## Ambiguity

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

### Ambiguity

I was playing a game, and felt sure that I'd found a set of numbers with an ambiguous solution. That is, there were 10 unknowns which could be filled in in one of two different ways, both giving a correct solution.

I stared harder and found a flaw, so it turned out to be untrue.

But it got me thinking, is there something in the mathematics behind it that means every correct set of numbers is necessarily and proveably unambiguous.

Hmm, thinking about that, the idea of 'ambiguity' depends on having some known and some unknown squares - you could argue that every correct set is a rearrangement of every other set if they're all unknown, unless you have some known ones that 'fix' the correct solution to only one.

So I'll modify my question to - does the sudoku application, and all the printed versions of them, assure no ambiguity of the answer? Is there (and I'll regret asking this) a technique by which the random ones are generated such that the given initial set give only one answer?
mortice

Posts: 1
Joined: 10 August 2005

### Re: Ambiguity

mortice wrote:So I'll modify my question to - does the sudoku application, and all the printed versions of them, assure no ambiguity of the answer? Is there (and I'll regret asking this) a technique by which the random ones are generated such that the given initial set give only one answer?

All decent Sudoku programs should guarantee a unique solution to the given puzzle.

Almost certainly, programs generate random puzzles, solve them exhaustively (either by emulating "human" logic, or just a quick backtrack program) and then throw out those with multiple solutions. Then, (optionally) add some more "unnecessary" clues either to make it symmetric or to make it easier (to fit into a certain "difficulty" group).

Gordon
gfroyle

Posts: 214
Joined: 21 June 2005

they could easily generate ambiguity, if they wanted, but they don't.
(If that's what you wanted to know)
dukuso

Posts: 479
Joined: 25 June 2005

they could, but ambiguous puzzles are quite annoying.
lobby__boy

Posts: 29
Joined: 08 June 2005