This has been a very difficult challenge to mathematicians and as per the recent article here, http://www.nature.com/news/mathematician-claims-breakthrough-in-sudoku-puzzle-1.9751 , they have proved by brute-force that it is 17. However as I understand, they have tried to come up with all the combinations to derive at this number which is not very efficient and very error prone.
While thinking on how to solve this problem, I realized that to prove that 17 is the number, I needed to represent Sudoku puzzle in linear algebraic equations with exactly 17 variables.
