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David Bryant
Gold Member

Joined: 20 Jan 2006
Posts: 86

Posted: Thu May 04, 2006 2:42 pm    Post subject: Hypotheses are not axioms

 Keith wrote: ... we'll have to counsel you about using T&E on UR's*. Can there be a greater sin?

Hi, Keith!

You're joking, right?

 Keith wrote: So, we recognize a UR (and its result) and then we find another way to reason the same result. This is logically defensible as not using Uniqueness?

I maintain that it is logically defensible, and it is not "using" Uniqueness. The difference is simple.

-- To "use" Uniqueness is to adopt as axiomatic the statement "The solution to this puzzle is unique."

-- To recognize the "deadly pattern" and use it as a clue for finding a cell which might usefully serve as the root of a forcing chain is to say "If the solution to this puzzle is unique, then assuming that value 'x' lies in this cell will lead to a contradiction."

In the first case I must accept an axiom. In the second case I form an hypothesis, and test it against the rules of the game. The difference between the two procedures is as clear, I think, as the distinction between night and day.

Trust, but verify.

 Keith wrote: Actually, it seems to me: Assume the deadly pattern, if it is a unique puzzle, you should pretty soon find a contradiction.

I've tried this route on quite a few puzzles. What I usually find is that the chain leading to a contradiction is very long.

On the other hand, the chain leading to a contradiction when I start working from a "conjugate" cell is often quite short and direct. So experience tells me that the second approach is (usually) preferable. dcb
keith
Hooked

Joined: 07 Feb 2006
Posts: 35
Location: near Detroit, Michigan, USA

 Posted: Thu May 04, 2006 5:05 pm    Post subject: David, My entire message was not intended to be taken too seriously. Keith
David Bryant
Gold Member

Joined: 20 Jan 2006
Posts: 86

 Posted: Thu May 04, 2006 7:07 pm    Post subject: I hope I'm not too serious Hi again, Keith! Sudoku's only a game. I hope I never take it too seriously! That said, I must confess that I'm very serious about logic. I have studied quite a bit of mathematics, which can be a lot of fun, but which also has some rather serious ramifications. Anyway, I always enjoy our conversations, and I've learned quite a bit from you. Thanks for introducing me to the concept of a "non-unique rectangle" in the first place. Was that really just 19 weeks ago? It seems like longer. dcb
keith
Hooked

Joined: 07 Feb 2006
Posts: 35
Location: near Detroit, Michigan, USA

 Posted: Thu May 04, 2006 11:25 pm    Post subject: David, My message was not really to you: It was to those who rant and rave over other people's solution techniques. I am also a logic person, but I think my logic is pattern recognition. Your logic is (I think) more to do with implications and consequences. Do you do jigsaw puzzles? My style is to stare at the puzzle, and then pick up the right piece and put it in its place. So far as I am concerned, everyone elses' jigsaw puzzle technique is Trial and Error! It was about five or six months ago that I decided to become a Sudoku expert. Unwittingly, I was among the first to propogate Robert Woodhead's work on Unique Rectangles. Fortuitously, I was among the first to connect Unique Rectangles with other solution methods. (Thanks to Ruud for his post "UR meets X-Wing".) Anyway, it's been fun. I've learned the most from you and from Tracy. Best wishes, Keith
David Bryant
Gold Member

Joined: 20 Jan 2006
Posts: 86

 Posted: Thu May 04, 2006 11:40 pm    Post subject: Re: Jigsaw Puzzles Boy, I haven't done a jigsaw puzzle in years. I can't claim to always find the right piece just by staring at the pile that's left. But when I did work on jigsaw puzzles I (thought that I) was very methodical. That is, I'd separate the pieces into piles (3 outies, one innie; 2 outies, 2 innies; one outie, 3 innies; etc) and try to at least restrict my search to the pieces that had the right general shape. My sister was a lot more interested in jigsaw puzzles than I ever was. I remember two puzzles in particular that I bought for her, years ago. One was all red, and the only "clue" was the shape of each piece. The other one was a sort of black and white zig-zag pattern where all the pieces (except the ones along the border, obviously) were cut in exactly the same shape, so the "clues" were all embedded in the details of the stripes of black and white. dcb
Ruud
Site Owner

Joined: 30 Dec 2005
Posts: 601

Posted: Fri May 05, 2006 12:05 am    Post subject:

 Keith wrote: Do you do jigsaw puzzles? My style is to stare at the puzzle, and then pick up the right piece and put it in its place.

I always created piles for each area of the puzzle. There was the "air" pile, the "forest" pile, the "roof" pile, etc. Then started the puzzle with border and all mixed pieces, like outlines of roofs and trees. Your method works best when there are recognizable patterns, Keith.

We're not too far off-topic?

Ruud.
_________________
“If the human brain were so simple that we could understand it, we would be so simple that we couldn't.” - Emerson M Pugh
zoltag
Expert

Joined: 01 Apr 2006
Posts: 126

Posted: Fri May 05, 2006 4:01 am    Post subject:

 Ruud wrote: We're not too far off-topic? Ruud.

If you were asking me, nope, bang on. I do jigsaws too. The wife has some insane ones. Same picture on both sides, offset, several extra pieces. I like puzzles, this does seem too tedious! Ok, way too, she likes them! <and does NOT do Sudokus, waste of time!>
Pete
Gold Member

Joined: 13 May 2006
Posts: 113
Location: Cincinnati Ohio, USA

 Posted: Sat Jun 03, 2006 5:00 pm    Post subject: ah perhaps I see now. this is jigsaw but not jigsaw sudoku sounds like its half on topic at least I usta call them sky piles or cloud piles not air piles perhaps my piles are more segregated. edges go first. I had one that is 500pcs. It's a photo of a tray of jelly beans. I never did get it._________________"It gets dark at night" - Olbers
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