To be considered well-constructed, a sudoku puzzle must have one unique answer. Some advanced solving techniques use that fact. And, yes, sudoku puzzles have nothing to do with arithmetic. They are puzzles in logic which is, after all, a subset of mathematics , and work equally well with letters or symbols in place of numbers. Numbers happen to be easier to manipulate because people all over the world recognize the digits from The puzzles can be solved using colors instead of numbers.
I think the key words of "chromatic polynomials" in the title, the key sentences "We will reformulate many of these questions in a mathematical context and attempt to answer them. More precisely, we reinterpret the Sudoku puzzle as a vertex coloring problem in graph theory", the authors as mathematicians, and the publication in "Notices of the AMS" is a tip off.
So we can still play with it. Btw, the coloring is just a map to a large class of "coloring problems" in mathematics. As Exterminator says, formal logic is considered math, so are many logical problems at the core, while logic at large as for example as fallacies in reasoning is in the philosophical domain.
Only if you refuse to hazard a guess. Since you can't know there are supposed to be 2 solutions left, those 4 boxes should remain empty to the very end.
I just played one like it, and that's why I found this article. Because I read somewhere that sodokus are supposed to only have 1 solution. This makes sense, though, that the thing which so often is a bar to progress should create the possibility of 2 solutions. Yes it is inevitable these squares are the last ones remaining because at that point the puzzler has to decide: "there is no clue available to decide whether each of these squares contains a 4 or a 9, therefore either must be the correct answer.
The next question is then can there be puzzles with more than just 2 pairs of numbers that are interchangeable. I suspect that 3 pairs would not work but am not sure about that. Atleast additional pairs can be added 2 pairs at a time.
When there are too many such pairs does it become impossible to solve for the remaining spot because of confusion caused by the empty spots left by switchable spots? You mentioned 3 pairs, and yes that is an open question.
Garbage sudoku publishing on the web these days. I would vote that they should be unique. How many of you are hooked? Oh, yeah. I'm not very quick and I sometimes make a careless error that screws up the puzzle.
The answer to this problem is While a concrete mathematical proof has not been found, mathematicians have analyzed every possible Sudoku puzzle with 16 clues through brute force and found that none have a unique solution. For example, if every 1, 2, and 3 digits in a grid was given, which would mean there are 27 clues to start with, the other digits could still be used interchangeably. This would give rise to multiple solutions. Thank you for submitting your email!
It looks like something went wrong. Try refreshing this page and updating them one more time. If you continue to get this message, reach out to us at customer-service technologyreview. Skip to Content. A big ask, I know, but surely one worth aiming for.
Deep Dive. Tech policy. By Darren Byler archive page. By Eileen Guo archive page. By Emran Feroz archive page. Kendall Frey Kendall Frey 3, 21 21 silver badges 27 27 bronze badges. That's one point of this answer. This would make an interesting question in its own right, here or on math. Show 4 more comments. Community Bot 1. So a single modern hard drive could actually store the full list of unique Sudoku solutions. The Wikipedia reference is completely irrelevant. Therefore you do not present two dissenting opinions , you present one opinion, and mistake an entirely different concept for another.
Add a comment. McLean Donald. McLean 1 1 silver badge 10 10 bronze badges. Bailey M On the other hand, it has been proven that the minimum number of digits that is required for a grid to have a unique solution is Featured on Meta.
Now live: A fully responsive profile. Linked 4. Related 9.
0コメント