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Questions tagged [sudoku]

Sudoku is a logic-based, combinatorial number-placement puzzle. The objective is to fill a $9\times9$ grid with digits so that each column, each row, and each of the nine $3\times3$ subgrids that compose the grid (also called "boxes", "blocks", "regions" or "subsquares") contain all the digits from $1$ to $9$. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a unique solution.

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Number of weak-sudoku tables

We say that an $n\times n$ table of integers in $\{1,\dots,n\}$ has the weak-sudoku property if each number appears exactly once in each row and each column. The main question is: how many weak-...
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Sudoku solution size

We know an $n$-Sudoku puzzle is with $n \times n$ subgrids consisting of $n \times n$ cells; you will fill it with numbers from $1$ to $n^2$. Candidate solution have size polynomial in $n$, and can ...
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Ideas for modelling the rules to Sudoku using first-order logic?

I'm trying to model the rules to sudoku using first order logic. I've got the first two rules down: (The notation I use is $a_{x,y,v} $, where $v$ is the digit and $x,y$ is the coordinates of the ...
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40 views

Figure out which region of sudoku the item is in

Suppose we have hyper sudoku. In the dark gray areas, we can have 1-9 only once. Therefore, when solving a sudoku graph, I need to figure out what region to look over, to see if any repeats occur. ...
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44 views

4x4 Chromatic Sudoku Graph

I was unsatisfied with existing Sudoku graphs online and my goal was to show the structure in a manner in which the regions are explicit. Nodes which share an edge cannot have be same color. Shaded ...
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2answers
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Equation to locate a square in a square

Good evening, I have been experimenting with different Sudoku checker and have come across a problem: For a nxn Sudoku where n is a square number (4,6,19,25 etcc.), there would be an n number of ...
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How many latin-square designs are orthogonal to this 4x4 latin square design

Where this Latin Square is similar to sudoku, in which each row has one and only one of 1,2,3 and 4, and each column has one and only one 1,2,3 and 4. Important: orthogonality means that the new ...
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1answer
48 views

Would an invalid Sudoku puzzle that becomes valid when you assume its validity be valid?

Suppose you have a sudoku puzzle that you will want to solve using logic. Furthermore suppose you solve the puzzle until you reach a point where a single cell can have two possible values ($a$ or $b$ ...
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1answer
68 views

Help needed in counting ways.

In the 3rd section titled : 'Counting Solutions' for the webpage here, there is calculation as shown here that has exercise based on filling the $9$ sub-cubes of Sudoku named as $B_1, B_2, B_3$ in the ...
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Magic Bingo Grids

In the realm of video game bingo, it is common to use magic squares to generate cards. If you have $25$ difficulty buckets for goals, then if you lay out those buckets onto a magic square, any bingo ...
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1answer
129 views

group theory and sudoko

I am given two Sudoku $S_1$ and $S_2$ and I have two check whether $S_1$ can be turned into $S_2$ with the symetry operators. The two Sudoko are in a "legal" state. So a given cell (numbers $1...9$) ...
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Number Theory - Regular Magic Squares (4x4)

Ok, so I think I found a neat way to solve a $4\times4$ regular magic square (A regular square has one of each number from $0$ to $n^2-1$ and is base $n$. So here's how I did it. We have $16$ ...
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Can a completely non-brute algo exist for solving Sudoku given it's NP-complete? [closed]

As far as I understand it, Sudoku is an NP-complete problem and the best known algorithm for solving it would therefore scale exponentially with grid-size, N. All the algorithms I have so far seen ...
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2answers
69 views

In how many ways can we to place an $X$ in four cells, such that there is exactly one $X$ in each row, column, and $2\times2$ outlined box?

I am a middle school student who would really appreciate it if somebody could explain how to solve this problem using simple terms. I saw this problem on this site and one other, but I am still unsure ...
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1answer
254 views

My Simple Combinatorial Method to Enumerate All Sudoku Solution Grids

How may possible Sudoku Solution Grids are there? The correct answer is: $6,670,903,752,021,072,936,960$ or $6,671E21$ as was proved $12$ years ago! Or was it? Their proof never really enumerated the ...
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Naïve approach to constructing a chaos sudoku

I was recently reminded of the jigsaw sudoku, which is a sudoku variant where each of the nine regions that need to be filled with the numbers from 1 to 9 are irregular regions instead of square ...
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1answer
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How to determine the size of the complete game tree for basic [M]?

You can read the rules of the game here, or actually play it free on the mobile mbrane app, but it's not required to address the question. Essentially: players take turns placing integers onto an ...
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3answers
217 views

Math formula to calculate inner square top left corner in a Sudoku's square

I'm programming a game with C# to solve Sudokus. I have the following Sudoku: It is a 4x4 squared divided into 2x2 squares. If a cell is in row 2, column 2, that cell is in the first inner square, ...
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268 views

Is there a sudoku (Latin Square Pattern) state in a Rubik's cube $6\times6\times6?$

Suppose, Initial state Rubik's Cube 6x6x6 444444 444444 444444 444444 444444 444444 000000 111111 222222 333333 000000 111111 222222 333333 000000 111111 222222 333333 000000 111111 222222 333333 ...
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100 views

A game concerning Sudoku

We (me and you) start with a blank $9\times 9$ blank square (as an empty Sudoku) and I fill the first three rows legally according to Sudoku rules. Is it always possible that you complete the Sudoku ...
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1answer
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Have incompletable Sudokus ever been studied?

Weird question, I know, but this is in relation to an extension of Sudoku into a set of sequential, partisan games which always results in incompletable Sudoku. (i.e. the requirements of strategic ...
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1answer
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Can a solved Sudoku game have an invalid region if all rows and columns are valid? [closed]

Given a $9 \times 9$ solved Sudoku game with $3 \times 3$ regions, is it possible that one (or more) of the regions are invalid if all rows and columns are valid (i.e. have a unique sequence of $1-9$)?...
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is there any size $N\cdot N$Sudoku Puzzle where the smaller $\sqrt N\cdot\sqrt N$ squares all form magic squares

Any $N\cdot N$ Sudoku Puzzle has $N$ squares size $\sqrt N\cdot\sqrt N$ that each have the numbers $1$ to $N$ in them.Is there a sudoku puzzle of any size that have magic squares for all of these sub-...
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Sudoku: What is the relationship between minimum number of clues and order n?

A Sudoku puzzle with order $n$ has $n^2 \times n^2$ squares and $n^2$ regions. For example, a Sudoku puzzle of order $n = 3$ has $9 \times 9$ squares and $9$ regions. A minimal Sudoku is one with ...
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137 views

Can a 9x9 sudoku with sum 45 and sum 285 of numbers squares of (rows,collunms,3x3) not be valid

Its a program that check a sudoku solution if it is correct. It checks ...
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1answer
56 views

Arrange 81 two-digit numbers to form two sudokus?

Take all the integers below 100 that don’t contain a digit 9. There are 81 of them. Is it possible to arrange these 81 numbers in a 9×9 grid in such a way that ...
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Rubik's to Super/Sudoku Cube Modification Possible?

Given a standard 3x3 rubik's cube, is it possible to scamble it and then paint a solved sudoku cube configuration on it - with all the digits on each face orientated the same way - such that when the ...
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1answer
67 views

Sudoku - good proof of one entry must be 1

The question is from here Let the set of numbers $N = \{1, 2,\ldots , 9\}$. Let the set of cells $C = N × N$. A Sudoku solution $f$ is a function $f : C \to  N$ satisfying the following properties: ...
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2answers
885 views

How to solve an empty sudoku?

I am making a computer game sudoku. I have a simple algorithm(more like a rule) : check rows and columns before placing a number. But solving like that sometimes get me stuck and I want to avoid ...
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2answers
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Can a sudoku with valid columns and rows be proved valid without evaluating every 3x3 inside it?

I'm trying to solve a computer science challenge and have readily been able to validate whether or not the outside dimensions of a sudoku puzzle are valid. However, it doesn't check the validity of ...
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3answers
345 views

Necessary conditions for a Sudoku puzzle to have no repetitions

Is it true that if a Sudoku puzzle has the following features there will be no repetitions in rows, columns and $3 \times 3$ subsquares? The sum of each row must be $45$ The sum of each column must ...
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From a Sudoku puzzle to a system of equations

I created the following system of equations to solve a Sudoku puzzle. It's easy to show that, if $a, b, c, \dots, i$ are distinct nonzero numbers, we have the following solution $$S=\{(a_1,\dots,...
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What is the best way to solve sudoku? [closed]

Title i think tells everything. I am curious what is your way to solve sudoku puzzle? What is your mind process, and algorithms you do in your head to solve sudoku the fastest? Looking forward for ...
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Is a Sudoku a Cayley table for a group?

I want to know if the popular Sudoku puzzle is a Cayley table for a group. Methods I've looked at: Someone I've spoken to told me they're not because counting the number of puzzle solutions against ...
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Determining if two Sudoku boards are in the same equivalence class

Consider the following $9 \times 9$ Sudoku board 963 174 258 178 325 649 254 689 731 821 437 596 496 852 317 735 961 824 589 713 462 317 246 985 642 598 173 ...
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The Hardest Sudoku Puzzle

I was playing a casual game of Sudoku today when a friend came by and asked "What's the hardest game of Sudoku possible?" My response: "A Sudoku puzzle with the minimal amount of starting numbers ...
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Sudoku with special properties

Sudoku is a puzzle, with the objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 sub-grids that compose the grid (also "sudoku-blocks") contains all of ...
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289 views

Diagonal-free Sudoku grid

I have a Sudoku grid with the property that diagonally adjacent elements are distinct (it is also a torus under the same property). My question is up to isomorphism, is the grid unique? Here's the ...
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1answer
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Minimum and maximum determinant of a sudoku-matrix

Let $A$ be a sudoku-matrix. Assume that its determinant is positive. What is the lowest, what the highest possible value for the determinant of $A$ ? $A$ must have the dominant eigenvalue $45$, but ...
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On the “solvability” of jigsaw Sudoku puzzles

I am making a computer program that is going to generate Sudoku puzzles of various types. One of these types is "jigsaw", in which the board is split into rows, columns and random 9-square contiguous ...
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1answer
672 views

Normalizing a matrix with row and column swapping

How do you canonicalize a matrix over column- and row-swap operations? Or more specifically, does there exist a function f(M) such that ...
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3answers
2k views

Maximum number of clues in a Sudoku game that does not produce a unique solution

You may have heard that recently it was proven that the smallest number of starting clues for a Sudoku game, guaranteeing a unique solution, is 17. An example is shown below. I am interested in the ...
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1answer
1k views

Sudokus as composition tables of finite groups

If $G$ is a finite group then the composition table of $G$ is a latin square (ie, each row and column contains each group element exactly once). Assume now that $|G| = n^2$ for some natural number $n$...
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Sudoku puzzles and propositional logic

I am currently reading about how to solve Sudoku puzzles using propositional logic. More specifically, they use the compound statement $$\bigwedge_{i=1}^{9} \bigwedge_{n=1}^{9} \bigvee_{j=1}^{9}~p(i,...