The Math of Sudoku

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IsomorphismsBoards that can be connected to each other using (finitely many of ) thetricks described in the previous slide are said to be essentially the same.How many boards can we get out of a single given board?Starting with one Sudoku puzzle, a daily calendar of Sudoku puzzlescan be produced... enough for the entire next century! 1 .There are 6,670,903,752,021,072,936,960 distinct Sudoku boards 2 .There are 5,472,730,538 essentially different boards 3 .1 Bartlett & Langville. An Integer Programming Model for the SudokuModel. The Journal of Online Mathematics and Its Applications, Vol. 8 (2008)2 Felgenhauer & Jarvis, Mathematics of Sudoku I (2006)3 Russel & Jarvis. Mathematics of Sudoku II (2006)
MinimalityQ. What is the minimum number of ‘givens’ in a Sudoku board that areneeded to have unique solution?A. Unknown.The minimum number known is 17. Gordon Royle has a collection of49151 distinct Sudoku configurations with 17 entries athttp://mapleta.maths.uwa.edu.au/∼gordon/sudokumin.phpGary McGuire is conducting a search for a 16-given Sudoku boardwith unique solution. He developed a program, called CHECKER forthis purpose. It seems that the program requires about 300,000 years(on a one-core computer equipped with CPU, Intel(R) Xeon(R)E5520 @ 2.27GHz) to finish the job.http://www.math.ie/checker.html
Page 1 and 2: T H EM A T HS U D O K UO FOscar Veg
Page 3 and 4: The GameA Sudoku board is a 9 × 9
Page 5 and 6: Sudo-HistoryThe modern version of S
Page 7 and 8: Pop Culture: Silly, Funny,.... WTH?
Page 9 and 10: Math Game?People say that sudoku is
Page 11 and 12: Direct Proof5 3 76 1 9 5 39 8 68 6
Page 13 and 14: Forcing Chains (Proof by Contradict
Page 19 and 20: Forcing Chains (Proof by Cases)2315
Page 25: Many-to-oneWe can create many other
Page 29 and 30: The graph of a Sudoku boardHerzberg
Page 31 and 32: More theoremsTheorem (Herzberg & Ra
Page 33 and 34: Latin squares of order 9Let us look
Page 35: T H A N KY O U

The Math of Sudoku

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