# Sudoku: Beyond Pastime

The main mathematical news

2005: The number of completed 9×9 Sudoku squares is: 6,670,903,752,021,072,936,960

2007: There exists a Sudoku puzzle with 17 clues that has a single solution, and there exists a 29 clues Sudoku puzzle with 2 distinct solutions.

2011: At least 17 clues are needed to ensure a single solution.

Sudoku has applications in many fields including agriculture, encryption and medicine.

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Additional Theorems / conjectures / Open questions

Open question: Given a complete solution to the Sudoku puzzle, how many different Sudoku puzzles exist for which the array is a solution?

2008: The Projection Algorithm is a computer program that seems to solve any 9×9 Sudoku puzzle.  No proof and no counter example.

2013: The general nxn Sudoku problem is NP-complete.

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The main mathematical concepts / Principles

Combinatorics (MSC2010#97K20)

*   Latin square

Logic (MSC2010#97E30)

*   Non-constructive proofs

*   Deductive proof

*   Refutation by counter example

*   Existence and uniqueness

*   Existence proof
*   A non-constructive proof

Graph Theory (MSC2010#97K30)

*   Graph Theory

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