# Taking Sudoku Seriously

@article{Taalman2007TakingSS, title={Taking Sudoku Seriously}, author={Laura Taalman}, journal={Math Horizons}, year={2007}, volume={15}, pages={5 - 9} }

A Sudoku puzzle is a partially filled-in Sudoku board that can be completed in exactly one way. Notice that we only call something a "puzzle" if it has a unique solution (all well-made Sudoku puzzles have this property), and also that any given Sudoku board has many possible puzzles. Figure 2 shows two different Sudoku puzzles that have the same solution. The "game," of course, is to extend a given Sudoku puzzle to its unique Sudoku board. In both puzzles shown in Figure 2, the set of cells…

## 32 Citations

### An Integer Programming Model for the Sudoku Problem

- Computer Science
- 2007

A binary integer linear program is presented to solve a feasibility problem to solve the traditional Sudoku puzzle and several theorems for generating many new puzzles from one given original puzzle are provided.

### The Mathematics Behind Sudoku and How to Create Magic Squares

- Mathematics
- 2016

Sudoku puzzles date back to the 1800s in France and were introduced to America in the late 1970s. Since then, the puzzle has become a worldwide phenomenon. This thesis will be of expositional nature…

### Nested Monte Carlo Tree Search as Applied to Samurai Sudoku

- Computer Science
- 2016

This paper shows that when the nested Monte Carlo search algorithm is implemented for solving Samurai Sudoku, a version of Sudoku in which a standard Sudoku puzzle is placed with four other standard Sudoka puzzles overlapping on each of the corners, it performs better than a completely random brute-force algorithm.

### There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration

- Computer ScienceExp. Math.
- 2014

An exhaustive computer search for 16-clue sudoku puzzles and did not find any, thus proving that the answer is indeed 17, which is one of Karp’s 21 classic NP-complete problems.

### On the Inoue invariants of the puzzles of Sudoku type II

- Computer Science, Mathematics
- 2016

Two kinds of new invariants of such a system, the virtual and the computable Inoue invariant, determined only by the system are defined to show that, when applied to the system arising from a Sudoku puzzle, these invariants are good indicator of the difficulty of the Sudoku puzzles.

### Generalizing Sudoku to three dimensions

- Computer ScienceMonte Carlo Methods Appl.
- 2010

A set of rules and constraints for both three-dimensional Sudoku variations are developed and the properties using the method of simulated annealing are studied.

### Approaching the minimum number of clues Sudoku problem via the polynomial method

- Mathematics
- 2014

Determining the minimum number of clues that must be present in a Sudoku puzzle in order to uniquely complete the puzzle is known as the minimum number of clues problem. For a 9× 9 Sudoku board, it…

### Approaching the minimum number of clues Sudoku problem via the polynomial method

- Mathematics
- 2014

Determining the minimum number of clues that must be present in a Sudoku puzzle in order to uniquely complete the puzzle is known as the minimum number of clues problem. For a 9 9 Sudoku board, it…

### Experimental study on Sudoku

- Computer Science
- 2013

This study may serve as a source for designing questions, examples, and programming assignments related to Sudoku, recursion, backtracking, and experimentation in courses such as algorithms, data structures, and discrete mathematics.

### Gröbner Basis Representations of Sudoku

- Philosophy
- 2010

Summary In this paper we use GrÖbner bases to explore the inherent structure of Sudoku puzzles and boards. In particular, we develop three different ways of representing the constraints of Shidoku…