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Inherent difficulty?

 
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cobnut

Joined: 30 May 2008
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PostPosted: Tue Jun 03, 2008 9:08 am    Post subject: Inherent difficulty? Reply with quote

This is a question to which I should really know the answer, but I'm afraid I don't.

Is any given order 3 suduko grid more difficult to solve than another, regardless of the givens? Or is it only the givens that determine difficulty?

Part of me suggests that certain arrangements of the numbers within the grid might make them inherently easier or harder to solve, but another part of me says that's rubbish.

Does my question make sense?

Jon
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Jean-Christophe

Joined: 19 Mar 2006
Posts: 126
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Location: Belgium

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PostPosted: Tue Jun 03, 2008 3:05 pm    Post subject: Reply with quote

The number and pattern of the givens has very few influence on the difficulty.
1. Some of the 17 clues minimal found by Gordon Royle can be solved with singles only.
2. The Pattern Game at Sudoku Payers' Forum demontrates the vast range of difficulties for the same pattern.
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Jean-Christophe
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." Sherlock Holmes.
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gsf

Joined: 18 Aug 2005
Posts: 411
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Location: NJ USA

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PostPosted: Tue Jun 03, 2008 3:51 pm    Post subject: Re: Inherent difficulty? Reply with quote

cobnut wrote:

Is any given order 3 suduko grid more difficult to solve than another, regardless of the givens? Or is it only the givens that determine difficulty?

Part of me suggests that certain arrangements of the numbers within the grid might make them inherently easier or harder to solve, but another part of me says that's rubbish.

interpreting grid as a solution grid (81 clues)
then there are many minimal puzzles that can be derived from the grid
the question is then: how much influence does a particular solution grid have on the ratings of its derived grids?
I'm pretty sure the answer is don't know
but we do know that a solution grid can influence some properties of its derived puzzles
e.g., the unavoidables control the minimum number of clues
and there are ways to determine if a particular solution grid contains 17 clue derived puzzles
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