Question

Advanced methods and approaches for solving Sudoku puzzles

Proof-By-Contradiction + Deducing-From-Uniqueness-Of-Answer

Postby Pat » Tue Jun 06, 2006 2:04 pm

ab wrote:Suppose you pick the right choice first. Using this technique is only logical if you then go on to check all other possibilities, something I doubt many solvers would do



[ an earlier discussion of guessing — one of many! — can be found mixed into the Topic I don't even know how to post a message for many members! ] quoting from that Topic:
Pat wrote:
em wrote:You can’t do just one chain and leave it at that - they require a proof by contradiction, don't they?

MCC wrote:They do.

yes, when i find myself forced to use a proof-by-contradiction, i do always insist on developing both branches

yet reading the discussions on Deducing-From-Uniqueness-Of-Answer, you could conclude that the extra Given (i.e. we are given that the puzzle has only one answer) permits ignoring the 2nd branch whenever the 1st branch did happen to produce an answer!
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Postby emm » Tue Jun 06, 2006 6:26 pm

ab wrote:Suppose you pick the right choice first. Using this technique is only logical if you then go on to check all other possibilities, something I doubt many solvers would do:!:


There are two things involved - one is the logic of it and the other is the guessing of it. I wouldn't argue that the technique of guessing is not logical nor that it's not 'acceptable'. Guessing is a value-laden word and generally not favoured, but some people prefer it. It's been said before that it can be the quickest way to find a solution and for this reason is often used by participants in Sudoku competitions - which is pretty logical.

Pat wrote:yet reading the discussions on Deducing-From-Uniqueness-Of-Answer, you could conclude that the extra Given (i.e. we are given that the puzzle has only one answer) permits ignoring the 2nd branch whenever the 1st branch did happen to produce an answer!


This seems as valid as any of the Uniqueness arguments - if there is only one solution then there's no need to backtrack if you fortuitously stumble across the correct candidate. But it's still guessing. Whether or not that's OK, is up to you.
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