent from the
> initial grid. Can one form a solvable puzzle with a unique solution if
> two, or if three symbols types are left out the initial starting grid?
> I suspect the minimum number of symbols would have to be increased to
> uniquely determine the solution.
>
>
> Silly question and quite off topic I know, but perhaps someone knows
> the answer. Perhaps there is a way of writing a program to work out
> the answer?
>

Slightly OT:
I don't have a direct answer to your question(s),
but if you intend to try some puzzles on an HP-48,
I'd recommend the fastest SuDoKu solver for the HP-48,
SDK48, available on www.hpcalc.org ...

Raymond

3. ## Re: Off topic question about Sudoku

On Dec 19, 2:38 pm, "Raymond Del Tondo" wrote:
> "Gary" schrieb im Newsbeitragnews:5ef8b315-3c0b-4ec7-99e9-cb8d5b755586@e4g2000hsg.googlegroups.com...
>
>
>
> >I read somewhere (I think in Scientific American, in an article on
> > Sudoku by a french mathematician) that the minimum number of symbols
> > (numbers 1 to 9) to be filled in
> > in a 9 x 9 Sudoku grid to guarantee a unique solution was 17. I can't
> > remember how he determined this number.

>
> > In a similar vein, does anyone know how many symbols-types (e.g.,
> > numbers 1 to 9) can be ommitted from an initial grid and still have a
> > unique solution? I have often seen puzzles with one ommitted, but I
> > don't think I have ever seen puzzles with two symbols absent from the
> > initial grid. Can one form a solvable puzzle with a unique solution if
> > two, or if three symbols types are left out the initial starting grid?
> > I suspect the minimum number of symbols would have to be increased to
> > uniquely determine the solution.

>
> > Silly question and quite off topic I know, but perhaps someone knows
> > the answer. Perhaps there is a way of writing a program to work out
> > the answer?

>
> Slightly OT:
> I don't have a direct answer to your question(s),
> but if you intend to try some puzzles on an HP-48,
> I'd recommend the fastest SuDoKu solver for the HP-48,
> SDK48, available onwww.hpcalc.org...
>
> Raymond- Hide quoted text -
>
> - Show quoted text -

Thanks! I have that software, thanks. The truth is I rather like
solving the puzzles myself. I just occasionally get silly niggling
questions in my head and wonder if anyone has an answer? In the case
of teh question i posted I don't know the answer, and am not quite
sure how to set about getting an answer.

Thanks for the reply

Lance

4. ## Re: Off topic question about Sudoku

Gary wrote:
> In the case
> of teh question i posted I don't know the answer, and am not quite
> sure how to set about getting an answer.

You should look here:

http://en.wikipedia.org/wiki/Mathematics_of_Sudoku

Laurent

5. ## Re: Off topic question about Sudoku

In article
<5ef8b315-3c0b-4ec7-99e9-cb8d5b755586@e4g2000hsg.googlegroups.com>,
Gary wrote:

> In a similar vein, does anyone know how many symbols-types (e.g.,
> numbers 1 to 9) can be ommitted from an initial grid and still have a
> unique solution? I have often seen puzzles with one ommitted, but I
> don't think I have ever seen puzzles with two symbols absent from the
> initial grid. Can one form a solvable puzzle with a unique solution if
> two, or if three symbols types are left out the initial starting grid?
> I suspect the minimum number of symbols would have to be increased to
> uniquely determine the solution.

I'm sure others will think deeper about this problem, but my initial
hunch is that if two or more symbols-types are not present in the
initial grid, then there will not be a unique solution.

My reasoning is that if you have a valid completely filled in grid, then
exchange all instances of two symbols (for example change all 8's to 9's
and all 9's to 8's), then you still have a valid grid. The numbers
themselves are just labels, so you can rename them without changing the
underlying structure of the puzzle.

Now assume you start with an initial grid that does not have any 8's or
9's in it. If at least one solution is possible, then you can swap the
8's and 9's in that solution to create another solution, thus the
original solution was not unique.

Dave

6. ## Re: Off topic question about Sudoku

Laurent wrote:
> Gary wrote:
> > In the case
> > of teh question i posted I don't know the answer, and am not quite
> > sure how to set about getting an answer.

>
> You should look here:
>
> http://en.wikipedia.org/wiki/Mathematics_of_Sudoku
>
>
> Laurent

Someone else gave me the answer:

"If there are two symbol types missing from the initial grid and you
find a
solution, it seems to me you could immediately find a second solution
by
swapping the positions of the two symbol types that were originally
missing,
so for the solution to be unique I don't think you can have more than
one
symbol type missing at the start."

Brilliantly simple.

Lance

7. ## Re: Off topic question about Sudoku

On Dec 19, 11:58 am, Dave Baum wrote:
> In article
> <5ef8b315-3c0b-4ec7-99e9-cb8d5b755...@e4g2000hsg.googlegroups.com>,
>
> Gary wrote:
> > In a similar vein, does anyone know how many symbols-types (e.g.,
> > numbers 1 to 9) can be ommitted from an initial grid and still have a
> > unique solution? I have often seen puzzles with one ommitted, but I
> > don't think I have ever seen puzzles with two symbols absent from the
> > initial grid. Can one form a solvable puzzle with a unique solution if
> > two, or if three symbols types are left out the initial starting grid?
> > I suspect the minimum number of symbols would have to be increased to
> > uniquely determine the solution.

>
> I'm sure others will think deeper about this problem, but my initial
> hunch is that if two or more symbols-types are not present in the
> initial grid, then there will not be a unique solution.
>
> My reasoning is that if you have a valid completely filled in grid, then
> exchange all instances of two symbols (for example change all 8's to 9's
> and all 9's to 8's), then you still have a valid grid. The numbers
> themselves are just labels, so you can rename them without changing the
> underlying structure of the puzzle.
>
> Now assume you start with an initial grid that does not have any 8's or
> 9's in it. If at least one solution is possible, then you can swap the
> 8's and 9's in that solution to create another solution, thus the
> original solution was not unique.
>
> Dave

But, gentlemen (and ladies)! Surely the questioner meant to exclude
the obvious. The real question is whether, having left out N symbol
types, there can be a unique solution aside from the N! permutations
of the N symbols.
--Irl
P.S. I have no clue about the answer.