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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Is there a technique for solving magic square-style puzzle using matrices on pen and paper?
The cells (in the puzzle below) must be filled with integers in {1,2,...,12} and they must all be distinct. The numbers on the outside indicate the sum of the cells. For example, the 1st row's cells ...
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What was the gap in Ariane Papke's proof that the minimum number of sudoku clues is 17?
I was reading McGuire's paper on why the minimum number of clues in a Sudoku puzzle is 17 when I came across a curious comment:
In 2008, a 17-year-old girl submitted a proof of the nonexistence of a ...
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Is there a 9×9 Sudoku Room Square?
The following is an order 9 Room square. Copying from Wikipedia,
Each cell of the array is either empty or contains an unordered pair from the set of symbols.
Each symbol occurs exactly once in each ...
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Can you efficiently determine the number of possible solutions for an arbitrary starting sudoku configuration?
I thought it would be fun to implement a solver which updates in real time to show how many possibilities remain as you fill in squares in any order. I'm able to find a number of resources explaining ...
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Is there a Sudoku solution with a entropic line covering all cells?
I stumbled upon a problem which seems easy but is actually hard to answer. It involves the sudoku game and a commonly used custom constraint rule called "entropic lines".
The rules of a ...
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Is there an underlying graph-theory representation of Sudoku solutions?
I have been puzzling for some time about how a completed 9x9 Sudoku solution can be represented mathematically, and how that mathematical representation can be used to enumerate the different ...
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Can you fill a 16x16 sudoku grid such that adjacent numbers have compatible binary layouts?
I had the thought about a year ago, but I still haven't come up with a solution for it yet.
Every number from $0$ to $15$ can be expressed in binary with four digits, but arrange the digits in a $2 \...
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Finding all valid 5x5 sudoku/bingo boards where diagonals must also be unique?
I'm working on a personal project to create a bingo card for a video game. The bingo card contains items the player can use during normal play, and my goal is to be able to generate a bingo board ...
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How many possible determinants are there for a $3 \times 3$ matrix made of the numbers $1$ to $9$?
How many possible determinants are there for a $3 \times 3$ matrix made of the numbers $1$ to $9$? Each integer from $1$ to $9$ must appear exactly once in the matrix (so that the matrix could appear ...
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What type of math should I use for this puzzle?
I could use help modeling this puzzle. I'm not looking for a solution but I need help in phrasing the problem mathematically. I need a change in paradigm. My friend asked me for help with this puzzle ...
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Does this linear function exist?
I'm trying to solve Sudoku using linear programming. In Sudoku, it is known that each row and column of the grid must contain number from 1 to 9 without duplicates. I need a constraint function that ...
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How many different $2 \times 2$ Sudokus are there?
PROBLEM
How many different $2 \times 2$ Sudokus are there?
APPROACH
This seems pretty easy to brute force. There are $576$ Latin squares of size $4$ (which are the sudokus without restriction on boxes)...
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Sudoku Puzzle with only 1 and 0 and other restrictions
For the following sudoku-style puzzle, you are given the following 9-by-9 grid,
and you need to fill it in with zeros and ones satisfying the following conditions:
(i) Each row, each column, and each ...
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Minimum Number of Clues for Unsolvable Sudoku
I am going to make a distinction between "unsolvable" and "invalid" Sudoku. A Sudoku is unsolvable if there is no way to fill in all the spaces without violating one of the rules ...
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Determinant of ModK Reduction of Matrix.
Let $M:=(m_{ij})$ be a square ($ n \times n $) matrix with entries in $\{ 1,2,3,.., n\}$ ,and non-zero determinant $D$ . Let $M_k$ be its reduction Mod($k$) ; $k=2,3,.., n-1$ , i.e., $M_k:=(m_{ij} ...
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