## More than one solution to the same puzzle?????

Everything about Sudoku that doesn't fit in one of the other sections

### More than one solution to the same puzzle?????

I've found a puzzle that has more than one solution, and I thought that was supposedly impossible? Anyone out there know anything about this?
dak98502

Posts: 1
Joined: 17 January 2006

### Re: More than one solution to the same puzzle?????

dak98502 wrote:I've found a puzzle that has more than one solution, and I thought that was supposedly impossible? Anyone out there know anything about this?

Unfortunately, it's not only possible, it's also not uncommon...

According to the (unwritten?) rules, though, a *real* Sudoku puzzle should have only one possible solution, reachable by logical reasoning alone. (The definition of the latter can be debated, though, since some regard trial and error as a logical means, while others don't.)

Multi-solution puzzles, though, *require* blind guessing, since at one point, there can not be a logical (as in reasoning/deduction) next step, since there are two (or more) possibilities for any given cell...

Hopefully the publishers of bad puzzles will smarten up some day. I suggest you to at least inform the source of the puzzle of your disappointment.
vidarino

Posts: 295
Joined: 02 January 2006

There’s nothing intrinsically wrong with multiple solution puzzles – some people prefer them. It’s just that the assumption is that a Sudoku puzzle has one solution, so multiples need to be labelled as such and it seems that in many cases they are not.
emm

Posts: 987
Joined: 02 July 2005

it could have been a sudoku x then the soultion would have 1-9 in the diagonals as well
Chessmaster

Posts: 191
Joined: 21 December 2005

dak98502 wrote:
I've found a puzzle that has more than one solution, and I thought that was supposedly impossible? Anyone out there know anything about this?

Unfortunately, it's not only possible, it's also not uncommon...

According to the (unwritten?) rules, though, a *real* Sudoku puzzle should have only one possible solution, reachable by logical reasoning alone. (The definition of the latter can be debated, though, since some regard trial and error as a logical means, while others don't.)

Multi-solution puzzles, though, *require* blind guessing, since at one point, there can not be a logical (as in reasoning/deduction) next step, since there are two (or more) possibilities for any given cell...

Hopefully the publishers of bad puzzles will smarten up some day. I suggest you to at least inform the source of the puzzle of your disappointment.
Last edited by Camchase on Fri Jan 20, 2006 11:13 pm, edited 1 time in total.
Camchase

Posts: 30
Joined: 03 January 2006

### Re: More than one solution to the same puzzle?????

Over on some other thread there's a sudoku product with puzzles having multiple solutions. Maybe we should start a list of books etc having puzzles with multiple solutions.

I can't resist a comment on

vidarino wrote:According to the (unwritten?) rules, though, a *real* Sudoku puzzle should have only one possible solution, reachable by logical reasoning alone. (The definition of the latter can be debated, though, since some regard trial and error as a logical means, while others don't.)

For me, a sudoku puzzle is a set of clues having exactly one solution. That's it. There's nothing about how that solution can be found.

Other people add extra conditions. That the puzzle be symmetrical is often a requirement, but a red herring in my opinion. Sometimes the setter has to add clues to a real puzzle to make it symmetrical, which seems artificial to me. Anyway, when you are solving it, once you put in your first number you have a new puzzle which is no longer symmetrical. Symmetry does not help in any way when solving. It's just for aesthetic reasons. Most published puzzles are symmetrical.

Some people add conditions that the puzzle be solvable using only certain logical rules (like Pappocom). Some people like this, some don't. This has been discussed over and over.

The wikipedia entry does not mention symmetry in the definition, or whether it must be solvable by certain means.
Moschopulus

Posts: 256
Joined: 16 July 2005

### Re: More than one solution to the same puzzle?????

Moschopulus wrote:For me, a sudoku puzzle is a set of clues having exactly one solution. That's it. There's nothing about how that solution can be found.

On second though, I agree completely and hereby retract my claim that they should be solvable without guessing.

And of course, if all proper puzzled had to be logically solvable only by hitherto known methods, we would never have seen any "unsolvables" (like Michael Mepham's) that lead to the discovery of new tehcniques.

What I do believe, though, is that any puzzle with a unique solution can be solved purely by non-trial-and-error means, but that all the patterns and methods required to do so might not be discovered yet. (Not that there's inherently anything wrong with blind T&E, but I don't like using it myself.)

Vidar
vidarino

Posts: 295
Joined: 02 January 2006

### Re: More than one solution to the same puzzle?????

Moschopulus wrote:Over on some other thread there's a sudoku product with puzzles having multiple solutions. Maybe we should start a list of books etc having puzzles with multiple solutions.

Hear, hear. Let's call it "Sudokus of Shame"
jf27

Posts: 34
Joined: 18 September 2005

### Re: More than one solution to the same puzzle?????

jf27 wrote:
Moschopulus wrote:Over on some other thread there's a sudoku product with puzzles having multiple solutions. Maybe we should start a list of books etc having puzzles with multiple solutions.

Hear, hear. Let's call it "Sudokus of Shame"

On the other thread we call them "pseudo-puzzles".

But of course, it just occurred to me that a multiple-solution grid could just be called a

PSUEDOKU

Cheers

Gordon
gfroyle

Posts: 214
Joined: 21 June 2005

Nice one

I know some of us are interested in pseudokus as well as sudokus, I certainly am, but I do think we should name and shame published books, games, etc that *claim* to have sudokus but actually have pseudokus.

Unfortunately it won't make any difference to the sales. The people who buy those don't read this forum anyway.
Moschopulus

Posts: 256
Joined: 16 July 2005

Moschopulus wrote:Unfortunately it won't make any difference to the sales. The people who buy those don't read this forum anyway.

True, but if such a list is put online, perhaps the publishers of bad puzzles will read it and smarten up... Then again, probably not, but hey...

It sad, really, considering how easy it is to generate perfectly valid one-solutions puzzles in bulk with a computer.
vidarino

Posts: 295
Joined: 02 January 2006