17 and Sudoku Clues - Numberphile
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Date: 2022-04-08
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Comments and reviews: 9
Bill
James, I wonder:
Is there a logical, algorithmic approach that always suffices to solve a sudoku puzzle? Or does a sudoku puzzle exist that is sufficiently random (in some sense lacking discernible patterns) that one must guess a solution and work the puzzle from there to see if the guess is valid?
I know a set of techniques for solving sudoku puzzles, but on some difficult puzzles, I end up guessing one or more squares and then have to work out the results to see if I guessed correctly or if I have to backtrack.
Are there more techniques I could learn, or is guessing sometimes inevitably required?
On reflection, this is related to writing a computer program to solve sudoku puzzles, and whether it could be completely algorithmic or would sometimes have to proceed by trial and error.
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James, I wonder:
Is there a logical, algorithmic approach that always suffices to solve a sudoku puzzle? Or does a sudoku puzzle exist that is sufficiently random (in some sense lacking discernible patterns) that one must guess a solution and work the puzzle from there to see if the guess is valid?
I know a set of techniques for solving sudoku puzzles, but on some difficult puzzles, I end up guessing one or more squares and then have to work out the results to see if I guessed correctly or if I have to backtrack.
Are there more techniques I could learn, or is guessing sometimes inevitably required?
On reflection, this is related to writing a computer program to solve sudoku puzzles, and whether it could be completely algorithmic or would sometimes have to proceed by trial and error.
reply
Daniel
Hi, I have an interesting question: this proof shows that you won't find a puzzle that is uniquely solved with fewer than 17 clues, alright. But there might be some of the 6. 7 thousand million million million distinct grids out there (or some of the 5 billion whatever grid families, for simplicity) requiring more than 17 clues to be uniquely solved. Now, how do we get to know which is the highest minimum number of clues that you will ever get from any of the possible grids/families? Does somebody know the answer, or any research on the subject? I find this is a valid and interesting problem too.
Thank You!
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Hi, I have an interesting question: this proof shows that you won't find a puzzle that is uniquely solved with fewer than 17 clues, alright. But there might be some of the 6. 7 thousand million million million distinct grids out there (or some of the 5 billion whatever grid families, for simplicity) requiring more than 17 clues to be uniquely solved. Now, how do we get to know which is the highest minimum number of clues that you will ever get from any of the possible grids/families? Does somebody know the answer, or any research on the subject? I find this is a valid and interesting problem too.
Thank You!
reply
Simon
For me the main problem I have is a computerized Sudoku puzzle always has hints that are if you place the wrong number it will tell you and that makes the game basically unplayable. Because there's no actually logic getting it out you just poke until it's done and I hate that. But a paper copy of a Sudoku I like
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For me the main problem I have is a computerized Sudoku puzzle always has hints that are if you place the wrong number it will tell you and that makes the game basically unplayable. Because there's no actually logic getting it out you just poke until it's done and I hate that. But a paper copy of a Sudoku I like
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I have two corollary questions:
(a) in a simpler 2X2 (instead of 3X3) sudoku, what is the minimum clues for a base-4 2X2 sudoku, ie, in a simple grid of 1, 2, 3, 4
(b) in a far more complex 4X4 sudoku, what is the mimum clues for a base 16, i. e. 1-9, a, b, c, d, e, f, g sudoku?
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I have two corollary questions:
(a) in a simpler 2X2 (instead of 3X3) sudoku, what is the minimum clues for a base-4 2X2 sudoku, ie, in a simple grid of 1, 2, 3, 4
(b) in a far more complex 4X4 sudoku, what is the mimum clues for a base 16, i. e. 1-9, a, b, c, d, e, f, g sudoku?
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NomadUniverse
The thing about enjoying Sudoku is to remember that its just logic and reasoning and elimination, no math in solving. The puzzles would work exactly the same with A-B-C-D-E-F-G-H-I, or any 9 other unique symbols. If you are repelled away because -ugh, math-, don't be: )
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The thing about enjoying Sudoku is to remember that its just logic and reasoning and elimination, no math in solving. The puzzles would work exactly the same with A-B-C-D-E-F-G-H-I, or any 9 other unique symbols. If you are repelled away because -ugh, math-, don't be: )
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gerald
Pedantic point: this doesn't prove that a smaller number than 16 clues could give rise to a unique sudoku grid - although it would seem on the face of it not to be possible.
But then, that's why we rely on mathematics rather than guy hunches.
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Pedantic point: this doesn't prove that a smaller number than 16 clues could give rise to a unique sudoku grid - although it would seem on the face of it not to be possible.
But then, that's why we rely on mathematics rather than guy hunches.
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Fabiano
In the end of this video, James Grime gives his opinion about if he personally likes Sudoku game and he answers he dont because -it is a game of pure logic-. Question: Do you think the work of Gary McGuire to discover 17 was pure logic?
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In the end of this video, James Grime gives his opinion about if he personally likes Sudoku game and he answers he dont because -it is a game of pure logic-. Question: Do you think the work of Gary McGuire to discover 17 was pure logic?
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funlover1977
Sudoku was invented by an american in late 70's actually so it does not come from Japan after all. It was first widely published in Japan magazines and that's where misunderstanding about it's origins may be coming from.
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Sudoku was invented by an american in late 70's actually so it does not come from Japan after all. It was first widely published in Japan magazines and that's where misunderstanding about it's origins may be coming from.
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Alkaws
If you are into Sudoku puzzles, then this is the books for you. It really gives you a challenge and it is so much fun. The more puzzles you solve the more you want to solve more puzzles. I love books for dr. khalid alzamili
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If you are into Sudoku puzzles, then this is the books for you. It really gives you a challenge and it is so much fun. The more puzzles you solve the more you want to solve more puzzles. I love books for dr. khalid alzamili
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