Posted on 08/29/2006 9:17:38 AM PDT by taxcontrol
Folks, I'm stumped... I need help with the following:
Given - Two completed suduko puzzles A (correct answer) and R (unknown result).
Question: What is the fewest number of checks that can be made to prove that A = R for the following assumptions:
Assumption1 Assume that in R, no sub area has any duplicate numbers (ie, 1-9 inclusive)
Assumption2 Assume that in R, no row has any duplicate numbers (can also be proven using columns instead of rows.
Also - prove true or false When A = R, the diagonals will always include at least 1 duplicate number
Write a proof for each.
END!CASE
Yep.... that line is fine. In fact all of it is fine. It solves any valid Soduko in less than a second.
;-)
I could be wrong, but I believe that is the longest post I've ever seen. Congratulations! : ' }
It is clarion. I can compile it and email you a zipped copy if you want.
freepmail me an email if you want a copy.
Wassup with #11 'puter dude?
You're gonna kill me. Simply push the cork into the bottle and remove coin.
I love riddles.
Easy for YOU to say!
It's been too long since I've done a proof. Don't know if it helps but if correctly solved, every row, column, and subarea in a 9x9 suduko puzzle will sum to 45.
Technically, if you push the cork into the bottle, you have removed it from the opening. LOL.
But you haven't "taken it out" of the bottle.
Force the cork all the way into the bottle, and dump out the coin. The cork hasn't been "taken out" and in fact is still very much "in the bottle."
I knew it! Thanks for confirming it for me!!
According to Owl, three.
A Sudoku puzzle has a unique solution (A), with no duplication in subareas, rows, or columns. You're told already that R, a proposed solution, has no duplication in subareas or rows. The only thing that would prevent R from being a solution (hence equal to A) is duplication in columns.
Let's consider cases: suppose R is different from A in only one position. No can do, because this would screw up subareas or rows. So R has to be different from A in an "entire" subarea or "entire" row. Consider a subarea: In order not to screw up the rows, I think R's subarea would have to be a reflection across its vertical midline, if the original problem permits this. Consider a row: I don't think it's possible. Any permutation of a row would screw up any subarea that the permutation crosses.
So for R to be different and obey the given constraints, one (or more) subareas would have to be a reflection across its vertical midline. I don't know if this is even possible with any solvable Sudoku puzzle, but this constrains the needed test to at most nine. You can reduce this number further by looking at which subareas could be so reflected given the initial puzzle data.
And that would be my answer. Check Row 1, Row 4, and Row 7 and you should have the identical puzzles. Not sure how to prove that is correct though. The smallest unique puzzles start out with 17 numbers.
Oh. I see you went for the simple to program one...
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