# 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.

44 questions
1answer
18 views

### 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-...
1answer
33 views

### 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 ...
1answer
87 views

### 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 ...
1answer
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. ...
1answer
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 ...
2answers
47 views

### 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 ...
0answers
56 views

### 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 ...
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 $b$ ...
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 ...
0answers
54 views

### 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 ...
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 $1...9$) ...
0answers
200 views

### 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 $16$ ...
1answer
75 views

### 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 ...
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 ...
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 ...
0answers
52 views

### 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 ...
1answer
81 views

### 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 ...
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, ...
1answer
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 ...
1answer
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 ...
1answer
110 views

### 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 ...
1answer
3k views

### 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 $1-9$)?...
1answer
57 views

### 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-...
1answer
189 views

### 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 ...
1answer
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 ...
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 ...
0answers
68 views

### 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 ...
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: ...
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 ...
2answers
822 views

### 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 ...
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 ...
0answers
1k views