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Joined: 12 Oct 2005
Posts: 21
Location: Cornwall

PostPosted: Thu Nov 03, 2005 8:33 am    Post subject: Gestalt/intuition Reply with quote

This thought occurs to me ...

Are there solvers on this forum who sometimes have the experience of 'knowing' a number must go in a particular square without going through the logical stages explicitly?

(It doesn't happen to me, I am essentially a plodder) but I have a sense that it is psychologically possible, as when people can do amazing mental arithmetic calculations very fast. I am not talking about guessing here. I am thinking that sometimes the brain processes data quicker than we can articulate the processes.

Most of the posts here about solving are admirably (no sarcasm) logical, clear and explained - that's because we are communicating with each other... but inside your head, do you ever have to post-rationalise a decision?
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David Bryant

Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Fri Nov 04, 2005 11:55 am    Post subject: "Intuition" Reply with quote

This happens to me occasionally. Today's puzzle (Nov. 4, 2005) is a good example.
 1  .  .    .  4  .    5  .  2
 .  9  .    .  .  .    .  .  .
 .  .  6    3  .  2    .  8  .

 .  .  4    5  .  .    .  9  .
 .  8  .    6  .  7    .  1  .
 .  7  .    .  .  9    3  .  .

 .  2  .    7  .  4    8  .  .
 .  .  .    .  .  .    .  6  .
 8  .  7    .  6  .    .  .  9

When I first looked at this puzzle, the grouping of four "7"s immediately caught my eye, and I had a strong suspicion that I would have to place a "7" in between the "5" and the "2" in the top right 3x3 box. So I examined the puzzle more closely, and this is what I found. (In the next table, the "X"s in the top left, top center, middle right, and bottom right 3x3 boxes indicate that a "7" is possible in that location.)
 1  .  .    .  4  .    5  .  2
 X  9  .    .  X  .    .  .  .
 X  .  6    3  X  2    .  8  .

 .  .  4    5  .  .    X  9  X
 .  8  .    6  .  7    .  1  .
 .  7  .    .  .  9    3  .  .

 .  2  .    7  .  4    8  .  .
 .  .  .    .  .  .    X  6  X
 8  .  7    .  6  .    .  .  9

There are two "X-Wing" formations in this puzzle, right at the beginning! And sure enough, there's a "7" in r1c8, because it can't possibly fit anywhere else in the top right 3x3 box. So I wrote the "7" in at r1c8 before I even noticed the obvious "6" at r7c1. dcb
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AZ Matt

Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Fri Nov 04, 2005 4:18 pm    Post subject: Reply with quote

I haven't experienced "knowing" a number was in a certain cell, but I have experienced intuitively knowing how to solve a puzzle. Or at least that was true before I started regularly visiting this site and learning about "advanced techniques."

Invariably, my moments of "revelation" have been revealed to be nothing more than unnecessarily complicated ways to solve otherwise simple puzzles. I "see" how to solve 15 cells at once; David Bryant points out it is a simple x-y wing. I intuit the 7s are the key to the solve and "see" the imbalance in the pattern ; someone_somewhere points out it's just a textbook swordfish. (See the immediately proceeding topic.)

A part of me longs for the days (only a week ago) when I was solving fiendish and diabolical puzzles with absolutely no clue as to what I was doing or how I was doing it. If you look at my post in the Daily Sudoku Puzzles forum on this board, about the the Friday Oct 28 Very Hard, you'll see that I actually solved a puzzle more quickly (or at an earlier stage of development) than David Bryant did, but that's only because I stalled before he did.

You should read about Garry Kasparov's chess battles with Deep Blue. The theory as to why he could beat so many machines is that chess is more than just math -- there is an art to it. Once you find a puzzle a computer can't solve, it can never "learn" how to solve it (and I mean when the program reaches the inevitable end of its learning capacity). And a machine doesn't have a "personality"; so therein is the human advantage -- you know that, and you can keep adapting until you figure out how to beat the machine (i.e., find what "personality" beats the machine).

PS: I find that my favorite puzzles are the ones someone can vouch for as solvable, but aren't recognized as solvable by the draw program here.
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