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

Postby cho » Sun Oct 30, 2005 7:15 am

DanO wrote:Until reading this thread I has equated Trial and Error with guessing. I have now changed my opinion.

Trial and Error is a logical deduction technique that removes a posibility by finding that it always leads to a contridiction. A trial that happens to find a solution is a guess and you have not completed the puzzle*.

(*unless you also include the uniquness principle that if you find 1 solution to a valid Sudoku you have found them all)

So on a coin toss, if I ask if it's a head, and it is, I need to also ask if it's a tail. Then I can say that I explored all possibilities and found one to be invalid. Therefore I didn't guess. Got it.

Unless I am aware of a rule that states that it can't be both a head and a tail, in which case I can say I didn't guess without actually verifying the non-tail status. Even better, T&E without the E.

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Postby emm » Sun Oct 30, 2005 10:32 am

Yes, I get it and yes, T & E is a misleading term.

At rockbottom, I still believe that guessing is a subjective frame of mind as much as anything else. A guesser is happy to take blind stabs and enters random numbers as if they were actual clues in the hope of a solution.

A solver using T & E considers herself to be still at the pencil marking stage and looking for a proof while considering all possible outcomes.

In T & E a number is not considered a clue unless it is a cert. In guessing any number is considered a clue while it works.
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Postby MCC » Sun Oct 30, 2005 1:13 pm

Hangs head in shame, again:(

em is right, it's the 'edit' button and not the 'quote' button I should have said.

DanO wrote:...(*unless you also include the uniquness principle that if you find 1 solution to a valid Sudoku you have found them all)

I find this a bit of cloudy thinking.

The uniqueness principle relies on the fact that a Sudoku puzzle has only one solution.

If you know that the puzzle has only one solution then you can use the uniqueness principle to eliminate candidates.
If you're unsure whether a puzzle has one or more solutions then you cannot use the uniqueness principle.
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